Extinction and Stationary Distribution of a Stochastic SIR Epidemic Model with Jumps

A stochastic susceptible-infective-recovered （ SIR ） epidemic model with jumps was considered. The contributions of this paper are as follows. （ 1 ） The stochastic differential equation （SDE） associated with the model has a unique global positive solution; （2） the results reveal that the solution of...

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Bibliographic Details
Published in东华大学学报（英文版） Vol. 33; no. 6; pp. 843 - 850
Main Author 朱敏 李俊平 朱永祥
Format Journal Article
LanguageEnglish
Published School of Mathematics and Statistics, Central South University, Changsha 410085, China 2016
College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China%School of Mathematics and Statistics, Central South University, Changsha 410085, China%College of Traffic Engineering, Hunan University of Technology, Zhuzhou 412007, China
Subjects
susceptible-infective-recovered (SIR) epidemic model
Feller
jumps
stationary distribution
extinction
stochastically ultimately bounded
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ISSN1672-5220

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Summary:A stochastic susceptible-infective-recovered （ SIR ） epidemic model with jumps was considered. The contributions of this paper are as follows. （ 1 ） The stochastic differential equation （SDE） associated with the model has a unique global positive solution; （2） the results reveal that the solution of this epidemic model will be stochastically ultimately bounded, and the non-linear SDE admits a unique stationary distribution under certain parametric conditions; （3） the coefficients play an important role in the extinction of the diseases.
Bibliography:ZHU Min , LI Jun-ping , ZHU Yong-xiang（1 School of Mathematics and Statistics, Central South University, Changsha 410085, China 2 College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China 3 College of Traffic Engineering, Hunan University of Technology, Zhuzhou 412007, China）
31-1920/N
A stochastic susceptible-infective-recovered （ SIR ） epidemic model with jumps was considered. The contributions of this paper are as follows. （ 1 ） The stochastic differential equation （SDE） associated with the model has a unique global positive solution; （2） the results reveal that the solution of this epidemic model will be stochastically ultimately bounded, and the non-linear SDE admits a unique stationary distribution under certain parametric conditions; （3） the coefficients play an important role in the extinction of the diseases.
susceptible-infective-recovered （SIR） epidemic model; stochastically ultimately bounded; Feller; stationary distribution; extinction; lumps
ISSN:1672-5220