Abstract
The dynamical behavior of a perturbed Human Immunodeficiency Virus (HIV)
model is investigated in this paper. We first determine a positively
invariant set in which the perturbed system admits a unique, positive,
global solution. Following that, we discuss the stability of
infection-free equilibrium of the deterministic model. We also obtain
the conditions required for the p th -moment
exponential stability, for the perturbed system. Later we show that if
R0 >1 for smaller intensity of noise, the
solution of stochastic system oscillates around E*.
Our results demonstrate that a large value of noise suppresses the
disease from persistence exponentially. We also derive the condition for
the persistence of the disease. Finally, comparison of our analytical
results with simulations is to be done.