The Mathematical Analysis of Malaria Transmission: The effect of Sanitation

A deterministic mathematical model for malaria is considered under different level of sanitation strategy. The malaria disease free equilibrium point is locally asymptotically stable when the reproduction number is less than unity and unstable when reproduction number is greater than unity. The Comparison theorem is used to establish the global stability of the disease free equilibrium. A bifurcation analysis of the model was performed by applying the Centre manifold theory. Sensitivity indices of the basic reproductive number R_m to the parameters in the model was calculated. The study reveals that increase in sanitation level results in decrease in number of mosquito bites and transmission rate of malaria. To illustrate the analytical results, numerical simulations using a set parameter values were provided.