TITLE:
Study on the Dynamics of an SIR Epidemic Model with Saturated Growth Rate
AUTHORS:
Yiting Lu, Wenwen Wang, Hui Chen, Yuming Yan, Xiaoliang Zhou
KEYWORDS:
SIR Epidemic Model, Ito Formula, Extinction, Persistence in the Mean Sense
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.7,
July
20,
2022
ABSTRACT: 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.