MS08 - ECOP-02

Advances in Spatial Ecological and Epidemiological Modeling and Analysis (Part 2)

Friday, July 18 at 10:20am

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Note: this minisymposia has multiple sessions. The other session is: and Part-1.

Daozhou Gao (Cleveland State University), Xingfu Zou, University of Western Ontario

Description:

Animal dispersal and human movement play a key role in ecology and epidemiology. Species with limited dispersal abilities are more likely to go extinct, especially in the face of habitat fragmentation and climate change. Meanwhile, massive travel and tourism accelerate the global spread of infectious agents. Mathematical models serve as powerful tools for describing and predicting population growth and the spatial-temporal spread of diseases. There are strong connections between population dynamics and disease dynamics, particularly when spatial heterogeneity and population mobility are concerned. By integrating ecological and epidemiological insights, such models provide valuable frameworks for conservation strategies, public health interventions, and policy planning. Despite substantial advances in model formulations, analysis and applications, some major challenges persist. These challenges include accounting for nonlinear interactions, understanding pathogen persistence in fluctuating environments, and addressing computational limitations in high-dimensional systems. The eight invited talks will cover topics on (1) diffusive population model; (2) pathogen persistence in variable environments; (3) partially degenerate reaction-diffusion system; (4) toxicant-taxis model. This mini-symposium provides a great opportunity to showcase some recent progresses in addressing these challenges, exchange ideas and foster interdisciplinary collaborations among diverse researchers.

Wenxian Shen

Auburn University

"Front Propagation Dynamics in Fisher KPP Equations on Unbounded Metric Graphs"

This talk is concerned with front propagation dynamics in Fisher KPP equations on unbounded metric graphs. Such equations can be used to model the evolution of populations living in environments with network structure. There are several studies on front propagation phenomenon in bistable equations on unbounded metric graphs. It is known that, in such equations, the network structure of the underlying environment may block the propagation of the fronts. It will be shown in this talk that the network structure of the environments does not block the propagation of the fronts in Fisher-KPP equations. In particular, it will be shown that the Fisher-KPP equation on an unbounded graph with finite many edges has the same spreading speed $c^*$ as the Fisher KPP equation on the real line $mathbb{R}$ and has a generalized traveling wave connecting the stable positive constant solution and the trivial solution with averaged speed $c$ for any $c > c^∗$.

Rachidi Salako

University of Nevada, Las Vegas

"On a Cross-diffusive SIS Epidemic Model with Singular Sensitivity"

We investigate the dynamics of solutions to a repulsive chemotaxis SIS (susceptible-infected-susceptible) epidemic model with logarithmic sensitivity and with mass-action transmission mechanism. Under suitable regular assumptions on the initial data, we firstly assert the global existence and boundedness of smooth solutions to the corresponding no-flux initial boundary value problem in the spatially one-dimensional setting. Second, we investigate the effect of strong chemotaxis sensitivity on the dynamics of solutions through extensive numerical simulations. Our studies on the asymptotic profiles of the endemic equilibrium indicate that the susceptible populations move to low-risk domains whereas infected individuals become spatially homogeneous when the repulsive-taxis coefficient is large. Additionally, our numerical simulations suggest that the susceptible population with larger chemosensitivity, tends to respond better to the infected population, revealing the effect of strong chemotaxis sensitivity coefficient on the dynamics of the disease.

Yun Kang

Arizona State University

"Migration Dynamics and Collective Decision-Making in Social Insect Colonies"

Social insects are among the most ecologically and evolutionarily successful organisms on Earth, known for exhibiting robust collective behaviors that emerge from local interactions among individuals. Colony migration is a particularly striking example of collective decision-making in these systems. In this talk, we introduce a piecewise dynamical model of colony migration incorporating recruitment switching to investigate the underlying mechanisms and synergistic effects of colony size and quorum thresholds on decision outcomes. Our theoretical findings suggest that larger colonies are more likely to successfully emigrate to a new site. Notably, the model also reveals several intriguing behaviors: (a) the system may exhibit oscillatory dynamics when the colony size falls below a critical threshold; and (b) it may display bistability, where the colony either migrates to a new site or remains at the original nest, depending on the initial distribution of recruiters. Bifurcation analysis further highlights how variations in colony size and quorum thresholds critically influence the overall system behavior. These results underscore the importance of distinguishing between different recruiter populations in modeling and offer valuable insights into how simple, local interactions can lead to complex and coordinated migratory behavior in social insect colonies.

Carolin Grumbach

Osnabrück University

"Allee Pits in Metapopulations: When Increasing Dispersal Can Backfire"

Habitat fragmentation divides populations into smaller subpopulations, while the Allee effect diminishes the viability of small populations. Together, these processes can synergistically amplify negative impacts on spatially structured populations. Conservation strategies often aim to counteract these effects by enhancing connectivity between subpopulations, for example, through corridors or stepping stones. However, increasing connectivity does not always lead to the desired positive outcomes. In this talk, I will demonstrate that due to the Allee effect, low connectivity leads to a decline in the asymptotic total population size, which we call the 'Allee pit'. However, increased connectivity facilitates the rescue effect, wherein a persistent subpopulation in one patch can save an extinction-prone subpopulation in another patch, ultimately increasing the total population size. Using simulations based on a generic discrete-time patch model with positively density-dependent growth, I will explore how enhanced connectivity influences a fragmented population subject to the Allee effect. Our results highlight that conservation strategies must carefully consider dispersal dynamics. Simply increasing connectivity is not enough; ensuring dispersal rates exceed a critical threshold is essential for achieving long-term benefits.

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Annual Meeting for the Society for Mathematical Biology, 2025.