Mathematical analysis of malaria transmission model with infective immigrants

Abstract

In this thesis, we developed an SEIR - SEI model of malaria transmission with the inclusion of susceptible, exposed and infected immigrants. Analysis of the model were carried out to find the equilibrium points and their stabilities. We have discovered that our model has no disease-free and hence no basic reproduction number ℜ0 due to the influx of exposed and infected immigrants. However, when the proportions of exposed and infected immigrants approaches zero, disease-free status will be attained whenever ℜ0 < 1. The unique endemic equilibrium point for which there are exposed and infected immigrants is both locally and globally stable. Numerical simulations were performed to know the effect of exposed and infected immigrants and the results from our simulations showed that exposed and infected immigrants entering the population rendered the basic reproduction number ℜ0 irrelevant and can not be used to determine the extinction and the prevalence of malaria. Sensitivity analysis was carried out on the parameters that the basic reproduction number ℜ0 depend on. The result from the sensitivity analysis revealed that the most sensitive parameter is the mosquito biting rate ν. We recommended that immigrants should be screened at our borders and be sure of malaria free before allowing them to enter the population to ensure the health and well-being of everyone in the community.