Author(s)

Yiting Lu¹, Wenwen Wang^2*, Hui Chen¹, Yuming Yan¹, Xiaoliang Zhou¹

¹School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, China.
²Zhanjiang Mechanical and Electrical School, Zhanjiang, China.

In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.

SIR Epidemic Model, Ito Formula, Extinction, Persistence in the Mean Sense

Lu, Y. , Wang, W. , Chen, H. , Yan, Y. and Zhou, X. (2022) Study on the Dynamics of an SIR Epidemic Model with Saturated Growth Rate. Journal of Applied Mathematics and Physics, 10, 2164-2174. doi: 10.4236/jamp.2022.107148.