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In order to study the effect of nonlinear perturbation on virus infection of target cells, in this paper, we propose a stochastic virus infection model with multitarget cells and exposed state. Firstly, by constructing novel stochastic Lyapunov functions, we theoretically prove that the solution of the stochastic model is positive and global. Secondly, we obtain the existence and uniqueness of an ergodic stationary distribution of the stochastic system and the exact expression of probability density function around a quasi-endemic equilibrium if R s > 1 , and we establish a sufficient condition R e < 1 for the extinction of infected cells and virus. Finally, we present examples and numerical simulations to verify our theoretical results. [ABSTRACT FROM AUTHOR]

• We propose a stochastic delayed SIS epidemic model with vaccination and double diseases which make the research more difficult. • We establish sufficient conditions for extinction and persistence in the mean of the two diseases. • We obtain the threshold between persistence in the mean and extinction of the stochastic system. • Time delay and environmental white noise have important effects on the persistence and extinction of the two diseases. • We give the survival analysis of the two diseases under appropriate conditions. In this paper, we investigate the threshold dynamics of a stochastic delayed SIS epidemic model with vaccination and double diseases which make the research more difficult. We establish sufficient conditions for extinction and persistence in the mean of the two diseases. We also obtain the threshold between persistence in the mean and extinction of the stochastic system. It is shown that: (i) time delay and environmental white noise have important effects on the persistence and extinction of the two diseases; (ii) the two diseases can coexist under certain conditions. Finally, some numerical simulations are provided to demonstrate the analytical results. [ABSTRACT FROM AUTHOR]