Mathematical model of Plasmodium Vivax and Plasmodium falciparum malaria

Abstract

Malaria is transmitted to the person by the biting of infectious Anopheles mosquitoes. This infectious disease caused by the parasite genus Plasmodium. Four species of this parasite cause human malaria, namely, Plasmodium vivax, Plasmodium falciparum, Plasmodium ovale and Plasmodium malariae. The difference between P.vivax and P. falciparum is that a person suffering from P. vivax infection can suffer relapses of the disease. This is due the parasite being able to remain dormant in the liver of the cases where it is able to re-infect the case after a passage of time. During this stage, the case is classified as being in the dormant class. The model to describe the transmission between falciparum and vivax malaria consists of a human population divided into four classes, the susceptible, the infectious, the dormant and the recovered classes. The vector population is separated into two classes, the susceptible and infectious classes. We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a basic reproductive number R0 is less than one. If R0 is greater than one, the endemic state E1 is stable. The conditions for the local stability of each equilibrium state are established. The numerical simulations are shown to confirm the results.