Mathematical analysis of malaria transmission model

Abstract

A mathematical analysis of a malaria transmission model was carried out. The model which is a system of five ordinary differential equations is guided by the following assumptions: mosquitoes do not recover from malaria. The rate at which infectious humans enter the recovered group is proportional to the number of infections; a human or mosquito can die naturally at any stage; The number of infected humans increases at a rate which is proportional to the rate of susceptible humans. The existence and uniqueness of the solution of the model were established. The basic reproduction number of the model was calculated and it is less than 1. The stability of the disease-free equilibrium point of the model showed that the model was asymptotically stable indicating that in time malaria disease will completely die out. It was recommended that: the use of active drugs, use of insecticide, use of mosquito bed-treated nets and regular education of the public by the government on malaria would help in controlling the transmission of malaria since there is currently no perfect vaccine against malaria in humans.