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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Asymptotic Behavior Analysis and Threshold Sharpening of a Staged Progression AIDS/HIV Epidemic Model with L'{e}vy Jumps

Discontinuity, Nonlinearity, and Complexity 12(3) (2023) 583--613 | DOI:10.5890/DNC.2023.09.008

Driss Kiouach, Salim El Azami El-idrissi, Yassine Sabbar

Mathematics Department, Faculty of Sciences Dhar Al Mahraz, Sidi Mohammed Ben Abdellah University, P.O. Box 1796, Fez-Atlas, 30003 Fez, Morocco

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Abstract

In this paper, we present and investigate a generalized stochastic AIDS/HIV epidemic model that includes both Brownian motions and L\'{e}vy jumps. Our proposed model is a staged progression compartmental one that takes the form of an It\^{o}-L\'{e}vy 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.

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