Analysis of a malaria model with two infectious classes

Abstract

In this paper we study a deterministic differential equation model for the spread and control of malaria, which involve two infectious classes. We derived the conditions for disease free and endemic equilibria. A comparison of this model and three other models is made and tables of ranges of parameter values are established. The main results shows that a simplifed NDM-system has a unique endemic equilibrium for certain values of the ratio of mosquito to human population, which is always a global attractor. Otherwise, there is no endemic equilibrium and the disease-free equilibrium is a global attractor. When the ratio of mosquito to human population changes the endemic equilibrium changes and forms a curve Ce in the phase space parameterized by this ratio. For a certain range of the rate of human population entering the susceptible class (either by birth or migration) the original NDM-system has an equilibrium on the curve Ce. This equilibrium is a saddle with a four dimensional stable and one dimensional unstable manifold. The unstable manifold is well approximated by this curve