The Effect of Mosquito Biting Rate on the Malaria Transmission Model using Bifurcation Analysis

Abstract

This paper analyses a simple malaria transmission model to investigate the effect of
parameter changes in mosquitoes per capita biting rate on human population,  , by using the
bifurcation analysis. For further investigation, we first formulated the malaria transmission model into
a non-dimensionalized equation. Next, we employed the stability analysis of disease-free equilibrium
and endemic equilibrium point of malaria transmission. Using the same non-dimensionalized
equation, the one-parameter bifurcation analysis was conducted. A few graphs of the bifurcation
diagram, phase plane and time series plot are displayed with the help of mathematical software such
as XPPAUT, Maple, and Matlab. Findings reveal that a transcritical bifurcation occurred due to
changes in the stability of the system’s equilibrium. When the parameter value of  increases, the
infected human and infected mosquito population decreases. This finding demonstrates that changes
in mosquito biting rates could have an effect on both infected humans and mosquito population.