Mathematical and numerical model for the malaria transmission: Euler method scheme for a malarial model

Abstract

This research study has developed a mathematical model for malaria disease which is not only applicable for the case when the recovered humans return to the susceptible class, but also provides the directions for the case when the recovered humans also return to the infectious class. The model is simulated by using the Euler, Runge-Kutta-4 (RK-4), and nonstandard finite difference (NSFD) scheme. Firstly, the model is simulated by the Euler scheme and RK4 scheme and obtained graphical depiction for the endemic equilibrium as well as for the disease-free equilibrium (DFE). Then the mathematical model of malaria is simulated by an NSFD scheme and its graphical interpretation shows that it is suitable for all step sizes, i.e., it gives converging results even for very large step sizes. It is shown that the NSFD scheme is an unconditionally stable numerical scheme at a large step size. It is concluded that parameter R is greater than unity in the disease manifestation of the landlord population in the long term and when the parameter R is less than unity then the DFE is asymptotically stable.