Optimal control of malaria with medicine and insecticide: A mathematical model

Abstract

Among the deadliest epidemics of the modern era is malaria. Its infection is brought by the plasmodium parasite, which bites humans when they are bitten by female mosquitoes such as anopheles generation. Plasmodium falciparum and P. vivax are two primary malaria species found in India. Several mathematical models-based scientific investigations have been carried out to reduce the impact of malaria on the world population. We discussed about a mathematical model of ordinary differential equations that is nonlinear and represents the dynamics of malaria transmission, taking climate change into account. The basic offspring number $R_b$, which is greater than 1, indicates the presence of immature mosquitoes, the reproduction number ${R_0}$, where $R_0>1$ disease is present and $R_0<1$ is absent, and other fundamental mathematical facts are discussed. Furthermore, Pontryagin's Maximum Principle can be utilized to acquire the necessary conditions for the most effective management of this illness. Consequently, we conclude that by managing the effects of climate change on emerging mosquitoes, we safeguard those with compromised immune systems.