Using mathematical model to illustrate the spread of malaria

Abstract

We present an ordinary differential equation mathematical model for the spread of malaria in human and Mosquito populations.Susceptible humans can be infected when they are bitten by an infectious Mosquito.They then progress through the infectious and asymptomatic classes, before re-entering the susceptible class.Susceptible Mosquitoes can become infected when they bite infectious and asymptomatic humans, and once infected they move through infectious class. The basic reproduction number is established and used to determine whether the disease dies out or persists in the population. We show that given R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out and ifR0> 1, there exists a unique endemic equilibrium which is globally stable and the disease persists.