Three Measures to Control a Spatiotemporal Epidemic Model: An Optimal Control Approach

ABSTRACT In this paper, we examine the impact of the main disease control measures such as vaccination, isolation, and treatment on the spread of a disease in a given population. based on a SIQRS spatio‐temporal epidemiological model. Our main objective is to characterize an optimal control that minimizes the number of infected individuals and the control costs over a finite spatial and temporal domain. Much of this work has been devoted to mathematical study, where the existence of optimal controls has been proved. We give their description in terms of state variables and adjoint variables, and the optimality system is solved numerically using a forward‐backward sweep method. To illustrate the effectiveness of our theoretical results, we present numerical simulations for several scenarios. Our results may be useful for the development of disease control strategies.