ANALYSIS OF A MALARIA DISEASE MODEL WITH DIRECT TRANSMISSION

Many of the contributors to the modeling of malaria have always consider that malaria disease are only transmitted to the human population through infected mosquitoes. However, evidences have shown that direct transmission is possible through blood transmission. Using the idea of Liming Cai and Xuezhi Li, a model for malaria disease with direct transmission is formulated. We showed that our model is mathematically well-posed and has a unique solution. It was shown that the stability of the equilibria in the model can be controlled by a threshold parameter Ro. That is, if ^h> ^m {yhV + 3- )i.e R° >1, the disease can persist in the population, and if ^m^m < Pm {rH + V + 3-lH2)ie Ro <1, the disease-free equilibrium point EO exists and is locally stable. We proved the global stability of our model using the Lyapunov function and showed that the disease-free equilibrium point Eo is globally asymptotically stable when RO <1.. The endemic disease free equilibrium was also established when RO >1