Abstract

This paper examines the combined effects of screening and variable inflow of infective immigrants on the spread of HIV/AIDS (human immunodeficiency virus/acquired immune deficiency syndrome) in a population of varying size. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. The results show that the reproductive number R₀ >1 as the rate of inflow of infective immigrants increases leading to persistence of the disease in the population. However, the presence of screening greatly reduces the spread of HIV/AIDS.Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.

Key words: Human immunodeficiency virus/acquired immune deficiency syndrome, screening, infective immigrants, reproductive number, stability analysis, numerical simulation.