HIV/AIDS model, a case study of Tigania west, Kenya

Abstract

HIV/AIDS is a disease caused by Human Immunodeficiency Virus. It has no cure but medication prolong the life of the infected. This research develops a deterministic model of HIV/AIDS. The analysis of the model include positivity and boundedness of the solutions, local and global stability of the disease free equilibrium, existence of equilibrium points, stability of the endemic equilibrium point and the sensitivity of the model with respect to the treatment. The control reproduction number represents the expected number of secondary infection HIV/AIDS infections produced by a single HIV/AIDS infected individuals in a completely susceptible population in the presence of treatment. The analysis shows that the model exist a stable disease free equilibrium point when < 1.. Simulation is performed using data from Tigania West Sub County hospital. The sensitivity analysis shows that treatment does not reduce HIV/AIDS from the population but reduces the mortality rate caused by the HIV/AIDS related illnesses.