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.
