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Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A class of stochastic SIRS infectious disease models with both logistic birth and Markov switching were investigated. The uniqueness of the existence of a globally positive solution to the stochastic infectious disease model was first analyzed through construction of suitable V functions and then by means of Itô’s formula. Afterwards, the results of the existence of an ergodic smooth distribution for the solution of the model and the sufficient conditions for the extinction of the disease were discussed. Finally, numerical examples were given to illustrate the conclusions. [ABSTRACT FROM AUTHOR]

A stochastic SIQR epidemic model with non-monotonic transmission rate is formulated. The exist ence and uniqueness of global solution to the model are obtained by using the stopping time theory. By using the Liapunov function method and the Ito's formula,the oscillation behavior of the solutions of the stochastic model near the disease-free equilibrium point of the corresponding deterministic model is discussed. Sufficient conditions for the extinction and the existence of a unique stationary distribution are obtained. Finally, the numerical simulations results show the difference of asymptotic behavior between the model solution and the corresponding deterministic model solution. [ABSTRACT FROM AUTHOR]