Stability of a Mathematical Model of Malaria Transmission with Relapse

Abstract

A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction number $R_0$ is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable if $R_0\le 1$, and the system is uniformly persistence if $R_0>1$. Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.