论文信息 - Stochastic SIR model with jumps

Stochastic SIR model with jumps

Abstract People have always attached importance to the prevention and the control of the epidemic disease. The study of the epidemic model provides us a powerful tool. Unfortunately the previous model cannot be applied to massive diseases, such as avian influenza. Therefore we need to revise the model. In this paper, we take the lead in using the stochastic differential equation with jumps to study the asymptotic behavior of the stochastic SIR model.

Ke Wang | Xianghua Zhang | Ke Wang | Xianghua Zhang

[1] C. Yuan,et al. Stochastic Population Dynamics Driven by Levy Noise , 2011, 1105.1174.

[2] W. O. Kermack,et al. A contribution to the mathematical theory of epidemics , 1927 .

[3] Feng Zhang,et al. Global stability of an SIR epidemic model with constant infectious period , 2008, Appl. Math. Comput..

[4] W. O. Kermack,et al. Contributions to the mathematical theory of epidemics—I , 1991, Bulletin of mathematical biology.

[5] Jean M. Tchuenche,et al. Global behaviour of an SIR epidemic model with time delay , 2007 .

[6] Zhidong Teng,et al. Permanence and extinction for a nonautonomous SIRS epidemic model with time delay , 2009 .

[7] X. Mao,et al. Competitive Lotka–Volterra population dynamics with jumps , 2011, 1102.2163.

[8] X. Mao,et al. Stochastic Differential Equations and Applications , 1998 .

[9] R. May,et al. Population biology of infectious diseases: Part I , 1979, Nature.

[10] Jiajia Yu,et al. Asymptotic behavior of global positive solution to a stochastic SIR model , 2011, Math. Comput. Model..

[11] X. Mao,et al. Environmental Brownian noise suppresses explosions in population dynamics , 2002 .

[12] R. May,et al. Population Biology of Infectious Diseases , 1982, Dahlem Workshop Reports.

[13] R. May,et al. Population biology of infectious diseases: Part II , 1979, Nature.