Periodic solutions of a periodic stochastic human immunodeficiency virus model with distributed delay and cytotoxic T lymphocytes immune response

In this paper, a periodic stochastic human immunodeficiency virus (HIV) model with distributed delay and cytotoxic T lymphocytes (CTL) immune response is investigated. First, by It 's formula, we show that the solution with any positive initial value is global and positive. Then, by the stochastic comparison theorem, we obtain the sufficient conditions guaranteeing the existence and global attractivity of infection-free periodic solution. Furthermore, we discuss the existence of the infective periodic solution by Has'minskii theory. Finally, numerical examples are given to illustrate the results.