A mathematical model to study the impact of irresponsible infective immigrants and vertical transmission on the dynamics of HIV/AIDS

Abstract

This paper examined the combined effects of irresponsible infective immigrants and vertical transmission in a varying population. A mathematical model for the problem was proposed and transformed into proportions in order to define the prevalence of infection. Using the next-generation method, the basic reproduction number  was computed in terms of the parameters of the transformed model. The disease free equilibrium was obtained and found to be locally asymptotically stable when  and unstable for  . By the method of the centre manifold theory, the existence of transcritical bifurcation was investigated. The study ascertained that forward bifurcation existed if certain conditions were met. Numerical simulation of the model was carried out to assess the effect of irresponsible HIV infective immigrants and vertical transmission in the spread of HIV/AIDS disease. The result showed that screening and counselling the irresponsible HIV infective immigrants will help to reduce the spread of HIV and prevent MTCT.