Modelling Malaria Transmission in a Population with SEIRSp Method

Most mathematical models for malaria transmission use the SEIR model in human population. However, the model is no longer suitable for malaria cases due to some medical results that the individuals who have recovered from malaria still have the plasmodium parasites in their bodies. Therefore, malaria has ability to relapse without any contact with mosquitos when the individual's immune system is decreased. In our case, we group the individuals who still have plasmodium in their bodies to the susceptible individuals with plasmodium (S-p) compartment. The S-p compartments is important to accommodate the presence of plasmodium in the human who have been infected by malaria. In this paper, we consider a mathematical model of malaria in human population by assuming that the infection rate of the disease in human population is constant and it depends only with the number of infected human. Furthermore, our analysis are also focused on the existence of a disease-free and the endemic equilibrium points, and also the local stability for both equilibrium points and the global stability for disease-free equilibrium point. We also do numerical simulations by using the fourth order Runge-Kutta method to describe the behavior of the malaria disease for certain parameters.