Complex dynamics in a stochastic internal HIV model

Highlights: → We establish a connecting thread through the Hale's reduction approach for the delay stochastic internal HIV model. → We prove that time delays or noise cause the equilibrium to lose or gain stability and Hopf bifurcation occurs. → Some new criteria ensuring stochastic stability and bifurcation for stochastic internal HIV model with delay are obtained. - Abstract: In this paper, we analyze a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modeling. By analyzing the Lyapunov exponent, singular boundary and probability density, some new criteria ensuring stochastic stability, D-bifurcation and P-bifurcation for stochastic internal HIV model are obtained, respectively. Numerical simulation results are given to support the theoretical predictions.