MATHEMATICAL MODELING OF MALARIA TRANSMISSION

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.