Bridging Biological Systems with Social Behavior, Conservation, Decision Making, and Well-being through Hybrid Mathematical Modeling

Mathematical modeling can achieve otherwise inaccessible insights into bio-logical questions. We use ODE (ordinary differential equations) and Game Theory models to demonstrate the breadth and power of these models by studying three very different biological questions, involving socio-behavioral and socio-economic systems, conservation biology, policy and decision making, and organismal homeostasis.

We adapt techniques from Susceptible-Infected-Recovered (SIR) epidemiological models to examine the mental well-being of a community facing the collapse of the industry on which it’s economically dependent. We consider the case study of a fishing community facing the extinction of its primary harvest species. Using an ODE framework with a complex contagion process, we track the mental health states of people as they shift to a sustainable source of income. We find that community connectivity has a meaningful impact on both the duration and transition dynamics.

Successful preservation of threatened species can depend on the appropriate deployment of limited resources to combat illegal poaching. Using mathematical game theory based on the ‘Colonel Blotto Game’, we model the battle between Conservationists and Poachers. Conservationists must allocate social, political, and financial resources to curtail poaching while Poachers can expend resources to nullify Conservationist activities in each of these ‘battlefields’. We analyze payoffs and player budget distributions to determine overall player success to provide novel tools for policy/decision support and improve efficacy in planning conservation strategy.

Recent advances in the field of stress physiology have presented the reactive scope model: a conceptual theory that extends beyond traditional homeostatic models to incorporate influences physiological state and life history on an animal's ability to respond to stressors. A recently published quantitative model of the reactive scope model made simplifying assumptions about types of energetic resources and how they are used and replenished [Wright et al., 2023]. We extend that model meaningfully by considering a realistic energy budget and the consideration of multiple mediators simultaneously. This improves the capabilities of the model to predict an animal’s health outcomes from exposures to stressors over time.

Together, these models demonstrate the power of modeling to advance understanding in fields ranging from population health to conservation to physiology.

Thank you so much for being patient with me with the corrections!