Abstract
The objective of this paper is to present a mathematical model formulated to investigate the dynamics of human immunodeficiency virus (HIV). The disease free equilibrium of the model was found to be locally and globally asymptotically stable. The endemic equilibrium point exists and it was discovered that the endemic equilibrium point is globally asymptotically stable; suggestion was also made in the research in regards to protection during sexual intercourse especially in a sexually active population. Keywords: Analysis, Equilibrium, Stability, Endemicity, Mathematical Model
Highlights
IntroductionThe stages of progression of human immunodeficiency virus (HIV) include; Acute infection which last within two to four weeks after infection
human immunodeficiency virus (HIV) is a virus that spread through body fluids that affects specific cells of the immune system called CD4 cells or T cells
Many of these cells are destroyed and the infection leads to Acquired Immunodeficiency Syndrome (AIDS) (Weiss, 1993)
Summary
The stages of progression of HIV include; Acute infection which last within two to four weeks after infection During this period, one may feel flu-like symptoms called acute retroviral syndrome (ARS) or primary HIV infection (CDC, 2015). One has the highest likelihood to spread HIV at this stage due to the amount of viral load in the blood After this period, the immune system begins to build up again but it may not return to pre infection levels (CDC, 2015). Clinical latency (inactivity or dormancy) sometimes called the asymptomatic HIV infection At this stage, the viruses reproduce but at very low levels, there may be no symptoms which can last up to a decade. A mathematical model is formulated and analysed to investigate the transmission pattern of HIV in a sexually active population in order to understand and transmission
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