Analysis of a malaria model with two infectious classes

摘要

Inthis paper we study a deterministic differential equation model for thespread and control of malaria, which involve two infectious classes. Wederived the conditions for disease free and endemic equilibria. A comparisonof this model and three other models is made and tables of rangesof parameter values are established. Themain results shows that a simplified NDM-system has a unique endemicequilibrium for certain values of the ratio of mosquito to human population,which is always a global attractor. Otherwise, there isno endemic equilibrium and the disease-free equilibrium is a global attractor.When the ratio of mosquito to human population changes the endemicequilibrium changes and forms a curve Ce in the phase space parameterizedby this ratio. For a certain range of the rate of human population entering thesusceptible class (either by birth or migration) the original NDM-system has anequilibrium on the curve Ce. This equilibriumis a saddle with a four dimensional stable and one dimensional unstablemanifold. The unstable manifold is well approximated by this curve.