| Issue |
Math. Model. Nat. Phenom.
Volume 12, Number 5, 2017
Mathematical models in physiology
|
|
|---|---|---|
| Page(s) | 15 - 32 | |
| DOI | https://doi.org/10.1051/mmnp/201712502 | |
| Published online | 13 October 2017 | |
Dynamics of a Stochastic Viral Infection Model with Immune Response
1
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco
2
Centre Régional des Métiers de l'Education et de la Formation (CRMEF) 20340 Derb Ghalef, Casablanca, Morocco
* Corresponding author. E-mail: k.hattaf@yahoo.fr
The aim of this work is to study the dynamical behavior of a stochastic viral infection model which is formulated by four nonlinear stochastic differential equations to describe the interactions between virus, host cells, and immune response represented by cytotoxic T lymphocytes (CTL) cells. The infection transmission process is modeled by Hattaf-Yousfi incidence function which includes many special cases existing in the literature. The positivity of solutions is investigated. In addition, the extinction of the infection is established in terms of the basic reproduction number R0. Moreover, sufficient conditions for the fluctuation of solutions around the two infection equilibria are obtained. Numerical simulations are presented to illustrate our theoretical results.
Mathematics Subject Classification: 60H10 / 60H30 / 92B05 / 93E15
Key words: Viral infection / immune response / stochastic differential equations / nonlinear incidence / stability
© EDP Sciences, 2017
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