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

被引：20

作者：

Lin, Yuguo ^{[1
]}

Jiang, Daqing ^{[2
]}

Jin, Manli ^{[1
]}

机构：

[1] Beihua Univ, Sch Math & Stat, Jilin 132013, Peoples R China

[2] China Univ Petr East China, Coll Sci, Qingdao 266580, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2015年 / 35卷 / 03期

关键词：

Diffusion process; Markov semigroups; asymptotic stability; EPIDEMIC MODEL; DYNAMICS;

D O I：

10.1016/S0252-9602(15)30008-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 L-1 to an invariant density.

引用

页码：619 / 629

页数：11

共 20 条

[1] ANDERSON R M, 1991
[2] POPULATION BIOLOGY OF INFECTIOUS-DISEASES .1.
ANDERSON, RM
MAY, RM
[J]. NATURE, 1979, 280 (5721) : 361 - 367
[3] [Anonymous], 2006, Can. Appl. Math. Q., DOI DOI 10.1016/J.CAMWA.2010.08.020
[4] Bell DenisR., 2006, MALLIAVIN CALCULUS
[5] BENAROUS G, 1991, PROBAB THEORY REL, V90, P377
[6] Global asymptotic stability of an SIR epidemic model with distributed time delay
Beretta, E
Hara, T
Ma, WB
Takeuchi, Y
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (06) : 4107 - 4115
[7] BROWN GC, 1995, J INVERTEBR PATHOL, V65, P10, DOI 10.1006/jipa.1995.1002
[8] GENERALIZATION OF THE KERMACK-MCKENDRICK DETERMINISTIC EPIDEMIC MODEL
CAPASSO, V
SERIO, G
[J]. MATHEMATICAL BIOSCIENCES, 1978, 42 (1-2) : 43 - 61
[9] The mathematics of infectious diseases
Hethcote, HW
[J]. SIAM REVIEW, 2000, 42 (04) : 599 - 653
[10] Contribution to the mathematical theory of epidemics
Kermack, WO
McKendrick, AG
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1927, 115 (772) : 700 - 721

← 1 2 →