Mathematical analysis and forecasting of controlled Spatio-temporal dynamics of the EG.5 Virus

In this article, we propose a mathematical approach that connects an innovative spatio-temporal model to the problem of the EG.5 variant of COVID-19 in a human population. We demonstrate the existence and uniqueness of the global positive solution for our suggested system. The implementation and analysis of an applicable optimal control issue are as follows. The methods of optimal control theory are applied in this work to demonstrate the existence of optimal control, and with necessary op-timality conditions, we discover the explicit expression of optimal control that minimizes the negative impacts of this infectious disease on countries. We provide numerical simulations at the conclusion to demonstrate the efficacy of our chosen strategy.