Mathematical Modeling and Analysis of Malaria Transmission Dynamics Incorporating Environmental Contamination

Abstract

Malaria is one of the main public health problems in Ethiopia. This inspires an urgent need of conducting a comprehensive study as input for policy makers and future preparation to mitigate malaria in the country and the region. Mathematical modeling of infectious diseases helped humankind to understand transmission speed and forecast disease outbreaks. Bearing in mind these points, in this thesis, mathematical model of malaria transmission was formulated based on compartmental model approach. The findings of this thesis encompass the following points. Existence of unique solution of the model was proved. Boundedness and positivity of the model were proved. Basic reproduction number was also calculated by using next generation matrix. The local stability conditions of disease free and endemic equilibrium points were also well investigated by the using Routh Hurwitz stability criteria. Particularly, disease free equilibrium point is unstable in the presence of contaminated environment. The endemic equilibrium point is locally asymptotically stable provided that basic reproduction number is greater than one. It is proved that endemic equilibrium point is also globally stable with some conditions by using Lyapunov method. Furthermore, sensitivity analysis of the model parameters was also carried out using Normalized forward sensitivity index. Finally, in order to verify the applicability of the result, MATLAB simulation was implemented and agrees with the analytical result.