An Inverse Problem for Epidemic Models

The first step of the project will be to understand the basic ideas of modeling as well as the simple theoretical arguments for the long-term behavior of the SIS model. Those arguments rely on a mix of explicit solutions, quantitative estimates, and the classical study of solutions in the neighborhood of steady states. As part of this first step, we implement numerical methods to illustrate the behavior of solutions to the deterministic SIS model.The final objective is to study an optimal control problem for an epidemic SIVS system. This model incorporates time-dependent and imperfect vaccination rates, which we attempt to optimize in terms of the balance of benefits-cost at the scale of the total population.