Asymptotic Behavior Analysis and Threshold Sharpening of a Staged Progression AIDS/HIV Epidemic Model with Lévy Jumps - Kiouach, Driss; El-idrissi, Salim El Azami; Sabbar, Yassine (Discontinuity, Nonlinearity, and Complexity, 2026)
In this paper, we present and investigate a generalized stochastic AIDS/HIV epidemic model that includes both Brownian motions and Lévy jumps. Our proposed model is a staged progression compartmental one that takes the form of an Itô-Lévy stochastic differential equations system. First, we demonstrate its well-posedness in the sense that it admits one and only one solution which is positive and global in time. Then, and based on some assumptions and nonstandard analytical techniques, we prove two principal asymptotic properties: extinction and persistence in the mean. The theoretical results show that the dynamical behavior of our AIDS/HIV model is mainly determined by the parameters that are closely related to the perturbations intensities. In the end, we provide some numerical simulation examples to corroborate our theoretical results and exhibit the effect of the new adopted mathematical techniques on the findings.