The retinal microcirculation supplies blood and oxygen to the cells responsible for vision, and vascular impairments – including compromised flow regulation, reduced capillary density, and elevated intraocular pressure – are involved in the progression of eye diseases such as glaucoma. Here, an established theoretical model of a retinal microvascular network will be presented and extended to investigate the effects of these impairments on retinal blood flow and oxygenation as intraluminal pressure is varied. A heterogeneous description of the arterioles based on confocal microscopy images is combined with a compartmental representation of the downstream capillaries and venules. A Green’s function method is used to simulate oxygen transport in the arterioles, and a Krogh cylinder model is used in the capillary and venular compartments. Acute blood flow autoregulation is simulated in response to changes in pressure, shear stress, and metabolism. The model predicts that impaired flow regulation mechanisms, decreased capillary density, and increased intraocular pressure all cause a loss in the autoregulation plateau over the baseline range of intraluminal pressures (meaning that blood flow is not maintained constant over those pressures), leading to a corresponding decrease in oxygenation in that range. Small impairments in capillary density or intraocular pressure are predicted to mostly be offset by functional flow regulation; however, larger changes and/or combinations of vascular impairments lead to a significant decrease in oxygenation. Clinically, since poor retinal tissue oxygenation could lead to vision loss in advanced glaucoma, model results suggest early identification of vascular changes to prevent these impairments from progressing.

Cells migrate in response to gradients in extra-cellular chemical signals in a process known as chemotaxis. Recent experiments on the model microorganism Dictyostelium discoideum have shown that dense aggregates of cells collectively undergoing chemotaxis exhibit emergent fluid-like properties such as viscosity and surface tension. In this work, we use simulations to explain how active interactions between cells give rise to these emergent phenomena. We propose an agent-based model for intermittent cell-cell attachments and show that it gives rise to emergent fluid-like behavior for an aggregate of cells. We generalize this model to include cell-surface attachments, and show that surface-associated aggregates display properties similar to a liquid droplet resting on a surface. Furthermore, we study the situation where cells self-generate and respond to a chemical gradient by consuming an externally supplied chemoattractant. Our simulations reveal how individual cells move inside the swarm as the cells move as a collective. Finally, we predict some of the key cellular processes that are responsible for this collective behavior, and provide hypotheses to be tested in future experimental studies.

Chemical signaling, or quorum sensing (QS), promotes collective behaviour in bacteria, from biofilm formation to swarming. By coupling QS systems with genes that control motility, bacteria can be engineered to generate tunable spatio-temporal patterns in vitro. However, it is not well-understood in general how the type of gene-regulatory network affects emergent population-level patterning. In this talk, we investigate the effect of the gene-regulatory network on emergent patterning in a population of motile bacteria that interact via QS. By formally upscaling a cell-level model in a biologically relevant scaling regime, we derive a continuum model that explicitly accounts for genetic regulation of motility and signal production through chemical structuring. Using a WKBJ-like framework, we derive criteria for the onset of two types of emergent patterning for a canonical QS circuit. We also uncover a new route to the well-known phenomenon of motility-induced phase separation (MIPS) through genetic regulation of tumbling frequency. Lastly, we discuss generalisations of our WKBJ-like analysis to more complex gene-regulatory networks that exhibit bistability.

Stem cells maintain and repair our tissues, but not all stem cells are identical. As organisms age, distinct stem cell 'clones' can begin to dominate the cell population. While this behavior has been observed across multiple species and organs, the mechanisms and consequences of stem cell clonality are still poorly understood. We have developed a novel experimental approach using a CRISPR-Cas9 system to uniquely “barcode” spermatogonial stem cell clones in the testes of male zebrafish. Once these fish reach sexual maturity, we sample sperm each month to determine the contribution of each stem cell clone to the sperm pool over time. The observed clonal dynamics may be driven by factors such as genetic drift, selection, or sampling error. We hypothesize that a small number of clones are under positive selection, resulting in their eventual dominance in the sperm pool. To bridge the gap between theory and data, we have developed stochastic models of stem cell dynamics in the testis. These models are formulated as hidden Markov models that describe rules for the division and differentiation of stem cells within the testis. We first evaluate our ability to estimate model parameters on simulated data. Then, we apply our model to the experimental data to quantify evidence for genetic drift and selection. Our models provide insight into how individual stem cell behavior can lead to population-level clonality.

Osteoporosis is a disease that affects more than 200 million people all over the world. Although its underlying mechanisms are gradually being revealed, effective treatments or preventive measures have not been established yet. This study focused on age-related osteoporosis by measuring bone mass and bone metabolism markers in mice from 4 to 52 weeks of age. We developed mathematical models describing bone metabolism and analyzed experimental data. From the result of data analysis, we quantitatively elucidated the mechanisms of bone loss. Furthermore, we conducted treatment intervention simulations by changing parameter values in mathematical models to identify effective bone metabolism pathways for increasing bone mass and new potential therapeutic strategies.

Retinal detachment occurs when the neurosensory retina separates from the retinal pigment epithelium (RPE), disrupting the nutrient supply to photoreceptor cells. There are three types of retinal detachment: exudative (ERD), tractional (TRD), and rhegmatogenous (RRD), with RRD being the most common. RRD develops when a retinal tear or hole allows vitreous humor to enter the subretinal space, causing the neurosensory retina to detach from the RPE. If left untreated, this condition can lead to irreversible vision loss. Although ophthalmological tools can detect RRD, its rate of progression—particularly due to continuous eye movement—remains poorly understood. This study develops a fluid-structure interaction model to examine how various factors, including retinal thickness, elasticity, adhesion strength between the retina and RPE, vitreous humor density and viscosity, and eye rotation speed, influence detachment progression. By quantifying detachment rates under different conditions, this research aims to enhance our understanding of RRD dynamics and refine estimates of effective treatment timelines to prevent permanent visual impairment. Student: William Ebo Annan Advisors: Prof. Diana White & Prof. Emmanuel O.A. Asamani

Collective cell migration plays a crucial role in numerous biological processes, including cancer growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This study derives a general mathematical framework for modelling cell migration into the micro-environment, which is coarse-grained from an underlying individual-based model that captures some of the dynamics of cell migration that are influenced by the phenotype of the cell, such as: random movement, proliferation, phenotypic transitions, and interactions with the external environment. The resulting model provides a continuum, macroscopic description of cell invasion, which represents the phenotype of the cell as a continuous variable and is much more amenable to simulation and analysis than its individual-based counterpart when considering a large number of phenotypes. The results highlight how phenotypic structuring impacts the spatial and temporal dynamics of cell populations, demonstrating that different environmental pressures and phenotypic transition mechanisms significantly influence invasion patterns.

Harmful algal blooms (HABs) are characterized by rapid growth of algae, and can be caused by toxin-producing phytoplankton (TPP). When HABs occur, oxygen in the water depletes and thus can kill fish and other marine creatures causing both environmental and economic damages. In this talk, we consider a zooplankton-phytoplankton model under the assumption that the TPP exhibits group defense so that zooplankton predation decreases at high TPP density. Furthermore, we assume that toxin liberation by the TPP is not instantaneous but is rather mediated by a time lag, which is also known as the toxin liberation delay (TLD). Our results show that the model system undergoes a Hopf bifurcation around a coexistence equilibrium when the value of the TLD reaches a certain threshold. For values of the TLD just above the threshold, the stable limit cycle that is created depicts the manageable periodic fluctuation of the populations. However, when the value of the TLD is increased further, recurring blooms of various periodicity were observed which can be attributed to the occurrence of period-doubling bifurcations.

The short-tailed field vole (microtus agrestis) is the most abundant mammal in the UK, with populations reaching up to 80 million individuals. However, voles experience huge fluctuations in population numbers with up to a tenfold change over the course of regular 3.5 year cycles. Previous research has aimed to understand the mechanics behind these oscillations, but most of this work focuses on tundra regions. The ongoing Glen Finglas grazing experiment spans over 20 years, focusing on how managing grazing pressures affects various groups of species - including voles - in the more temperate upland acid grasslands of Scotland. Here, I will first present new data analysis on the Glen Finglas experiment, in particular the relationship between voles and the vegetation they use as a food source and shelter. I will then show how this data can be used to create and fit a mathematical model, capturing the vole's complex life history and interactions. Understanding these small animals is important as they are a key prey species for many predators and can also cause massive damage to plants and tree saplings. This mathematical model furthers our understanding of vole dynamics in temperate regions.

Understanding the mechanisms behind the spatial distribution, self-organisation and aggregation of organisms is a central issue in both ecology and cell biology. Since self-organisation at the population level emerges from individual behaviour, a mathematical approach is essential to elucidate these dynamics. In nature, individuals - whether cells or animals - inspect their environment before moving. This process is typically nonlocal, meaning that individuals gather information from a part of their environment rather than just their immediate location. Empirical research increasingly highlights nonlocality as a key aspect of movement, while mathematical models incorporating nonlocal interactions have gained attention for their ability to describe how interactions shape movement, reproduction and well-being. In this talk, I will present a study of a class of advection-diffusion equations that model population movement driven by nonlocal species interactions. Using a combination of analytical and numerical tools, I will show that these models support a wide range of spatio-temporal patterns, including segregation, aggregation, time-periodic behaviour, and chase-and-run dynamics. I will also discuss the existence of parameter regions with multiple stable solutions and hysteresis phenomena. Overall, I will explore various methods for analysing the bifurcation and pattern formation properties of these models, which provide essential mathematical tools for understanding the many aggregation phenomena observed in nature.

Coral reefs are some of the most threatened ecosystems on the planet but also some of the most important, hosting upwards of 25% of marine biodiversity while also providing food and livelihood to almost 1 billion people. Coral reefs are also connected together into reef networks by coral larval dispersal, meaning that management or damage at one reef may have consequences for any reefs it is connected to. For this reason, coral reef management is of interest to many industries (e.g., fisheries, tourism) and governments. The potential impact of tourism in the context of coral reef management is unclear, as tourism is a source of damage for reefs but may also be a source of income that motivates conservation actors to keep reefs healthy for future tourists. Tourism groups also often focus on a subset of coral reefs, meaning that any management initiatives driven by tourism income would also only be focused on a subset of coral reefs in a reef network. We develop a socio-ecological model composed of a system of differential equations. This model represents a network of coral reefs visited by tourists to determine whether tourism income could help sustain a healthy network of coral reefs into the future. We explore this question under a variety of different tourism paradigms, management methods (coral restoration, fisheries management) and network types. Overall, we find that management funded by tourism can help counteract tourism damage, but is unable to save reefs that are unhealthy (low initial coral cover, high fishing). Management also has limited potential to help connected reefs in the network. This study demonstrates the limited effectiveness of tourism to drive coral reef conservation and instead encourages active investment in management methods that focus on the entire reef network.

We propose a mathematical model describing the dynamics of photo fermentative bacteria leading to hydrogen production and polyhydroxybutyrate accumulation in an engineered environment. The model is derived from mass balance principles and consists of a system of differential equations describing the biomass growth, the substrate degradation and conversion into hydrogen and other catabolites, such as intracellular polyhydroxybutyrate, a precursor for bioplastics. The model accounts for crucial inhibiting phenomena and catabolic interactions affecting the evolution of the process. The study of the model has been performed also in terms of calibration with real experimental data related to specific photo-fermentative species, and it is supported by a sensitivity analysis study. The effective application of photo-fermentation for the concomitant hydrogen production and polyhydroxybutyrate accumulation was investigated.

Mosquito-borne diseases pose a significant public health challenge, and effective prevention requires accurate forecasting of mosquito populations. In this study, we developed a statistical forecasting framework that leverages climate factors, such as temperature and precipitation, to improve mosquito population predictions in Maricopa County, Arizona. Our approach combines adaptive modeling techniques and filtering methods to infer precise model parameters and address previously observed limitations, particularly the inability to capture spring dynamics. By incorporating an Ensemble Kalman Filter (EnKF) method, we estimated time-varying parameters (baseline population growth rate) and static parameters while resolving the spring problem observed in prior models. Using Generalized Additive Models (GAMs), we forecasted the baseline population growth rate on a weekly basis, integrating precipitation and temperature data as covariates. These forecasts were further used to run a mechanistic ordinary differential equation (ODE) model to predict mosquito abundance and estimate associated uncertainties. Our iterative framework was applied weekly over a 52-week period, successfully capturing seasonal variations in mosquito populations from 2014 to 2015. The EnKF demonstrated superior performance compared to traditional Markov Chain Monte Carlo (MCMC) approaches for fitting mosquito abundance data. This enhanced methodology provides actionable insights for public health decision-makers, supporting resource allocation and improving outcomes in mosquito-borne disease prevention. Our findings underscore the value of integrating climate data and adaptive filtering techniques to address forecasting challenges, ultimately enabling more effective responses to emerging or reemerging pathogens of mosquito-borne disease risks, which can be driven by human behavior to become a pandemic.

Plant-arthropod relationships are crucial to the health of global ecosystems and food production. Through co-evolution, arthropods have acquired a variety of novel senses in response to the emergence of floral cues such as scent, colour and shape. The recent discovery that several terrestrial arthropods can sense electrical fields (e-fields) motivates the investigation of floral e-fields as part of their wider sensory ecology. That is, how does a flower's morphology and material properties produce and propagate detectable, ecologically relevant electrical signals? To investigate this, we modelled the e-field interior and exterior of a flower using a novel modification of the popular AAA-least squares algorithm, extending it to two domain boundary value problems. Physically, flowers typically act as dielectrics that inductively charge in the presence of a background electrical field, e.g. charged pollinators or the Earth's atmospheric potential gradient. We therefore present the development and application of this new method for these cases and discuss the biological relevance of the results for sensory and ecological studies. Our adapted AAA algorithm gives accurate and rapid results dependent on only three parameters: the relative permittivity of the flower, flower shape and the location of the pollinator(s). The results show how flowers display distinct information about their morphology, pollen availability and nearby pollinators, at distance, through the perturbed e-field. As well as how predators, such as the crab spider, can use flowers to mask their own electrical presence and draw in unsuspecting prey. The results of the two-dimensional AAA method also shows good qualitative agreement with equivalent three-dimensional finite element models. Biologically, our results highlight the significant role floral electrics may play in plant-pollinator and predator-prey relationships, unveiling previously unstudied facets.

In this study, we utilize the species Pogonomyrmex californicus, a type of queen ant that exhibits two distinct behavioral subtypes, as inspiration for our mathematical model. The first, known as solitary queens, establish colonies independently and represent the ancestral lineage. The second subtype, cooperative queens, form groups that collectively found a single colony—an evolutionary adaptation. Laboratory experiments have revealed that these queen types display distinct behavioral traits, or personalities. To better understand the ecological implications of these differences, we develop an ordinary differential equations (ODE) model that incorporates the effects of resource availability and social organization among adult ants, particularly in relation to brood care and foraging behaviors. Our model allows for Hopf bifurcations, enabling us to analyze the conditions under which colony coexistence is promoted or collapses. With this framework, we seek to address the following key questions: How does dependency on resource availability impact the survival of each queen type? How do social organization and resource dependency together influence queen survival, and what new conditions must be met for their persistence?

Overharvesting is a pressing global problem, and spatial management, such as protecting designated areas, is one proposed solution. This talk examines how dispersal between protected and harvested areas affects the asymptotic total population size and the asymptotic yield, which are key questions for conservation management and the design of protected areas. We utilize a two-patch model with heterogeneous habitat qualities, symmetric dispersal and density-dependent growth functions in both discrete and continuous time. One patch is subject to proportional harvesting, while the other one is protected. Our results demonstrate that increased dispersal does not always increase the asymptotic total population size or the asymptotic yield. Depending on the circumstances, dispersal enables the protected patch to rescue the harvested patch from overexploitation, potentially increasing both total population size and yield. However, high levels of dispersal can also lead to a lower total population size or even cause extinction of both patches if harvesting pressure is strong. The population in the protected patch needs to have high reproductive potential and the patch needs to be the effectively larger patch in order to benefit monotonically from increased dispersal. These findings provide a fundamental understanding of how dispersal influences dynamics in fragmented landscapes under harvesting pressure.

Understanding how organisms make choices about what to eat is a fascinating puzzle explored in this study, which employs stoichiometric modeling and optimal forag- ing principles. The research delves into the intricate balance of nutrient intake with foraging strategies, investigating quality and quantity-based food selection through mathematical models. The stoichiometric models in this study, encompassing pro- ducers and a grazer, unveils the dynamics of decision-making processes, introducing fixed and variable energetic foraging costs. Analysis reveals cell quota-dependent pre- dation behaviors, elucidating biological phenomena such as “compensatory foraging behaviors” and the “stoichiometric extinction effect”. The Marginal Value Theorem quantifies food selection, highlighting the profitability of prey items and emphasizing its role in optimizing foraging strategies in predator–prey dynamics. The environ- mental factors like light and nutrient availability prove pivotal in shaping optimal foraging strategies, with numerical results from a multi-species model contributing to a comprehensive understanding of the intricate interplay between organisms and their environment.

Phototaxis, the ability of microorganisms to move in response to light, plays a crucial role in shaping the dynamics of phototrophic biofilms. While sessile cells remain typically embedded within the extracellular polymeric matrix, planktonic cells can navigate through the biofilm’s porous structure, adjusting their position in response to light cues. This directed movement optimizes exposure to favorable light conditions while avoiding harmful intensities, influencing the spatial organization and development of the biofilm community. In this talk, I will present a mathematical model for planktonic cell invasion in biofilms, where phototaxis acts as a driver of directed motility. The model incorporates a volume-filling term into the transport equation for planktonic cells, enabling the representation of phototactic behavior. A light-dependent sensitivity function captures both positive and negative phototaxis, governing cell movement toward favorable light conditions and away from excessive illumination. The biofilm is modeled as a homogeneous, viscous, incompressible fluid, with velocity described by Darcy’s law. The governing equations are solved numerically to explore the role of phototaxis in shaping biofilm dynamics. Numerical simulations reveal that motile cells accumulate in well-lit regions, enhancing sessile phototrophic growth and promoting biofilm development. The distribution of phototrophic biomass results from the interplay between random diffusion and phototactic movement. Under high-light stress conditions, photoinhibition reduces phototrophic growth and reverses phototaxis, slowing overall biofilm growth. Additionally, biofilm density modulates light penetration, either limiting phototrophic growth or providing protection against excessive exposure. These findings offer valuable insights into biofilm behavior in natural environments and can guide the optimization of biofilm-based processes in fields like wastewater treatment and bioremediation.

Evolutionary rescue occurs when a population facing environmental stress avoids extinction by rapidly acquiring beneficial mutations. While higher mutation rates can enhance rescue, the role of mutators—genotypes with elevated mutation rates—remains unclear. We develop a theoretical framework and use stochastic simulations to investigate how mutators emerge and fix under selective pressure. Our results show that mutators cannot persist in stable environments but are favored when environmental deterioration occurs, with their fixation probability influenced by the speed of environmental change and wildtype mutation rates. Pre-existing mutators further increase rescue likelihood, particularly under rapid environmental shifts. These findings provide insights into antibiotic resistance, cancer evolution, and adaptation to climate change by highlighting how environmental stress shapes mutation rate evolution.

The supplementation of additional food (AF) to introduced predators has been explored as a strategy to enhance pest control. However, AF models with prey-dependent functional responses can lead to unbounded predator growth. To address this, an AF model incorporating mutual interference has been proposed, demonstrating that pest eradication is feasible when the AF quantity ξξ exceeds a threshold function of the interference parameter ϵϵ. In this study, we revisit and extend this model, uncovering novel dynamical behaviors. We show that pest eradication occurs within a narrower AF range and can be bi-stable or globally attracting, arising through a saddle-node bifurcation. Additionally, we identify Hopf and global homoclinic bifurcations, revealing a unique dynamic where the pest extinction state becomes an 'almost' global attractor. This is the first analytical proof of such a structure in AF models, providing insights into bio-control strategies under varying predator interference conditions.

The impacts of invasive alien pests and diseases are routinely estimated and measured in the context of agriculture, but less so in the context of biodiversity and ecosystem services. In this study, we developed a new 'contribution modelling' approach to systematically estimate the impacts of pests and diseases at a continent scale. We developed this method using a case study of myrtle rust in Australia. We estimated the potential reduction of carbon sequestration in Australia due to myrtle rust using various national and scientific ecological datasets. We found that myrtle rust could lead to over 3% loss in national annual carbon sequestration if it were to spread across Australia, or over $700 million AUD value loss. While developed using a case study, this model is designed to be readily adaptible to other species and their impact on other environmental assets. Our work shows the need to systematically compile the potential impacts and costs of invasive pests and diseases to the environment and ecosystem services globally, to support both biosecurity decision-making and climate-change related initiatives such as net-zero emissions targets and reforestation efforts.

Mosquito-borne diseases pose a significant public health challenge, and effective prevention requires accurate forecasting of mosquito populations. In this study, we developed a statistical forecasting framework that leverages climate factors, such as temperature and precipitation, to improve mosquito population predictions in Maricopa County, Arizona. Our approach combines adaptive modeling techniques and filtering methods to infer precise model parameters and address previously observed limitations, particularly the inability to capture spring dynamics. By incorporating an Ensemble Kalman Filter (EnKF) method, we estimated time-varying parameters (baseline population growth rate) and static parameters while resolving the spring problem observed in prior models. Using Generalized Additive Models (GAMs), we forecasted the baseline population growth rate on a weekly basis, integrating precipitation and temperature data as covariates. These forecasts were further used to run a mechanistic ordinary differential equation (ODE) model to predict mosquito abundance and estimate associated uncertainties. Our iterative framework was applied weekly over a 52-week period, successfully capturing seasonal variations in mosquito populations from 2014 to 2015. The EnKF demonstrated superior performance compared to traditional Markov Chain Monte Carlo (MCMC) approaches for fitting mosquito abundance data. This enhanced methodology provides actionable insights for public health decision-makers, supporting resource allocation and improving outcomes in mosquito-borne disease prevention. Our findings underscore the value of integrating climate data and adaptive filtering techniques to address forecasting challenges, ultimately enabling more effective responses to emerging or reemerging pathogens of mosquito-borne disease risks, which can be driven by human behavior to become a pandemic.

Plant-arthropod relationships are crucial to the health of global ecosystems and food production. Through co-evolution, arthropods have acquired a variety of novel senses in response to the emergence of floral cues such as scent, colour and shape. The recent discovery that several terrestrial arthropods can sense electrical fields (e-fields) motivates the investigation of floral e-fields as part of their wider sensory ecology. That is, how does a flower's morphology and material properties produce and propagate detectable, ecologically relevant electrical signals? To investigate this, we modelled the e-field interior and exterior of a flower using a novel modification of the popular AAA-least squares algorithm, extending it to two domain boundary value problems. Physically, flowers typically act as dielectrics that inductively charge in the presence of a background electrical field, e.g. charged pollinators or the Earth's atmospheric potential gradient. We therefore present the development and application of this new method for these cases and discuss the biological relevance of the results for sensory and ecological studies. Our adapted AAA algorithm gives accurate and rapid results dependent on only three parameters: the relative permittivity of the flower, flower shape and the location of the pollinator(s). The results show how flowers display distinct information about their morphology, pollen availability and nearby pollinators, at distance, through the perturbed e-field. As well as how predators, such as the crab spider, can use flowers to mask their own electrical presence and draw in unsuspecting prey. The results of the two-dimensional AAA method also shows good qualitative agreement with equivalent three-dimensional finite element models. Biologically, our results highlight the significant role floral electrics may play in plant-pollinator and predator-prey relationships, unveiling previously unstudied facets.

In this study, we utilize the species Pogonomyrmex californicus, a type of queen ant that exhibits two distinct behavioral subtypes, as inspiration for our mathematical model. The first, known as solitary queens, establish colonies independently and represent the ancestral lineage. The second subtype, cooperative queens, form groups that collectively found a single colony—an evolutionary adaptation. Laboratory experiments have revealed that these queen types display distinct behavioral traits, or personalities. To better understand the ecological implications of these differences, we develop an ordinary differential equations (ODE) model that incorporates the effects of resource availability and social organization among adult ants, particularly in relation to brood care and foraging behaviors. Our model allows for Hopf bifurcations, enabling us to analyze the conditions under which colony coexistence is promoted or collapses. With this framework, we seek to address the following key questions: How does dependency on resource availability impact the survival of each queen type? How do social organization and resource dependency together influence queen survival, and what new conditions must be met for their persistence?

Overharvesting is a pressing global problem, and spatial management, such as protecting designated areas, is one proposed solution. This talk examines how dispersal between protected and harvested areas affects the asymptotic total population size and the asymptotic yield, which are key questions for conservation management and the design of protected areas. We utilize a two-patch model with heterogeneous habitat qualities, symmetric dispersal and density-dependent growth functions in both discrete and continuous time. One patch is subject to proportional harvesting, while the other one is protected. Our results demonstrate that increased dispersal does not always increase the asymptotic total population size or the asymptotic yield. Depending on the circumstances, dispersal enables the protected patch to rescue the harvested patch from overexploitation, potentially increasing both total population size and yield. However, high levels of dispersal can also lead to a lower total population size or even cause extinction of both patches if harvesting pressure is strong. The population in the protected patch needs to have high reproductive potential and the patch needs to be the effectively larger patch in order to benefit monotonically from increased dispersal. These findings provide a fundamental understanding of how dispersal influences dynamics in fragmented landscapes under harvesting pressure.

Understanding how organisms make choices about what to eat is a fascinating puzzle explored in this study, which employs stoichiometric modeling and optimal forag- ing principles. The research delves into the intricate balance of nutrient intake with foraging strategies, investigating quality and quantity-based food selection through mathematical models. The stoichiometric models in this study, encompassing pro- ducers and a grazer, unveils the dynamics of decision-making processes, introducing fixed and variable energetic foraging costs. Analysis reveals cell quota-dependent pre- dation behaviors, elucidating biological phenomena such as “compensatory foraging behaviors” and the “stoichiometric extinction effect”. The Marginal Value Theorem quantifies food selection, highlighting the profitability of prey items and emphasizing its role in optimizing foraging strategies in predator–prey dynamics. The environ- mental factors like light and nutrient availability prove pivotal in shaping optimal foraging strategies, with numerical results from a multi-species model contributing to a comprehensive understanding of the intricate interplay between organisms and their environment.

Phototaxis, the ability of microorganisms to move in response to light, plays a crucial role in shaping the dynamics of phototrophic biofilms. While sessile cells remain typically embedded within the extracellular polymeric matrix, planktonic cells can navigate through the biofilm’s porous structure, adjusting their position in response to light cues. This directed movement optimizes exposure to favorable light conditions while avoiding harmful intensities, influencing the spatial organization and development of the biofilm community. In this talk, I will present a mathematical model for planktonic cell invasion in biofilms, where phototaxis acts as a driver of directed motility. The model incorporates a volume-filling term into the transport equation for planktonic cells, enabling the representation of phototactic behavior. A light-dependent sensitivity function captures both positive and negative phototaxis, governing cell movement toward favorable light conditions and away from excessive illumination. The biofilm is modeled as a homogeneous, viscous, incompressible fluid, with velocity described by Darcy’s law. The governing equations are solved numerically to explore the role of phototaxis in shaping biofilm dynamics. Numerical simulations reveal that motile cells accumulate in well-lit regions, enhancing sessile phototrophic growth and promoting biofilm development. The distribution of phototrophic biomass results from the interplay between random diffusion and phototactic movement. Under high-light stress conditions, photoinhibition reduces phototrophic growth and reverses phototaxis, slowing overall biofilm growth. Additionally, biofilm density modulates light penetration, either limiting phototrophic growth or providing protection against excessive exposure. These findings offer valuable insights into biofilm behavior in natural environments and can guide the optimization of biofilm-based processes in fields like wastewater treatment and bioremediation.

Evolutionary rescue occurs when a population facing environmental stress avoids extinction by rapidly acquiring beneficial mutations. While higher mutation rates can enhance rescue, the role of mutators—genotypes with elevated mutation rates—remains unclear. We develop a theoretical framework and use stochastic simulations to investigate how mutators emerge and fix under selective pressure. Our results show that mutators cannot persist in stable environments but are favored when environmental deterioration occurs, with their fixation probability influenced by the speed of environmental change and wildtype mutation rates. Pre-existing mutators further increase rescue likelihood, particularly under rapid environmental shifts. These findings provide insights into antibiotic resistance, cancer evolution, and adaptation to climate change by highlighting how environmental stress shapes mutation rate evolution.

The supplementation of additional food (AF) to introduced predators has been explored as a strategy to enhance pest control. However, AF models with prey-dependent functional responses can lead to unbounded predator growth. To address this, an AF model incorporating mutual interference has been proposed, demonstrating that pest eradication is feasible when the AF quantity ξξ exceeds a threshold function of the interference parameter ϵϵ. In this study, we revisit and extend this model, uncovering novel dynamical behaviors. We show that pest eradication occurs within a narrower AF range and can be bi-stable or globally attracting, arising through a saddle-node bifurcation. Additionally, we identify Hopf and global homoclinic bifurcations, revealing a unique dynamic where the pest extinction state becomes an 'almost' global attractor. This is the first analytical proof of such a structure in AF models, providing insights into bio-control strategies under varying predator interference conditions.

The impacts of invasive alien pests and diseases are routinely estimated and measured in the context of agriculture, but less so in the context of biodiversity and ecosystem services. In this study, we developed a new 'contribution modelling' approach to systematically estimate the impacts of pests and diseases at a continent scale. We developed this method using a case study of myrtle rust in Australia. We estimated the potential reduction of carbon sequestration in Australia due to myrtle rust using various national and scientific ecological datasets. We found that myrtle rust could lead to over 3% loss in national annual carbon sequestration if it were to spread across Australia, or over $700 million AUD value loss. While developed using a case study, this model is designed to be readily adaptible to other species and their impact on other environmental assets. Our work shows the need to systematically compile the potential impacts and costs of invasive pests and diseases to the environment and ecosystem services globally, to support both biosecurity decision-making and climate-change related initiatives such as net-zero emissions targets and reforestation efforts.

What should you do if you miss a dose of antibiotics? Despite the prevalence of missed antibiotic doses, there is vague or little guidance on what to do when a dose is forgotten. In this paper, we consider the effects of different patient responses after missing a dose using a mathematical model that links antibiotic concentration with bacteria dynamics. We show using simulations that, in some circumstances, (a) missing just a few doses can cause treatment failure, and (b) this failure can be remedied by simply taking a double dose after a missed dose. We then develop an approximate model that is analytically tractable and use it to understand when it might be advisable to take a double dose after a missed dose.

Natural killer (NK) cells are members of the innate immune system and are proving to be a lethal weapon against cancer. To unlock the full power of NK cells, we must first address the central question: How does an NK cell recognize a malignant cell? To assess a target cell, an NK cell forms an immunological synapse, which is the interaction zone between the two cells. Ligand-receptor binding within the synapse triggers downstream activating and inhibitory signaling pathways that integrate to control the actin cytoskeleton network. Dominating activating signals causes the NK cell’s actin network to reorganize which transports more receptors to the synapse, thereby generating a positive feedback loop. Mechanistically, activating signals lead to the activation of the Arp2/3 complex which creates a branched actin network. In return, the flow of this network drives the centripetal transport of receptors to the synapse. We propose an advection-diffusion model to capture this phenomenon. Furthermore, we test what ligand-receptor densities permit synapse formation.

Kaposi’s sarcoma-associated herpesvirus (KSHV) is a causative agent of several lymphoproliferative diseases, particularly in immunocompromised individuals. These malignancies originate from latently infected B cells, where KSHV persists as extrachromosomal episomes. While the viral protein LANA is essential for viral maintenance during latency, the mechanisms enabling lifelong persistence remain unclear. To quantify episome dynamics, we developed a mathematical model of latent KSHV replication and segregation during cell division, and a statistical framework to infer viral dynamics from fluorescent microscopy images. We built a Gibbs sampler to extract episome counts from imperfectly resolved images of pre- and post-division cells. Using these counts, we estimate the efficiency of replication and segregation, propagating imaging uncertainty into our parameter estimates. Our framework, validated on synthetic data, provided similar estimates of replication efficiency (78%, 95% CI [53%, 90%]) and segregation efficiency (91% [78%, 100%]) when applied to fixed and live images of cells transfected with either full-length KSHV or a minimal plasmid capable of episome maintenance. Simulations of a dividing cell population showed that imperfect replication and segregation preclude decades-long persistence without the assistance of additional mechanisms such as cell-survival benefits to infection or occasional lytic replication. We also modeled KSHV-dependent malignancies to evaluate episome replication and segregation as targets to control tumor growth. Simulations revealed that reducing replication effectively disrupts tumor growth, with the required reduction dependent on cell division kinetics. Our results suggest that KSHV employs a partitioning mechanism, as opposed to random segregation, though replication and segregation are imperfect. Furthermore, targeting episome replication may offer a viable strategy to reduce tumor burden in KSHV-associated malignancies.

Individual bacterium make decisions at a genetic level as a result of various types of gene regulation; this process plays out on a population level to inform colony growth. Vibrio vulnificus is an opportunistic Gramnegative marine pathogen with a limiting growth factor of iron. Compared to other foodborne pathogens, Vibrio vulnificus has a high mortality rate and relatively poorly understood virulence mechanisms. When inside a human host, this bacteria utilizes heme as a source of iron, necessitating the ability to turn pieces of the heme acquisition system off and on in response to various environmental signals. As establishment of infection depends on Vibrio vulnificus’s ability to change from a marine to human environment, the ability to switch on the heme-intake system is an important part of establishment of initial infection. One such part of this system is the hemolysin VvhA. This toxin is excreted by the bacterium to lyse erythrocytes, thereby releasing heme into the extracellular environment where the bacteria can use it as a source of iron. This toxin is regulated by a complex set of factors including nutrient availability and quorum sensing. Exploring this gene regulatory network via bifurcation analysis reveals a complex bifurcation structure. These dynamics allow an individual bacterium to integrate a variety of signals in response to a changing environment. In particular, bistability in the system points to the likelihood of a heterogenous bacterial colony, where many bacteria benefit from a smaller number of hemolysin producers. This allows for modeling both a heterogeneous population and incorporation of the physiological mechanism by which cells make the decision to switch states. The interdependence between toxin production, nutrient availability, and colony growth result in interplay between the bacteria and their environment, allowing for insights into the overall course of infection.

Identifying early warning signals (EWS) of shifts in vaccinating behaviors can be helpful in predicting disease outbreaks. Evolutionary game theory has been used to model individual vaccination decisions, while bifurcation theory has identified statistical EWS, such as increasing variance and lag-1 autocorrelation, near critical transitions. However, these conventional methods often struggle with noisy data. In this study, we improve coupled behavior-disease models by incorporating population heterogeneity, distinguishing between social media users and non-users, and examining the role of homophily in shaping disease dynamics. We develop deep learning classifiers, including Long Short-Term Memory (LSTM) and Residual Neural Networks (ResNet), trained on simulated data from a stochastic coupled model with Lévy noise that captures the heavy-tailed fluctuations characteristic of real-world systems. Our results show that these models outperform traditional statistical indicators in both sensitivity and specificity while offering clearer interpretability on empirical data. This approach provides a robust framework for detecting EWS and improving outbreak prediction, highlighting the power of deep learning in real-time public health monitoring.

Evaluating vaccine efficacy (VE) during emerging epidemics is challenging due to unpredictable transmission dynamics. An age-structured SEIAR compartmental model was developed using South Korea’s 2022 population and parameters from COVID-19 and the 2009 H1N1 pandemic to optimize RCT timing and sample size. Simulations varied trial initiation (±10%, ±20%, ±30% of the epidemic peak), follow-up (4–12 weeks), recruitment (2–12 weeks), and non-pharmaceutical interventions (10–20%). Results showed that VE remained stable, but sample size requirements fluctuated, decreasing post-peak before rising sharply. Starting trials 30% before the peak with extended recruitment minimized sample sizes without compromising power. NPIs expanded trial feasibility, and sample size estimates from simulated placebo cases maintained >85% power, avoiding under- or over-powering. This model provides a framework for designing adaptive and efficient vaccine trials in future respiratory epidemics.

Social contact patterns are crucial for understanding infectious disease transmission, but detailed data has been scarce in South Korea. We conducted a two-week survey covering various periods, including school vacations and holidays. Participants provided information on their contacts, including location, duration, frequency, and characteristics of the contact person. Analysis of the data from 1,987 participants revealed 133,776 contacts, averaging 4.81 contacts per person daily. Contact numbers varied by age, household size, and time period. The highest number of contacts was observed in the 5-19 age group, lowest in the 20-29 group, and gradually increased up to the 70+ group. Larger households tended to have more contacts. Contact patterns differed significantly across time periods. Weekdays during the school semester showed the highest number of contacts, followed by weekdays during vacations, the Lunar New Year holidays, and weekends. During the Lunar New Year, there was an increase in contacts with extended family members, enhancing subnational social mixing. These findings provide valuable insights into social contact patterns in South Korea, which can improve our understanding of disease transmission and aid in developing region-specific epidemiological models.

The unpredictable timing of infectious disease outbreaks poses significant challenges for public health preparedness. For many pathogens, this unpredictability is due to uncertainty regarding introduction rates—the frequency with which the pathogen is introduced into at-risk populations. We present three model-driven advances toward quantifying pathogen introduction rates and their effects on outbreak timing and size. Our method relies on the assumption that pathogen introductions can only cause large outbreaks when population immunity is sufficiently low (i.e., the reproduction number R(t) > 1). First, we demonstrate that, for pathogens that cause lifelong immunity, introduction rates can be estimated from age-structured serological data. Second, we estimate annual rates of chikungunya virus (CHIKV, a mosquito-borne pathogen) introductions into 17 populations in Africa and Asia using serological data collected between 1973 and 2015. Our median estimates ranged from 1 to 70 CHIKV introductions per 10 million people per year. Finally, we used simulations to show how the introduction rate of a pathogen can shape its transmission patterns over time in affected populations. A lower introduction rate allows population immunity to wane between introductions, leading to large but infrequent outbreaks. In contrast, a higher introduction rate causes frequent low-level transmission, resulting in elevated population immunity that precludes large outbreaks. Together, these results illustrate how age-structured serology, a common type of epidemiological data, can be leveraged to better understand both historical and future transmission patterns in different populations.

As mpox spread continues across several endemic and non-endemic countries around the world, vaccination has become an integral part of the global response to control the epidemic. Some vaccines have been recommended for use against mpox by the World Health organization (WHO). As the roll-out of mpox vaccines continue across the globe, it is imperative to develop mathematical models to support public health officials and governments agencies in optimizing vaccination strategies to curtail the resurgence of mpox. In this article, we develop a compartmental mathematical model to investigate the impact of vaccination in controlling a potential mpox resurgence in Canada. The model categorizes individuals into high- and low-risk groups and incorporates pre-exposure vaccination in the high-risk group and post-exposure vaccination in the high- and low-risk groups. The vaccine-free version of the model was calibrated to the daily reported cases of mpox in Canada from April to October 2022, from which we estimated key model parameters, including the sexual and non-sexual transmission rates. Furthermore, we calibrated the full model to the daily reported cases of mpox in Canada in 2024, to estimate the current mpox vaccination rates in Canada. Our results highlight the importance of pre-exposure vaccination in the high-risk group on controlling a potential resurgence of mpox in Canada, and the minimal effects of post-exposure vaccination in the high- and low-risk groups on the outbreak. In addition, our model predicts the possibility of mpox becoming endemic in Canada, in the absence of pre-exposure vaccination in the high-risk group. Overall, our modeling result suggests that pre-exposure vaccination in the high-risk group is crucial in controlling mpox outbreak in Canada. Stepping up this vaccination is sufficient to avert a potential mpox resurgence in Canada.

A deterministic nonlinear mathematical model describing the population dynamics for Dengue and Chikungunya virus taken into consideration the effect of misdiagnosis due to the co-endemicity of the two viruses in the human population. It is necessary to understand the most important parameters involved in their dynamics that may help in developing strategies for prevention, control and joint treatments. The model is rigorously analyzed qualitatively and thresholds for eradication are established.

Mosquito-borne diseases, such as malaria, remain a major global health challenge, necessitating the exploration of innovative vector control strategies. Naturally occurring entomopathogenic fungi have been shown to reduce mosquito lifespan, but their slow-acting nature has limited their practical application. Advances in biotechnology have led to the development of transgenic fungus strains (this study will focus on Metarhizium pingshaense strain) engineered to express insecticidal toxins, significantly increasing their efficacy against malaria vector mosquitoes. To our knowledge, this is the first deterministic model designed to assess the impact of fungal-based mosquito control. The proposed model accounts for multiple transmission pathways of the fungal infection, including mating-based transmission from infected males to females and indirect transmission via contact with infectious mosquito carcasses. The model is analyzed to determine equilibrium states, local stability conditions, and the reproduction number. Numerical simulations explore various release scenarios, evaluating the effectiveness of periodic versus continuous fungal release in different ecological settings. The results indicate that transgenic Metarhizium pingshaense has the potential to significantly reduce mosquito populations, particularly when release strategies are optimized.

Human Papillomavirus (HPV) is a major sexually-transmitted infection that causes various cancers and genital warts in humans. In addition to accounting for about 99% of cervical cancer cases, it significantly contributes to anal, penile, vaginal, and head and neck cancers. Although HPV is vaccine-preventable (and highly efficacious vaccines exist for preventing infection with some of the most oncogenic HPV subtypes in the targeted population), the disease continues to cause major public health burden globally (largely due to inequity in access to the main control resources (i.e., access to Pap smear and vaccination) and low vaccination coverage in most communities that implement routine HPV vaccination). This lecture is based on the use of a new mathematical model (for the natural history of HPV, together with the associated neoplasia) for assessing the combined population-level impacts of Pap cytology screening and vaccination against the spread of HPV in a heterogeneous (heterosexual and homosexual) population. The model, which takes the form of a deterministic system of nonlinear differential equations, will be calibrated and validated using HPV-related cancer data from South Korea. Theoretical and numerical simulation results will be presented. Conditions for achieving vaccine-derived herd-immunity threshold (for achieving HPV elimination in Korea) will be derived.

A genome consists of a long string of four letters (bases A, T, C, G). How the information of biochemical processes stored in this string of bases is an open question. Are their higher order structures, such as, words, sentences, semantics, and a grammar in the DNA language (compositional complexity)? DNA from different species exhibit differences in global sequence composition, and this is used as markers to align larger sequences - grouping of genomes based on homology. Classification of genomes through similarity and dissimilarity is at the heart of Phylogenetics/Genomic Epidemiology. It uses several statistical-mathematical methods to align and compare the base sequences of multiple genomes, which are both computational resource intensive and time consuming for similar sequences. We develop and use an “alignment-free” method based on the Chaos-Game-Representation (CGR) of Statistical Physics, to successfully classify very closely related genomes of sub and sub-sub-species of HIV1 and mutants of Covid19. This useful approach requires less computational resources and time for analysis.

Biological systems evolve across different spatial and temporal scales. Modeling such complex systems gives rise to multi-scale differential equations that may be written as ODEs, PDEs, DDEs, SDEs, or Difference Equations. Particularly, vector-borne disease models are often described using ordinary differential equations with multiple time scales, which can involve singular perturbations—situations where rapid transitions or significant changes in system behavior occur due to small parameter variations or the interaction between fast and slow dynamics. To analyze these multi- time scale problems, we employ tools such as Geometric Singular Perturbation Theory (GSPT), Tikhonov’s Theorem, and Fenichel’s Theory. These methods provide insights into complex phenomena, including the loss of normal hyperbolicity and other intricate behaviors. Particularly, applying singular perturbation theory to vector-borne diseases allows us to reduce the dynamics to a one-time scale and understand their dynamics. To illustrate this, we present a Zika virus model and apply Tikhonov’s theorem and GSPT to investigate the model’s asymptotic behavior. Additionally, we conduct a bifurcation analysis to explore how the system’s behavior changes with variations in the parameter . We illustrate the various qualitative scenarios of the reduced system under singular perturbation. We will show that the fast–slow models, even though in nonstandard form, can be studied by means of GSPT.

Despite being curable and preventable, tuberculosis (TB) still causes the highest mortality rates in the human population. However, the number of TB cases significantly reduced globally in 2020, according to the Global Tuberculosis Report by the World Health Organization, coinciding with the COVID-19 pandemic. These reductions in TB cases are likely due to a complex interplay between disruptions in TB health services and the case counts resulting from COVID-19. We developed a compartmental model for the co-infection of tuberculosis and COVID-19 in the human population to assess the impact of medical resources, mobility, under-reporting, and the social behavior (follow social distancing and face mask) of infected individuals with either disease. We computed the basic reproduction numbers for TB alone, COVID-19 alone, and the co-infection scenario. Additionally, key parameters and basic reproduction numbers were estimated by utilizing case studies from low-income, middle-income, and high-income countries in a multi-patch scenario. Our results indicate that increased social behavior among infected individuals significantly reduces the number of co-infected individuals. The impact of mobility was assessed using a two-patch model with emigration and immigration rates. It shows that the mobility of unreported infectious individuals significantly increases both active cases of TB and COVID-19. This study provides significant recommendations for medical providers and public health officials regarding TB elimination in high-income countries and TB reduction in lower-income countries with a high disease burden. The findings are also relevant for studying TB in the context of future pandemic scenarios.

Chlamydia trachomatis (CT) infection is the most reported bacterial sexually transmitted infection (STI) in the United States (US). Despite many cases being asymptomatic, infection can lead to complications such as pelvic inflammatory disease (PID) in females, and infertility in both females and males. We developed an agent-based transmission model to evaluate the impact of a potential CT vaccine on the prevalence of CT infections and associated PID in the US population. The model simulates an evolving sexual network of 10,000 sexually active agents aged 15–54, including heterosexuals, female sex workers, and men who have sex with men, following Susceptible–Exposed–Infected–Recovered–Susceptible (SEIRS) transmission dynamics. A key strength of the model is its rigorous two-step calibration procedure, which first matches real CT prevalence by age and sex, followed by real PID prevalence by age in the US. This ensures realistic alignment with epidemiological patterns. The model incorporates both vaccination and test-and-treat strategies, enabling direct comparisons between interventions. We then evaluated the impact of different scenarios of vaccination coverage and targeting, assuming a vaccine with 80% efficacy against infection and a 5-year duration of protection. The results demonstrate a gender-neutral vaccine recommendation is projected to achieve the highest impact in reducing CT prevalence and PID burden, even with a moderate vaccination coverage. Beyond CT, this is flexible, computationally efficient framework is adaptable to study other STIs and assess the effectiveness of various intervention strategies, given appropriate epidemiological and behavioral data. By providing actionable insights, this framework serves as a decision-support tool for policymakers, public health officials, and vaccine developers.

A deterministic nonlinear mathematical model describing the population dynamics for Dengue and Chikungunya virus taken into consideration the effect of misdiagnosis due to the co-endemicity of the two viruses in the human population. It is necessary to understand the most important parameters involved in their dynamics that may help in developing strategies for prevention, control and joint treatments. The model is rigorously analyzed qualitatively and thresholds for eradication are established.

Mosquito-borne diseases, such as malaria, remain a major global health challenge, necessitating the exploration of innovative vector control strategies. Naturally occurring entomopathogenic fungi have been shown to reduce mosquito lifespan, but their slow-acting nature has limited their practical application. Advances in biotechnology have led to the development of transgenic fungus strains (this study will focus on Metarhizium pingshaense strain) engineered to express insecticidal toxins, significantly increasing their efficacy against malaria vector mosquitoes. To our knowledge, this is the first deterministic model designed to assess the impact of fungal-based mosquito control. The proposed model accounts for multiple transmission pathways of the fungal infection, including mating-based transmission from infected males to females and indirect transmission via contact with infectious mosquito carcasses. The model is analyzed to determine equilibrium states, local stability conditions, and the reproduction number. Numerical simulations explore various release scenarios, evaluating the effectiveness of periodic versus continuous fungal release in different ecological settings. The results indicate that transgenic Metarhizium pingshaense has the potential to significantly reduce mosquito populations, particularly when release strategies are optimized.

Human Papillomavirus (HPV) is a major sexually-transmitted infection that causes various cancers and genital warts in humans. In addition to accounting for about 99% of cervical cancer cases, it significantly contributes to anal, penile, vaginal, and head and neck cancers. Although HPV is vaccine-preventable (and highly efficacious vaccines exist for preventing infection with some of the most oncogenic HPV subtypes in the targeted population), the disease continues to cause major public health burden globally (largely due to inequity in access to the main control resources (i.e., access to Pap smear and vaccination) and low vaccination coverage in most communities that implement routine HPV vaccination). This lecture is based on the use of a new mathematical model (for the natural history of HPV, together with the associated neoplasia) for assessing the combined population-level impacts of Pap cytology screening and vaccination against the spread of HPV in a heterogeneous (heterosexual and homosexual) population. The model, which takes the form of a deterministic system of nonlinear differential equations, will be calibrated and validated using HPV-related cancer data from South Korea. Theoretical and numerical simulation results will be presented. Conditions for achieving vaccine-derived herd-immunity threshold (for achieving HPV elimination in Korea) will be derived.

A genome consists of a long string of four letters (bases A, T, C, G). How the information of biochemical processes stored in this string of bases is an open question. Are their higher order structures, such as, words, sentences, semantics, and a grammar in the DNA language (compositional complexity)? DNA from different species exhibit differences in global sequence composition, and this is used as markers to align larger sequences - grouping of genomes based on homology. Classification of genomes through similarity and dissimilarity is at the heart of Phylogenetics/Genomic Epidemiology. It uses several statistical-mathematical methods to align and compare the base sequences of multiple genomes, which are both computational resource intensive and time consuming for similar sequences. We develop and use an “alignment-free” method based on the Chaos-Game-Representation (CGR) of Statistical Physics, to successfully classify very closely related genomes of sub and sub-sub-species of HIV1 and mutants of Covid19. This useful approach requires less computational resources and time for analysis.

Biological systems evolve across different spatial and temporal scales. Modeling such complex systems gives rise to multi-scale differential equations that may be written as ODEs, PDEs, DDEs, SDEs, or Difference Equations. Particularly, vector-borne disease models are often described using ordinary differential equations with multiple time scales, which can involve singular perturbations—situations where rapid transitions or significant changes in system behavior occur due to small parameter variations or the interaction between fast and slow dynamics. To analyze these multi- time scale problems, we employ tools such as Geometric Singular Perturbation Theory (GSPT), Tikhonov’s Theorem, and Fenichel’s Theory. These methods provide insights into complex phenomena, including the loss of normal hyperbolicity and other intricate behaviors. Particularly, applying singular perturbation theory to vector-borne diseases allows us to reduce the dynamics to a one-time scale and understand their dynamics. To illustrate this, we present a Zika virus model and apply Tikhonov’s theorem and GSPT to investigate the model’s asymptotic behavior. Additionally, we conduct a bifurcation analysis to explore how the system’s behavior changes with variations in the parameter . We illustrate the various qualitative scenarios of the reduced system under singular perturbation. We will show that the fast–slow models, even though in nonstandard form, can be studied by means of GSPT.

Despite being curable and preventable, tuberculosis (TB) still causes the highest mortality rates in the human population. However, the number of TB cases significantly reduced globally in 2020, according to the Global Tuberculosis Report by the World Health Organization, coinciding with the COVID-19 pandemic. These reductions in TB cases are likely due to a complex interplay between disruptions in TB health services and the case counts resulting from COVID-19. We developed a compartmental model for the co-infection of tuberculosis and COVID-19 in the human population to assess the impact of medical resources, mobility, under-reporting, and the social behavior (follow social distancing and face mask) of infected individuals with either disease. We computed the basic reproduction numbers for TB alone, COVID-19 alone, and the co-infection scenario. Additionally, key parameters and basic reproduction numbers were estimated by utilizing case studies from low-income, middle-income, and high-income countries in a multi-patch scenario. Our results indicate that increased social behavior among infected individuals significantly reduces the number of co-infected individuals. The impact of mobility was assessed using a two-patch model with emigration and immigration rates. It shows that the mobility of unreported infectious individuals significantly increases both active cases of TB and COVID-19. This study provides significant recommendations for medical providers and public health officials regarding TB elimination in high-income countries and TB reduction in lower-income countries with a high disease burden. The findings are also relevant for studying TB in the context of future pandemic scenarios.

Chlamydia trachomatis (CT) infection is the most reported bacterial sexually transmitted infection (STI) in the United States (US). Despite many cases being asymptomatic, infection can lead to complications such as pelvic inflammatory disease (PID) in females, and infertility in both females and males. We developed an agent-based transmission model to evaluate the impact of a potential CT vaccine on the prevalence of CT infections and associated PID in the US population. The model simulates an evolving sexual network of 10,000 sexually active agents aged 15–54, including heterosexuals, female sex workers, and men who have sex with men, following Susceptible–Exposed–Infected–Recovered–Susceptible (SEIRS) transmission dynamics. A key strength of the model is its rigorous two-step calibration procedure, which first matches real CT prevalence by age and sex, followed by real PID prevalence by age in the US. This ensures realistic alignment with epidemiological patterns. The model incorporates both vaccination and test-and-treat strategies, enabling direct comparisons between interventions. We then evaluated the impact of different scenarios of vaccination coverage and targeting, assuming a vaccine with 80% efficacy against infection and a 5-year duration of protection. The results demonstrate a gender-neutral vaccine recommendation is projected to achieve the highest impact in reducing CT prevalence and PID burden, even with a moderate vaccination coverage. Beyond CT, this is flexible, computationally efficient framework is adaptable to study other STIs and assess the effectiveness of various intervention strategies, given appropriate epidemiological and behavioral data. By providing actionable insights, this framework serves as a decision-support tool for policymakers, public health officials, and vaccine developers.

Deterministic and stochastic models, though often used to describe the same biological systems, can yield qualitatively different predictions. In particular, deterministic bistability does not necessarily imply stochastic bimodality, and vice versa. Multistability and multimodality are typically seen as indicators of distinct system behaviors, often inferred from stochastic simulation trajectories. In this talk, I explore the disconnect between probability modes and behavioral modes in the context of transient bimodality—also known as “adiabatic explosions”—which refers to metastable probability modes that do not correspond to distinct dynamical behaviors at the trajectory level. I present recent findings that link the emergence of these transient modes to a breakdown of the central limit theorem, specifically in the context of first-passage time distributions to absorbing states. I conclude by discussing how transient bimodality challenges conventional interpretations of system behavior in biological contexts and highlight conditions under which this phenomenon becomes particularly relevant.

Mathematical models of ecological and epidemiological systems often focus on asymptotic dynamics, such as equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain variables of interest remain in a slowly evolving state for an extended period before undergoing rapid change. These transient dynamics can have significant implications for population persistence, disease outbreaks, and ecosystem stability. In this work, we analyze long-lasting and slowly varying transient dynamics in discrete-time systems. We extend previous theoretical frameworks by identifying conditions under which an observable of the system can exhibit prolonged transients and derive criteria for characterizing these dynamics. Our results show that specific points in the state space, analogous to transient centers in continuous-time systems, can generate and sustain long transients in discrete-time models. We further demonstrate how these properties manifest in predator-prey models and epidemiological systems, particularly in contexts where populations or disease prevalence remain low for an extended period before experiencing a sudden shift. These findings provide a foundation for understanding and predicting long transients in discrete-time ecological and epidemiological models. (Joint Work with FMG Magpantay)

Reinforcement learning (RL) is a powerful machine learning paradigm in which an RL agent learns to discover optimal strategies in uncertain environments. The RL control strategy has achieved remarkable success in complex tasks such as playing Chess, Go, and StarCraft. For RL, the prevailing application interface (API) standard is Gymnasium, a Python library [1]. Agent-based (AB) modeling is a mathematical, dynamical system modeling approach where the parts of the system, the so-called agents, autonomously act according to agent-type specific rules. PhysiCell is an AB modeling framework written in C++ and was implemented to model multicellular systems based on Newtonian physics. Cells are the agents. The cell type specifies the rule set the agents apply. Tissue structure emerges from the cell interactions. Substrates like oxygen can be modeled with the integrated BioFVM diffusive transport solver. Additionally, intracellular models can be integrated into cell agents [2]. The resulting AB models are 2 or 3-dimensional, off-lattice, center-based, and multiscale in space and time. In this talk, we will introduce PhysiGym, a well-documented and on all major operating systems tested open-source framework written in C++ and Python that allows to control PhysiCell models over the Gymnasium API. After a brief introduction to AB models and RL, we will discuss the implementation and obtained results from our tumor microenvironment model and the RL algorithms we applied to the model. In the future, PhysiGym can be used to learn from simulations possible mechanisms that might explain how biology systems react to similar real-world control. Furthermore, if cancer patient digital twins are written as PhysiCell models, PhysiGym could ultimately be used by oncologists to explore RL reward functions to improve treatment efficacy, reduce side effects, and slow or prevent resistance. References: [1] https://gymnasium.farama.org/ , [2] https://PhysiCell.org

Microinvasions in ductal carcinoma in situ (DCIS) are malignant cells that have broken through the basement membrane (BM) and extend into the stroma with no focus larger than 1 mm. Since microinvasions constitute the first step in the metastatic cascade, identifying the causes of microinvasions will help distinguish between progressors or non-progressors among the DCIS patients, thus improving treatment. The mechanical tumor-stroma interactions play an important role in this process. Studies have shown that elevated collagen stiffening, deposition, and fibril crosslinking are correlated with tumor aggressiveness and invasion in breast cancer. Therefore, here we present SilicoDCIS, a 2D off-lattice center-based agent-based model (ABM) of ductal carcinoma in situ (DCIS) growth and its interaction with the extracellular matrix (ECM) to investigate the mechanical conditions that may lead to tumor microinvasions. SilicoDCIS simulates the division, growth, and migration of tumor cells in DCIS while interacting with other cell types and the ECM. This includes the BM, the myoepithelial and epithelial cell layers, and the collagen in the ECM. The ECM was modeled as a vector field, where the direction of each vector gives the orientation of a collagen bundle, and the vector magnitude is related to the bundle density. The growing DCIS can remodel the ECM (density and orientation), and in turn, the ECM applies a reciprocal force (proportional to the local collagen density) opposite to the tumor growth. With SilicoDCIS, we studied the mechanical effects of cancer cell proliferation and migration on the BM and the ECM. We found that higher cell migration force leads to increased BM stress and ECM density (on the tumor edges where cells migrate) and that the escape of the migrating cells from the duct vs. their intraductal confinement depends on cell speed. SilicoDCIS may provide insights into the mechanics of DCIS microinvasions to guide the design of future experiments.

Compound birth-death processes are widely used to model the age-incidence curves of many cancers [1]. There are efficient schemes for directly computing the relevant probability distributions in the context of linear multi-stage clonal expansion (MSCE) models [2]. However, these schemes have not been generalised to models on arbitrary graphs, forcing the use of either full stochastic simulations or mean-field approximations, which can become inaccurate at late times or old ages [3, 4]. Here, we present a numerical integration scheme for directly computing survival probabilities of a first-order birth-death process on an arbitrary directed graph, without the use of stochastic simulations. As a concrete application, we show that this new numerical method can be used to infer the parameters of an example graphical model from simulated data.

Melanoma is the most aggressive type of skin cancer, yet survival rates are excellent if it is diagnosed early. However, if metastasis occurs, five-year survival rates drop significantly. During the early stages of tumour initiation, melanoma cells form clusters within the primary tumour which promote metastasis. In the absence of biological tools to visualise cluster formation at primary tumour sites, we develop mathematical models to generate mechanistic insight into their formation. For this work we utilise in vitro data for two distinct melanoma cell phenotypes, one more proliferative and the other more invasive. This data consists of experiments for each phenotype individually, resulting in homogeneous clusters, as well as mixtures of the two phenotypes, resulting in heterogeneous clusters. We develop a series of differential-equation-based models using a coagulation-fragmentation-proliferation framework to describe the growth dynamics of homogeneous clusters, incorporating different functional forms for cell proliferation and cluster splitting. We then extend these models to describe the formation of heterogeneous cell clusters by considering both cluster size and phenotypic composition. We fit the models to experimental data, using a Bayesian framework to perform parameter inference and information criteria to perform model selection. In this way, we characterise and quantify differences in the clustering behaviour of two melanoma phenotypes in homogeneous and heterogeneous clusters, particularly the cluster coagulation, proliferation, and splitting rates. We find that the coagulation rate for the invasive phenotype is much larger than that for the proliferative phenotype, and evaluate how well different modelling assumptions fit the data in order to increase our understanding of the mechanisms driving metastasis. In future work, the models will be used to inform further experiments and, in particular, to suggest and test strategies for inhibiting metastasis.

A hallmark of colorectal cancer is the structural disruption of the colonic tissue, a process correlated with disease progression. Intestinal crypts, glands essential for homeostasis, lose their tubular morphology - and function - due to uncontrolled cell proliferation and tissue invasion. Evaluating this deterioration in biopsied samples is critical for both patient diagnosis and prognosis. Histopathological methods are essential for assessing colorectal cancer status, but their precision and reproducibility can be improved. Spatial biology provides a mathematical framework to analyse the structural properties of biological data; in this work, we apply techniques from topological data analysis and network science to quantify architectural changes in colorectal cancer progression. Using cell point clouds derived from immunohistochemistry imaging, we construct cell networks that encode topological tissue features. We employ these networks to segment large, imaged samples into smaller, biologically meaningful regions of interest that preserve tissue architecture. We compare the performance of our approach to conventional segmentation methods such as quadrat division. Within these segmented regions, we further employ methods from persistent homology to quantify tissue structure, with the long-term goal of identifying novel biomarkers of disease progression.

Cell-cell fusion is a known phenomenon throughout the human body. It characterizes a wide range of physiological and pathological processes, ranging from placentation and embryogenesis to cancer stem cell (CSC) formation. There is increasing evidence that cell-cell fusion can play key roles in the development and progression of cancer, particularly by increasing intratumor heterogeneity and potentiating somatic evolution. There are many unanswered questions surrounding the characteristics that define cancer cell-cell fusion events, their frequency in in vivo tumor conditions, and whether or not cell-cell fusion is a universal phenomenon across cancer. Using a combination of in vitro and in silico approaches, we can begin to answer some of these questions. We have developed a preliminary cellular automata model using HAL to evaluate the effect of variable cell-cell fusion rates and behaviors under a range of tumor microenvironmental conditions. By comparing our spatial model to a suite of ordinary differential equations, we can begin to estimate the effects of cell-cell fusion on the genomic heterogeneity and malignancy potential of cancers in vivo. I demonstrate the importance of improving fusion rate estimates using the simplest iteration of an in silico cellular automata model (coined SimpleFusion). The preliminary SimpleFusion model results illustrate how much the impact of cell fusion, as measured by the percentage of cells that have had a fusion event in their lineage, changes between orders of magnitude of fusion rates. Corresponding ODE models demonstrate similar results despite the lack of encoded spatial information. By studying these two types of models (ABM, ODEs) in combination, we can begin to understand what parameters most directly define the cell-cell fusion population dynamics in our in vitro fusion experiments and, in turn, in vivo conditions as well.

Blood cancers pose a growing medical and economic challenge in aging societies. Every day, the human bone marrow (BM) generates more than 100 billion blood cells. This process is driven by hematopoietic stem cells (HSCs), which retain their ability to proliferate and self-renew throughout life. However, over time, HSCs accumulate mutations that may lead to malignant transformation, as seen in acute myeloid leukemia (AML), one of the most aggressive cancers. Even in healthy individuals, the BM undergoes age-related changes, including a decline in cell numbers, remodeling of the BM micro-environment, and a bias in HSC differentiation. Emerging evidence suggests that these alterations create a favorable environment for the expansion of mutated cells, thereby promoting blood cancer development and progression. Mathematical and computational models facilitate our understanding of how BM aging contributes to malignant cell growth. We propose nonlinear ordinary differential equation models to describe blood cell formation and clonal competition in the human BM. The models incorporate micro-environmental and systemic feedback loops and are informed by data from both healthy individuals and cancer patients. Our findings suggest that the age-related decline in HSC self-renewal, combined with increased chronic inflammation (inflammaging), makes the BM more susceptible to the expansion of mutated cells and at the same time impairs treatment response. Through mathematical analysis, quantitative simulations, and patient data fitting, we study the following questions: 1. How do HSC proliferation & self-renewal change during physiological aging? 2. How do age-related alterations in healthy BM contribute to blood cancer development? 3. What is the impact of chronic inflammation on HSC function and blood cancer progression? 4. How do age-related BM changes affect treatment responses, e.g., in AML patients? 5. How could treatment protocols be adapted to elderly patients?

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction–diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction–diffusion GBM model based on the ‘go or grow’ hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

Patients with inflammatory bowel disease (IBD) face an elevated risk of colorectal cancer (CRC), necessitating lifelong surveillance to find and remove precancers before they become malignant. Current one-size-fits-all approaches are inadequate and tailored strategies that consider cancer evolution are needed. To address this, we developed a mechanistic framework of IBD-CRC progression. Our multi-type branching process model accounts for IBD onset, mutational processes, and both precancerous (adenoma/dysplasia) and malignant clonal expansion. Initial parameter estimation for mutation and growth rates when fitting the multi-stage clonal expansion model to epidemiological IBD-CRC data yielded similar estimates to those found previously in sporadic CRC but suggest higher mutation rates and slightly lower growth rates in IBD. However, this data may not perfectly represent the natural history, as surveillance colonoscopy with lesion removal and colectomy alter the observable progression. Further, fitting to cancer incidence data alone presents parameter identifiability issues, restricting our initial fit to four parameters. To address these limitations, our study draws upon extensive clinical data from the U.S. Veterans Health Administration, employing validated methods using large language models to construct high-quality datasets with detailed information on surveillance colonoscopy timing, colectomies, and intermediate lesions extracted from pathology reports. To integrate these data, we developed a complementary fast simulation model, which will be released as an R package. This simulation model incorporates clinical interventions, such as colonoscopy with size-dependent lesion removal. Our combined analytical and simulation approach captures the complex precancerous evolution in IBD, providing a quantitative foundation for more effective, personalized surveillance guidelines. Further, this approach can be adapted to improve surveillance in the general population.

Blood cancers pose a growing medical and economic challenge in aging societies. Every day, the human bone marrow (BM) generates more than 100 billion blood cells. This process is driven by hematopoietic stem cells (HSCs), which retain their ability to proliferate and self-renew throughout life. However, over time, HSCs accumulate mutations that may lead to malignant transformation, as seen in acute myeloid leukemia (AML), one of the most aggressive cancers. Even in healthy individuals, the BM undergoes age-related changes, including a decline in cell numbers, remodeling of the BM micro-environment, and a bias in HSC differentiation. Emerging evidence suggests that these alterations create a favorable environment for the expansion of mutated cells, thereby promoting blood cancer development and progression. Mathematical and computational models facilitate our understanding of how BM aging contributes to malignant cell growth. We propose nonlinear ordinary differential equation models to describe blood cell formation and clonal competition in the human BM. The models incorporate micro-environmental and systemic feedback loops and are informed by data from both healthy individuals and cancer patients. Our findings suggest that the age-related decline in HSC self-renewal, combined with increased chronic inflammation (inflammaging), makes the BM more susceptible to the expansion of mutated cells and at the same time impairs treatment response. Through mathematical analysis, quantitative simulations, and patient data fitting, we study the following questions: 1. How do HSC proliferation & self-renewal change during physiological aging? 2. How do age-related alterations in healthy BM contribute to blood cancer development? 3. What is the impact of chronic inflammation on HSC function and blood cancer progression? 4. How do age-related BM changes affect treatment responses, e.g., in AML patients? 5. How could treatment protocols be adapted to elderly patients?

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction–diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction–diffusion GBM model based on the ‘go or grow’ hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

Patients with inflammatory bowel disease (IBD) face an elevated risk of colorectal cancer (CRC), necessitating lifelong surveillance to find and remove precancers before they become malignant. Current one-size-fits-all approaches are inadequate and tailored strategies that consider cancer evolution are needed. To address this, we developed a mechanistic framework of IBD-CRC progression. Our multi-type branching process model accounts for IBD onset, mutational processes, and both precancerous (adenoma/dysplasia) and malignant clonal expansion. Initial parameter estimation for mutation and growth rates when fitting the multi-stage clonal expansion model to epidemiological IBD-CRC data yielded similar estimates to those found previously in sporadic CRC but suggest higher mutation rates and slightly lower growth rates in IBD. However, this data may not perfectly represent the natural history, as surveillance colonoscopy with lesion removal and colectomy alter the observable progression. Further, fitting to cancer incidence data alone presents parameter identifiability issues, restricting our initial fit to four parameters. To address these limitations, our study draws upon extensive clinical data from the U.S. Veterans Health Administration, employing validated methods using large language models to construct high-quality datasets with detailed information on surveillance colonoscopy timing, colectomies, and intermediate lesions extracted from pathology reports. To integrate these data, we developed a complementary fast simulation model, which will be released as an R package. This simulation model incorporates clinical interventions, such as colonoscopy with size-dependent lesion removal. Our combined analytical and simulation approach captures the complex precancerous evolution in IBD, providing a quantitative foundation for more effective, personalized surveillance guidelines. Further, this approach can be adapted to improve surveillance in the general population.

Musculoskeletal injuries can significantly impact the careers of racehorses, and are a common cause of lost training days and fatality. Most bone injuries arise from the gradual accumulation of microcracks through repeated training rather than spontaneous events. If severe enough, cracks may propagate through the bone and lead to fractures, often necessitating euthanasia. While training promotes bone adaptation to higher mechanical loads, overtraining can cause excessive damage. To better understand the biological processes underlying bone injury, we developed a lumped parameter model that combines the processes of bone adaptation, microdamage accumulation and bone repair. The model parameters were calibrated to experimental observations of bone volume fraction and time to fracture in racehorses. A sensitivity analysis identified joint loads (arising from training speed) and strides per day (arising from training distance) as key factors contributing to bone damage. Simulations of a typical training program showed that the majority of damage is incurred from training at racing speeds. While some microdamage is repaired during training, our model estimates that this process is insufficient to offset the damage accumulated. These findings emphasise the critical role of regular rest in preventing bone injury.