Optimal control of a periodically switched epidemic model

In this paper, we examine a modified susceptible–infected–treatment–recovered (SITR) model. The SITR model is assumed to be a periodically switched system, where two parameters, i.e., transmission rate and treatment rate, are periodically switched. In the first part of the article, we analyze the stability of the switched model in the presence of periodic switching. Moreover, with the periodic switching, we obtain a discontinuous dynamical system where the optimal vaccination control cannot be calculated directly using Pontryagin’s maximum principle. Hence, an optimal control problem of the periodically switched system is formulated by modifying Pontryagin’s maximum principle. The aim is to study the optimization of control strategies for infectious disease outbreaks in a dynamic and resource-limited environment. Finally, several numerical examples are provided to support the results discussed.