A mathematical model for malaria involving differential susceptibility,exposedness and infectivity of human host

The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called “non-immune” comprising all humans who have never acquired immunity against malaria and the second type is called “semi-immune”. Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R ₀ which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R _0a , and the weight of the transmission non-immune-mosquito-non-immune, R _0e . Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R ₀ crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes.