MATHEMATICAL MODELING OF HIV-AIDS USING STOCHASTIC DIFFERENTIAL EQUATIONS IN DIRE DAWA AND HARER

Abstract

The human immunodeficiency virus (HIV) is a retrovirus that causes HIV infection and over time it becomes acquired immunodeficiency syndrome (AIDS). In this thesis we developed a mathematical model of the human immunodeficiency virus (HIV) transmission dynamics. The developed deterministic model is extended into a stochastic by incorporating the effect of fluctuating environment. The model divides the total population into four epidemiological classes depending on their disease status like, susceptible individuals, infected individuals, AIDS class, and ART treatment individuals. Firstly, we analyzed the qualitative behavior of the model like; the invariant region, the positivity of the solution, equilibrium point, basic reproductive number, the sensitivity of the analyzed basic parameter, local stability of the equilibrium point. Stochastic model is closer to the real when we compare to deterministic model. If the basic reproductive number is less one then the disease eradicated from the population and the basic reproductive number greater than one the disease persist from the population. We can reduce the disease transmission by initiating the people to take ART medicines correctly. Finally we performed numerical simulation for both deterministic and stochastic models. From the numerical simulation, we investigated the effect of some basic parameters on the control of the disease like rate of change of HIV-AIDS clinical symptom class(I(t)) to ART treatment class(T(t)), the treatment rate of HIV-infected individual with AIDS symptom, the rate of HIV-infected individual with no AIDS clinical symptom that does not take ART treatment goes to AIDS class D, the rate HIV-infected individual under ART treatment changes to HIV-infected individual with no clinical symptom, the rate of newborn children are infected during birth by the virus and, the rate of the fluctuating environment