Mathematical Modeling Of The Dynamics Of Malaria And Its Transmission With Treatment

Abstract

Malaria is a deadly disease transmitted to human through the bite of infected female mosquitoes. It can also be transmitted through blood transfusion from infected mother (congenitally). In this thesis we developed a mathematical model which describes the dynamics of malaria transmission with treatment based on SIRS-SI frame work,using the system of ordinary differential equations(ODE).In addition we derive a conditions for the existence of equilibrium points of the model and investigate their stability.Our results shows that if the reproduction R0 is less than 1 the disease free equilibrium point is stable, so that the disease dies out.If R0 is greater than 1, then the disease free equilibrium point is unstable.In this the endemic state has unique equilibrium and the disease persists within the human population.A qualitative study based on bifurcation theory reveals that backward bifurcation may occur. The stable disease free equilibrium of the model coexists with the stable endemic equilibrium when the basic reproduction number is less than one.Numerical simulations were carried out using Matlab to support our analytical solutions.And these simulations show that how treatment affect the dynamics of human and mosquito population.