LAUSR

This paper investigates the dynamics behavior of the mathematical model of Human Immunodeficiency Virus (HIV) influenced by stochastic perturbations. This paper is involved in exploring the disease-free equilibrium’s stochastic global exponential stability with a basic reproductive number $$R_{0} < 1$$ . Necessary and sufficient conditions for stochastic global exponential stability of the disease-free equilibrium $$E^{0}$$ of the nonlinear HIV stochastic system are derived. This can be accomplished by the exponential analysis of the global mean square stability of trivial equilibrium of the corresponding linear system. Finally, we provide areas of stability of $$E^{0}$$ and numerical simulations to confirm the analytical results by using the fundamental Euler–Maruyama (EM) algorithm.