Dynamics of a stochastic and periodic virus model with Beddington-DeAngelis functional response

We consider a periodic virus model with Beddington-DeAngelis functional responses, which is assumed that not only the death rate of the uninfected, the infected CD4 \(^{+}\) $_{}^{+}$ T cells but also the removed rate of HIV-1 virus particles are influenced by white noises. With the helps of Itô’s formula and Has’minskii theory for periodic solution, and by constructing some crucial functions we discuss the extinction of the virus. Moreover, the existence of the uninfected periodic solution and the infected periodic solution are investigated. At last, we analyze the influence of noises and illustrate our results by numerical simulations.