Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment

The COVID-19 pandemic has seen the development of several mathematical models. In recent years, the very topical issue of re-susceptibility has led to the proposal of more complex models to address this issue. The paper deals with an optimal control problem applied to COVID-19. The Pontryagin maximum principle and the dynamic programming principle are used to solve the problem. A compartmental Ordinary Differential Equation (ODE) model is proposed to study the evolution of the pandemic by controlling the effectiveness of the detection campaign and the treatment. We prove the global stability of the Disease-Free Equilibrium (DFE) and the existence of optimal control and trajectories of the model. In the optimal control problem, we bring the system back to the DFE. Numerical simulations based on COVID-19 data in Senegal show possibilities to reduce the disease evolution, sometimes by emphasizing the detection campaign and/or the treatment proposed to patients.