Stationary distribution of a delayed HIV/AIDS epidemic model with vertical transmission and environmental fluctuations

Abstract

In this work we look at the dynamics of HIV/AIDS model with discrete delay influenced by stochastic perturbation. We prove the positivity of unique global solution of the underlying perturbed system. Furthermore, we set a threshold value R^d_e for the delay model with perturbation which is higher than basic reproduction rate of underlying non-perturbed model. We derive the necessary condition for the disease’s eradication and we also establish a threshold value R^d_p which governs the presence of a unique stationary distribution. Our results demonstrate that the time delay and stochastic perturbation serve as crucial for reducing disease spread. When the noise is really high, the disease dies off and there are periodic outbreaks due to time delay. Numerical simulations corroborated our analytical findings.