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.
