Deterministic models assume that the environment is unvarying and therefore, birth rate, death rate, etc. are constant through time and space. However, any environment is bound to be subject to random fluctuations of one sort or another. Particularly, human immunodeficiency virus interacts with CD4+T cells and immune system within human body where the environment is completely uncertain and stochastic. Therefore, one has to consider the system parameters which characterize populations as random or fluctuating, giving rise to a multidimensional stochastic system of differential equations. Emerging data reveal that aging, nutrition, physical activity and other physiological factors have large impact on viral replication and immune system in HIV infected individuals. Due to these factors, virus replication may vary from 10-2500 virons per cell lysis. Thus, incorporation of fluctuating environment is important to make the model biologically close to realistic and to predict the future dynamics of the system accurately. The main objective of this project is to compare the results of deterministic system with its stochastic counter part and to verify whether introduction of noise modifies the deterministic stability threshold of the disease-free and endemic equilibrium.
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