Mathematical model for transmission dynamics of Malaria disease: impact of invasive alien plants

Abstract

A mathematical model to study the impact of invasive alien plants on the dynamics of malaria transmission and its analyses is studied in this work. The resulted model equations are divided into homogeneous and non-homogeneous equations. The homogeneous equations are solved to determine its disease free equilibrium (DFE) and their stabilities. A basic reproduction number was determined from the DFE. It was found that when R0 < 1, the disease will die out, when R0 = 1, the model undergoes a backward bifurcation, R0 = 0, the model undergoes forward bifurcation and whenever R0 > 1, the disease will persist in the population. At R0 > 1, the global analysis of the model was carried out and it was found to be globally and asymptotically
stable (GAS). A sensitivity analysis of the model parameters was also investigated to determine the parameters that are sensitive for malaria transmission. A travelling wave equations and solutions were also provided for possible understanding of the behaviour of mosquito’s mobility in human environment.