Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine.

Two types of stochastic epidemic models are formulated, in which both infectivity in the latent period and household quarantine on the susceptible are incorporated. With the help of Lyapunov functions and Has'minskii's theory, we derive that, for the nonautonomous periodic version with white noises, it owns a positive periodic solution. For the other version with white and telephone noises, we construct stochastic Lyapunov function with regime switching to present easily verifiable sufficient criteria for the existence of ergodic stationary distribution. Also, we introduce a series of numerical simulations to support our analytical findings. At last, a brief discussion of our theoretical results shows that the stochastic perturbations and household quarantine measures can significantly affect both periodicity and stationary distribution.