Dynamics of a kind of stochastic SIRS models with two different nonlinear incidences

• Main Authors: Jiabing Huang, Nantian Huang, Yuming Wei, Yongjian Liu
• Format: Article
• Language: English
• Published: SAGE Publishing 2019-04-01
• Series: Advances in Mechanical Engineering
• Online Access: https://doi.org/10.1177/1687814019842497

A new kind of stochastic SIRS models with two different nonlinear incidences are extended. The obtained results can be expressed in two dimensions. In mathematics, the threshold values R 1 s and R 2 s which ensure permanent or extinct disease are presented, respectively. More concretely, when R i s > 1 ( i = 1 , 2 ) , the two diseases are persistence in mean. When R i s < 1 or R i s > 1 ( i = 1 , 2 ) , the two diseases will either be extinct or be permanent, respectively. What’s more interesting is the numerical results which show that the two diseases go to extinction at a large time, when R 1 s = 1 and R 2 s = 1 . Furthermore, the sufficient conditions for the diseases that are extinct and permanent are given. In addition, the stochastic boundedness of the model is investigated. Epidemiologically, we can conclude that large noise fluctuations can effectively prevent the outbreak of disease, which can supply us beneficial methods to control the spreading of two diseases. Finally, a few numerical simulations are presented to demonstrate and verify the findings obtained.