Abstract:
Malaria is an infectious disease caused by the Plasmodium parasite and transmitted between humans through bites of female anopheles mosquito. In this thesis, we present
an ordinary differential equation mathematical model in order to investigate the effect of
immigration of susceptible human and contact rates (contact rates of infected human to
susceptible mosquito and infected mosquito to susceptible human ) in the transmission of
malaria in human and mosquito populations. We develop a dimension less malaria transmission model by introducing some dimensionless parameters.And then we perform the
stability analysis of the model and the basic reproduction number was determined by using
the next generation matrix approach.We have proved that the Diseases Free equilibrium
point is locally asymptotically stable if R0 < 1 and unstable when R0 > 1. Global stability
of the DFE point is also performed by using the concept of Lyapunov Function and Invariance Principle(that is DFE point Global asymptotically stability if R0 ≤ 1). We also
proved that the endemic equilibrium point is locally asymptotically stable if R0 > 1 and
unstable when R0 < 1. Numerical simulation have been done by applying the mathematical
soft ware MATLAB. These numerical simulations shows that immigration of susceptible
human and contact rates have significant effect in the transmission of malaria in human
and mosquito populations.
