An Optimal Control Experiment for an SEIRS Epidemiological Model

Abstract

This work studies an optimal control model for a discrete-time Susceptible/Exposed/Infective/Removed/Susceptible (SEIRS) deterministic epidemiological model with a finite time horizon and changing population. The model presented converts a continuous SEIRS model that would typically be solved using differential equations into a discrete model that can be solved using dynamic programming. The discrete approach more closely resembles real life situations, as the number of individuals in a population, the rate of vaccination to be applied, and the time steps are all discrete values. The model utilizes a previously developed algorithm and applies it to the presented SEIRS model. To demonstrate the applicability of the algorithm, a series of numerical results are presented for various parameter values. KEYWORDS: Control; Cost; Discrete; Disease; Epidemiology; Minimization; Modeling; Optimality; SEIRS; Vaccination