Numerical simulation of malaria transmission model considering secondary infection

Malaria is an infectious disease caused by Plasmodium and transmitted through the bite of female Anopheles mosquitoes. This article constructs a mathematical model to understand the spread of malaria by considering the vector–bias phenomenon in the infection process, secondary infection, and fumigation as a means of malaria control. The model is constructed as a SIRI-UV model based on six-dimensional non-linear ordinary differential equations. Analysis of the equilibrium points with their local stability and sensitivity analysis of the basic reproduction number R0 is shown analytically and numerically. Based on the analytical studies, two types of equilibrium points were obtained, namely the disease-free equilibrium points and the endemic equilibrium points. We find that the disease-free equilibrium is locally stable if R0 < 1. Our proposed model shows the possibility of a forward bifurcation, backward bifurcation, or forward bifurcation with hysteresis. To support the interpretation of the model, a numerical simulation for the sensitivity of R0 and some autonomous simulations conducted to see how the change of parameter will affect the dynamics of our model. Simulation results show that the increasing of mortality rate on mosquitoes due to fumigation will increase the probability that malaria is eliminated.