Optimizing Epidemic Control on Networks: Vaccine Allocation Coupled with SIRS-Based Modeling

Abstract

This thesis develops a data-driven framework for optimizing vaccine allocation across U.S. states. We embed a constrained optimization problem directly within a network coupled SIRS epidemic model. Using state level COVID-19 case data from The New York Times spanning January 2020 through March 2023, we calibrate a piecewise constant transmission rate and simulate epidemic dynamics across all 50 states. Interstate transmission is encoded through a row stochastic weight matrix derived from geographic adjacency. Self weights are scaled by population density to reflect heterogeneous intra-state contact intensity. We formulate vaccine allocation as a nonlinear optimal control problem that minimizes cumulative infected days subject to daily supply, budget, and per state capacity constraints. Given the computational intractability of the full horizon problem, we implement a rolling horizon approximation analogous to Model Predictive Control, in which short planning windows are solved iteratively using Gurobi's non convex QCP solver as the epidemic state evolves. We compare this approach against a greedy myopic heuristic and an uncontrolled baseline, evaluating each strategy's ability to suppress peak infections and prevent resurgence across major pandemic waves.