Asymptotic behavior of a multigroup SIS epidemic model with stochastic perturbation

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• 作者：Jing Fu (1)
  Qixing Han (1) (2)
  Yuguo Lin (2) (3)
  Daqing Jiang (2) (4)
  
  1. School of Mathematics ; Changchun Normal University ; Changchun ; 130032 ; China
  2. School of Mathematics and Statistics ; Northeast Normal University ; Changchun ; 130024 ; China
  3. School of Mathematics and Statistics ; Beihua University ; Jilin ; 132013 ; China
  4. College of Science ; China University of Petroleum (East China) ; Qingdao ; 266580 ; China
  
• 关键词：60H10 ; 93E15 ; 34E10 ; stochastic SIS model ; extinction ; stationary distribution ; ergodicity
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,048 KB
• 参考文献：1. Beretta, E, Capasso, V Global stability results for a multigroup SIR epidemic model. In: Hallam, TG, Gross, LJ, Levin, SA eds. (1986) Mathematical Ecology. World Scientific, Singapore, pp. 317-342
  2. Feng, Z, Huang, W, Castillo-Chavez, C (2005) Global behavior of a multi-group SIS epidemic model with age structure. J.聽Differ. Equ. 218: pp. 292-324 CrossRef
  3. Guo, H, Li, MY, Shuai, Z (2006) Global stability of the endemic equilibrium of multigroup SIR epidemic models. Can. Appl. Math. Q. 14: pp. 259-284
  4. Guo, H, Li, MY, Shuai, Z (2008) A graph-theoretic approach to the method of global Lyapunov functions. Proc. Am. Math. Soc. 136: pp. 2793-2802 CrossRef
  5. Hethcote, HW (1978) An immunization model for a heterogeneous population. Theor. Popul. Biol. 14: pp. 338-349 CrossRef
  6. Huang, W, Cooke, KL, Castillo-Chavez, C (1992) Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appl. Math. 52: pp. 835-854 CrossRef
  7. Koide, C, Seno, H (1996) Sex ratio features of two-group SIR model for asymmetric transmission of heterosexual disease. Math. Comput. Model. 23: pp. 67-91 CrossRef
  8. Li, MY, Shuai, Z (2010) Global-stability problem for coupled systems of differential equations on networks. J. Differ. Equ. 248: pp. 1-20 CrossRef
  9. Sun, R (2010) Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence. Comput. Math. Appl. 60: pp. 2286-2291 CrossRef
  10. Yuan, Z, Wang, L (2010) Global stability of epidemiological models with group mixing and nonlinear incidence rates. Nonlinear Anal., Real World Appl. 11: pp. 995-1004 CrossRef
  11. Yuan, Z, Zou, X (2010) Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population. Nonlinear Anal., Real World Appl. 11: pp. 3479-3490 CrossRef
  12. Lajmanovich, A, Yorke, JA (1976) A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28: pp. 221-236 CrossRef
  13. Cornelius, CE (1971) Seasonality of gonorrhea in the United States. H.S.M.H.A. Health Rep. 86: pp. 157-160
  14. Gray, A, Greenhalgh, D, Hu, L, Mao, X, Pan, J (2011) A stochastic differential equation SIS epidemic model. SIAM J. Appl. Math. 71: pp. 876-902 CrossRef
  15. Hasminskii, RZ (1980) Stochastic Stability of Differential Equations. Sijthoff & Noordhoff, Alphen aan den Rijn CrossRef
  16. Berman, A, Plemmons, RJ (1979) Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York
  17. Mao, X (1997) Stochastic Differential Equations and Applications. Horwood, Chichester
  18. Gard, TC (1988) Introduction to Stochastic Differential Equations. Dekker, New York
  19. Zhu, C, Yin, G (2007) Asymptotic properties of hybrid diffusion systems. SIAM J. Control Optim. 46: pp. 1155-1179 CrossRef
  20. Malinowski, M (2013) Some properties of strong solutions to stochastic fuzzy differential equations. Inf. Sci. 252: pp. 62-80 CrossRef
  21. Malinowski, M, Agarwal, R (2014) On solutions to set-valued and fuzzy stochastic differential equations. J. Franklin Inst..
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, we introduce stochasticity into a multigroup SIS model. We present the sufficient condition for the exponential extinction of the disease and prove that the noises significantly raise the threshold of a deterministic system. In the case of persistence, we prove that there exists an invariant distribution which is ergodic.