An optimal control problem of malaria model with seasonality effect using real data

Abstract

In this study, we present a mathematical model of malaria transmission with a seasonality effect to describe the dynamics of the infection. In the absent seasonality effect, we prove the local stability of the malaria-free equilibrium point. The parameters of the model are fitted to the cumulative number of malaria cases of Papua province, Indonesia for the year 2018 and parameterized using the least-squares technique. The sensitivity analysis of the model to changes in the parameters is explored. Further, the malaria model with the seasonality effect via a periodic mosquito birth rate is investigated numerically. Finally, we formulate an optimal control problem with a control function and obtain the optimal control characterization. The optimal control problem is solved numerically, and the results comprised of a controls system for different strategies.