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.
Highlights
Full Length Research PaperThis paper examines the combined effects of screening and variable inflow of infective immigrants on the spread of HIV/acquired immunodeficiency syndrome (AIDS) (human immunodeficiency virus/acquired immune deficiency syndrome) in a population of varying size
The acquired immunodeficiency syndrome (AIDS) emerged in 1981 and has become an important sexuality transmitted disease throughout the world
This paper examines the combined effects of screening and variable inflow of infective immigrants on the spread of HIV/AIDS in a population of varying size
Summary
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. 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
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