MS03 - MFBM-02

Bayesian Applications in Mathematical Biology

Tuesday, July 15 at 10:20am

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Daniel Glazar (Moffitt Cancer Center & Research Institute), Renee Brady-Nicholls, Moffitt Cancer Center & Research Institute

Description:

Development and employment of models in mathematical biology often involve tasks such as parameter estimation, uncertainty quantification, identifiability analysis, sensitivity analysis, and quantification of intra- and inter-subject heterogeneity. Bayesian inference methods naturally lend themselves to fulfill each of these tasks by defining distributions which characterize prior knowledge about the problem (prior) as well as how the accumulation of data updates and refines this knowledge (likelihood). In this minisymposium, we showcase a wide array of Bayesian methods across the various subgroups of mathematical biology. These methods include, but are not limited to: Monte Carlo simulations, data assimilation techniques, Approximate Bayesian Computation, nonlinear mixed effects modeling, joint modeling, individual dynamic predictions, and Bayesian networks. Finally, we provide a forum to discuss the ubiquitous p-value and the corresponding phenomenon of “statistical significance” within the world of Bayesian mathematical biology.

Franz Kuchling

Allen Discovery Center, Tufts University

"Uncertainty Minimization as an Adaptive and Evolutionary Imperative in Biology"

Recent advances in molecular biology have enabled precise manipulation of signaling pathways in living organisms, yet a unifying framework for predicting the organismal-level emergence of form and function remains elusive. The free energy principle, originally developed for neuroscience, offers a Bayesian inference approach to model cellular decision-making during morphogenesis and emergent aneural behavior. Simulations demonstrate the utility of this framework in explaining developmental anomalies (e.g., planarian axial polarity defects) and early carcinogenesis as consequences of maladaptive cellular 'beliefs.' Complementing this, evolutionary metacognition theory formalizes adaptation across timescales, illustrating how coevolutionary processes naturally favor the emergence of multi-scale regulatory systems. These metacognitive architectures promote energy-efficient responses to fluctuating selection pressures. Experimental observations in aneural systems such as Volvox algae support these predictions: Volvox colonies display adaptive phototaxis and retain stimulus-associated behaviors beyond exposure, suggesting a primitive form of memory. These insights offer a cross-disciplinary framework—integrating developmental biology, evolutionary theory, and basal cognition—to model adaptive behavior across biological scales. This foundation may inform future directions in modeling complex diseases such as cancer, particularly where cell-state decisions and misregulation mirror maladaptive inference processes.

Nathanaël Hozé

Université Paris Cité, INSERM, IAME, F-75018, Paris, France

"A multi-scale modelling framework to assess the relationship between SARS-CoV-2 viral load and transmission in household studies"

Understanding the drivers of SARS-CoV-2 transmission is essential for designing effective interventions, particularly in close-contact settings such as households. While viral load is widely believed to influence infectiousness, quantifying its role remains challenging due to individual variability, asymptomatic infections, and the unobservability of transmission events. Household studies offer a controlled context for investigating the link between viral load dynamics and transmission, especially when combined with high-frequency sampling. However, such designs are costly, and their added value relative to simpler approaches is unclear. We present a multi-scale modelling framework that integrates within-host viral dynamics and between-host transmission processes in household settings. We developed a stochastic agent-based model of viral dynamics that includes inter-individual variability. We developed a Bayesian inference approach implemented in rstan, in which we jointly estimate individual-level parameters, infection times, and the relation between viral load and transmissibilty. Our simulation-based framework evaluates whether monitoring viral load at high temporal resolution improves the reconstruction of transmission chains and the estimation of key epidemiological parameters. We compare this rich sampling design to two more commonly used alternatives: (i) designs based solely on symptom onset, and (ii) designs based on qualitative viral detection (i.e., positive/negative status without quantification). We show that incorporating quantitative viral load data improves the accuracy of transmission chain reconstruction and enhances the estimation of key metrics, including the probability of infection, generation interval, and incubation period. This work provides quantitative insights into the potential benefits of incorporating viral load measurements into household transmission studies and informs the design of future studies aimed at elucidating the role of viral kinetics in infectious disease spread.

Kathleen Wilkie

Toronto Metropolitan University

"Practical Parameter Identifiability and Handling of Censored Data with Bayesian Inference in Models of Tumour Growth"

Mechanistic mathematical models are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use five models with an increasing number of parameters to explore how certain (often overlooked) decisions in estimating parameters from data affect the outcome of the analysis. In particular, we propose a framework for including tumour volume measurements that fall outside the upper and lower limits of detection, which are normally discarded. We demonstrate how excluding censored data results in an overestimation of the initial tumour volume and the model-predicted tumour volumes prior to the first measurements, and an underestimation of the carrying capacity and the predicted volumes beyond the latest measurable time points. We show how the choice of prior for the model parameters can impact the posterior distributions, and illustrate that reporting the most likely parameters and their 95% credible interval can lead to confusing or misleading interpretations. We hope this work will encourage others to carefully consider the choices made in parameter estimation and to consider adopting the approaches discussed in this talk.

Ernesto A. B. F. Lima

The University of Texas at Austin

"Modeling tumor sensitivity and resistance: a bayesian framework for predicting combination therapies"

Understanding the heterogeneous response of tumors to therapy remains a major challenge in oncology, particularly in the presence of treatment resistance. We present a framework to model the growth dynamics of radiation-sensitive and radiation-resistant breast cancer cells receiving radiotherapy, immunotherapy, and their combination. Using experimental data from murine models, we construct a family of ordinary differential equation models and apply Bayesian calibration and model selection to identify the most parsimonious model capable of capturing and predicting the observed experimental dynamics. Our approach quantifies differences between sensitive and resistant tumors. Resistant cells exhibited not only faster intrinsic growth rates but also a greater capacity for post-radiotherapy repair compared to sensitive cells. These biological differences were incorporated into the modeling through group-specific parameters, selected using the Bayesian Information Criterion to balance model complexity and predictive ability. In the immunotherapy arm, a pronounced heterogeneity in treatment response was observed. By performing mouse-specific calibration of key parameters governing immunotherapy efficacy and linking them to imaging-derived biomarkers, we successfully captured this variability across subjects. For the combination therapy predictions, the concordance correlation coefficient and Pearson correlation coefficient increased from 0.31 and 0.34 (without biomarkers) to 0.34 and 0.54 (with biomarkers), demonstrating the added predictive value of imaging-informed modeling. The Bayesian framework enabled robust parameter estimation, uncertainty quantification, and assessment of model identifiability, providing insights into the dynamics of combination therapy. Our results emphasize the importance of accounting for intra-tumoral heterogeneity in predictive modeling to improve treatment planning and evaluation.

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Annual Meeting for the Society for Mathematical Biology, 2025.