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 R0 is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable if R0≤1, and the system is uniformly persistence if R0>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.