数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (3): 619-629.doi: 10.1016/S0252-9602(15)30008-4

• 论文 • 上一篇    下一篇

STATIONARY DISTRIBUTION OF A STOCHASTIC SIR MODEL WITH SATURATED INCIDENCE AND ITS ASYMPTOTIC STABILITY

林玉国1, 蒋达清2, 靳曼莉3   

  1. 1. School of Mathematics and Statistics, Beihua University, Jilin 132013, China;
    2. College of Science, China University of Petroleum(East China), Qingdao 266580, China;
    3. School of Mathematics and Statistics, Beihua University, Jilin 132013, China
  • 收稿日期:2014-02-27 修回日期:2014-10-08 出版日期:2015-05-01 发布日期:2015-05-01
  • 基金资助:

    The work was supported by Program for Changjiang Scholars and Innovative Research Team in University, NSFC of China (11371085 and 11201008), and the Ph.D. Programs Foundation of Ministry of China (200918).

STATIONARY DISTRIBUTION OF A STOCHASTIC SIR MODEL WITH SATURATED INCIDENCE AND ITS ASYMPTOTIC STABILITY

Yuguo LIN1, Daqing JIANG2, Manli JIN3   

  1. 1. School of Mathematics and Statistics, Beihua University, Jilin 132013, China;
    2. College of Science, China University of Petroleum(East China), Qingdao 266580, China;
    3. School of Mathematics and Statistics, Beihua University, Jilin 132013, China
  • Received:2014-02-27 Revised:2014-10-08 Online:2015-05-01 Published:2015-05-01
  • Supported by:

    The work was supported by Program for Changjiang Scholars and Innovative Research Team in University, NSFC of China (11371085 and 11201008), and the Ph.D. Programs Foundation of Ministry of China (200918).

摘要:

In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.

关键词: Diffusion process, Markov semigroups, asymptotic stability

Abstract:

In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.

Key words: Diffusion process, Markov semigroups, asymptotic stability

中图分类号: 

  • 47D07