Mathematical Modeling on Assessing the Impact of Screening on HIV/AIDS Transmission Dynamics

Abstract

Human Immunodeficiency Virus /Acquired Immune Deficiency Syndrome is a globally prevalent and deadly sexually transmitted disease that has had a profound impact on human history, causing widespread fatalities and devastating economic consequences. In this model, we presents a four compartmental class of susceptible S(t), symptomatic infective I(t), asymptomatic infective I(t), and full blown AIDS class model for the transmission dynamics of HIV/AIDS in which we considered the significant role that screening played among those who are symptomatic and asymptomatic infective for the disease control and its management. We determined the positivity and boundedness of the model and the existence of its unique solution which showed clearly that the model is epidemiological meaningful and well posed. The disease-free and endemic equilibrium states were identified, and their stability is analyzed which reveals that if the disease free equilibrium is locally asymptotically stable and unstable if otherwise. Sensitivity analysis was also carried out using normalized forward sensitivity index and result showed that the recruitment rate and transmission rate is the most sensitive parameter. However, its observed from the numerical simulation that the importance of screening is evident in its ability to detect and reduce the number of asymptomatic infective individuals, which in turn leads to an increase among the symptomatic population highlighting the importance of early detection of their status and preventing the spread of HIV/AIDS. The susceptible should also exercise caution to avoid interactions with those who are infectious, further reducing the risk of transmission.

Keywords

• HIV/AIDS; Screening; Basic Reproduction Number; Sensitivity Analysis