Optimal control analysis of a mathematical model of malaria and COVID-19 co-infection dynamics

In this paper, we analyze a deterministic model of malaria and Corona Virus Disease 2019 co-infection within a homogeneous population. We first studied the single infection model of each disease and then the co-infection dynamics. We calculate the basic reproduction number of each model and study the existence and stability of the steady states. Then, we show that under some suitable conditions, both the malaria single infection model and co-infection model exhibit backward bifurcation. Furthermore, we analyze the conditions of extinction, competitive exclusion and co-existence of these two diseases. In addition, a local sensitivity analysis of the basic reproduction numbers is performed to explore the impact of the different parameters' variability on the dynamics of each disease. Moreover, we apply Pontryagin's maximum principle to determine optimal strategies to control the two diseases in case of co-infection. Finally, some numerical simulation results are presented to support the theoretical findings.