Regional Control Strategies for a Spatiotemporal SQEIAR Epidemic Model: Application to COVID-19

In this work, we develop a spatial SEIAR-type epidemic model considering a quarantined population (denoted as Q), which we call the SQEIAR model. The dynamics of the SQEIAR model are described by six Partial Differential Equations (PDEs) that represent the changes in the susceptible, quarantined, exposed, asymptomatic, infected, and recovered populations. Our goal is to reduce the number of susceptible, exposed, asymptomatic, and infected individuals while accounting for the environment, which plays a critical role in the spread of epidemics. We then propose a novel strategy for epidemic control, incorporating two key control measures: regional quarantine for the susceptible population and treatment for the infected. This approach serves as an alternative to widespread quarantine, minimizing the economic, social, and other potential impacts. Additionally, we consider the possibility of reinfection among recovered individuals, a common occurrence in many diseases. To demonstrate the practical utility of our results, a numerical example centered on COVID-19 is presented.