The influence of Lévy noise on the dynamical behavior of a stochastic HIV/AIDS model with vertical transmission.

This paper examined the behavior of the HIV/AIDS epidemic stochastic model driven by both White Noise and Lévy jumps. Initially, we demonstrated that the stochastic model under consideration has one and only one positive solution which exists globally. Based on the analytical results on the model, we obtained the threshold parameters which are responsible for the eradication and the permanence of the disease. Finally, we verified our analytical results numerically. [ABSTRACT FROM AUTHOR]