Modeling and optimal control of COVID-19 and malaria co-infection based on vaccination

Malaria is a serious health problem in Africa, and the ongoing COVID-19 pandemic has affected the implementation of key malaria control interventions. This jeopardizes the gains made in malaria. As a result, a new co-infection model of COVID-19 and malaria is constructed, and the role of vaccination in COVID-19-malaria co-infection is analyzed. The existence and stability of the equilibria of each single infection are first studied by their respective basic reproduction numbers. When the basic reproduction numbers $R_{C0}$ and $R_{M0}$ are both below unity, the COVID-19-malaria-free equilibrium is locally asymptotically stable. Sensitivity analysis reveals that the main parameters affecting the spread of diseases are their respective disease transmission rate and vaccine efficacy. Further, we introduce the effect of vaccination rate and efficacy on controlling the co-infected population. It also shows that under the condition of a low recovery rate caused by the shortage of medical resources, improving the vaccination rate and effectiveness of vaccines has a positive impact on suppressing diseases. The model is then extended into an optimal control system by introducing prevention and treatment measures for COVID-19 and malaria. The results suggest that applying each strategy alone can reduce the scale of co-infection, but strategy A increases the number of malaria cases and strategy B prolongs the period of COVID-19 infection. Measures to control COVID-19 must be combined with efforts to ensure malaria control is maintained.