Math Colloquium talk - Optimal Control and Cost-Effectiveness Analysis in Computational Epidemiology

Optimal control theory and cost-effectiveness analysis provide rigorous frameworks for designing intervention strategies in infectious disease systems. This talk presents their application to Norovirus transmission dynamics, characterized by environmental reservoirs and reinfection through waning immunity. We formulate a compartmental model incorporating environmental pathogen dynamics, dual transmission pathways, and reinfection via susceptible compartment re-entry and time-dependent control functions. Equilibrium analysis establishes existence conditions for disease-free and endemic states. Global asymptotic stability of the disease-free equilibrium is proven via linear Lyapunov functional when R_c < 1, while endemic equilibrium stability follows from quadratic Lyapunov construction. Optimal control characterization applies Pontryagin’s maximum principle to minimize a functional balancing infection burden against intervention costs. An adjoint system is derived explicitly with transversality conditions determining costate boundary behavior. Cost-effectiveness analysis employs incremental cost-effectiveness ratios (ICERs) and averaged cost-effectiveness ratios (ACERs) to rank strategies, identifying dominant interventions on the efficiency frontier. Numerical implementation uses forward-backward sweep methods with fourth-order Runge-Kutta integration for the state and adjoint systems. Simulations demonstrate that environmental interventions achieve superior ICERs compared to isolation-based controls across epidemiologically plausible parameter ranges, with synergistic effects emerging only under specific cost ratio thresholds.