Stability Analysis for Stochastic Differential Equations in Virology
Marouane Mahrouf *
Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
El Mehdi Lotfi
Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
Mehdi Maziane
Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
Khalid Hattaf
Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco and Centre Régional des Métiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.
Noura Yousfi
Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we propose a viral infection model governed by three stochastic differential equations. The global existence and positivity of solutions is investigated. Further, we give sufficient conditions for the stability in probability of the endemic equilibrium by using the direct Lyapunov method. Moreover, an application and numerical simulations are given to illustrate our theoretical results.
Keywords: Viral infection, stochastic differential equations (SDEs), general incidence rate, mean square stability, stability in probability