Mathemaical Model of Malaria Transmission Dynamics with Treatment

Abstract

In This Thesis, A Sixth Dimensional System Of Non-Linear Ordinary Di??�Erential Equation Is Formulated To Describes The Dynamics Of Malaria Transmission With Treatment. The Model Is Analyzed For Disease Free And Endemic Equilibrium Point. We De???Ne The Reproduction Number Interms Of Parameters. It Shows That If The Reproduction Number R0 < 1, Then The Disease Free Equilibrium Point Is Locally Asymptotically Stable So That The Disease Dies Out After Some Period Of Time. In Addition We Showed That If An Appropriate Treatment Is Given For Infectious Human At The Condition Of Number Of Reproduction R0 ???Pq1q2 Nm , Where Q1 Recruitment Rate Of Human Per Death Rate Of Human And Q2 Is Recruitment Rate Of Mosquito Per Death Rate Of Mosquito Then The Disease Free Equilibrium Point Is Globally Asymptotically Stable So That Disease Dies Out In Short Period Of Time. We Also Established That When R0 > 1, Then The Endemic Equilibrium Point Is Locally Asymptotically Stable. We Supplemented The Analytical Solution By Numerical Simulation Using Matlab Code With Appropriate And Biologically Meaningful Parameter Values.