Nonlinear Analysis and Differential Equations, Vol. 4, 2016, no. 9, 435 - 445 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/nade.2016.6642 A Stochastic Viral Infection Model with General Functional Response Marouane Mahrouf a, 1 , El Mehdi Lotfi a , Mehdi Maziane a Khalid Hattaf a,b and Noura Yousfi a a Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955 Sidi Othman, Casablanca, Morocco b Centre R´ egional des M´ etiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco Copyright c  2016 Marouane Mahrouf et al. This article is distributed under the Cre- ative Commons Attribution License, which permits unrestricted use, distribution, and repro- duction in any medium, provided the original work is properly cited. Abstract In this paper, we propose a stochastic viral infection model with general functional response. The well posedness of the proposed model is investigated. Also, the extinction of the infection is fully determined by the basic reproduction number R 0 . Furthermore, the dynamical behavior around the chronic infection equilibrium is established. Finally, Numerical simulations are given to illustrate our theoretical results. Keywords: Viral infection, stochastic differential equations, extinction, Lyapunov functional. 1 Corresponding author