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

Stability Analysis of a Stochastic Viral Infection Model with General Infection Rate and General Perturbation Terms

Discontinuity, Nonlinearity, and Complexity 8(3) (2019) 313--323 | DOI:10.5890/DNC.2019.09.007

Marouane Mahrouf$^{1}$, Khalid Hattaf$^{1}$,$^{2}$, Noura Yousfi$^{1}$

$^{1}$ 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

Abstract

In this paper, we propose a stochastic viral infection model with general incidence rate. In the proposed model, the stochastic perturbations are modeled by general functions. Further, the global existence and positivity of solutions are investigated. In addition, the stochastic stability of the model is established by using the direct Lyapunov method. Finally, an application of the hepatitis B virus (HBV) is given to validate our theoretical results.

Acknowledgments

We would like to express our gratitude to the editor and the two anonymous reviewers for their constructive comments and suggestions, which helped to enrich this paper.

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