Optimal Control applied to SIRD model of COVID 19

In this study, we present an epidemic-controlled SIRD model with two types of control strategies: mask wear and screening. The aim of this study is to minimize the number of deceased keeping a minimal cost of mask advertising and screening. The model is proved to be well-posed and to have an invariant region. Also, a thorough study of the dynamics is effected and the basic reproduction number is used to study the stability of the steady states of the model. As for the optimal control analysis, the existence of an optimal control was checked. Then its characterization was carried out using Pontryagin's minimum principle. Numerical simulations are conducted after that with different values of maximal screening for comparison. The findings of the optimal control analysis and numerical simulations both reveal that the optimal pair of strategies contribute enormously in lowering the number of infected and dead individuals. Although zero infection is not achieved in the population, this study implies that carrying an optimal approach constitutes a major step in controlling the spread of the disease to the barest minimum that can buy time for middle and low-income countries to carry on with their vaccination strategies.