Application of Differential Equations in Malaria Transmission

This paper focuses on the development of a mathematical model suitable for calculating equilibrium points in the transmission process of malaria. The research takes into account human-to-human transmission: maternal and infant transmission, in addition to most of the transmission modes considered: human-to-mosquito transmission. In the process of maternal and infant transmission, there are two routes of infection that affect the probability of infection and transmission: one is sexual transmission; the other is transfusion transmission. The mathematical model is based on the SEIR model, and the data come from the report of the World Health Organization and statistics from other literature. The model includes susceptible S(t), exposed E(t), infectious I(t), and recovered R(t) classes for humans and mosquitoes. By solving the differential equations, the obtained results are simulated and analyzed. This study found that disease-free equilibrium and optimal treatment points during malaria transmission when considering sexual transmission and blood transfusion transmission. The results in this study may offer some references for further studying the malaria transmission and treatment.