Mathematical Model For The Dynamics And Control Of Malaria

Abstract

In this study a deterministic mathematical model is developed to investigate the spread of malaria. The model has five non-linear differential equations which describe the spread of malaria with three state variables for humans and two state variables for mosquitoes which are Sh, Eh, Ih,Sv and, Iv . Analysis of the model showed that there exists a domain where the model is epidemiolog ically and mathematically well- posed. The existence and stability of disease-free and endemic malaria equilibria are analyzed. The key to the analysis is the definition of the basic reproductive number which was de rived by use of next generation method. The disease-free equilibrium is locally asymptotically stable, if the reproduction number is less than one and globally asymptotically stable, if the reproduction number is greater than one. And the endemic equilibrium exists provided that the basic reproductive number is greater than one. Ordinary differential equations were used to model malaria where humans and mosquitoes interact and infect each other.