Threshold behaviour of a stochastic SIR model

作者: Chunyan Ji , Daqing Jiang

DOI: 10.1016/J.APM.2014.03.037

关键词:

摘要: Abstract In this paper, we investigate the threshold behaviour of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation. When noise is small, show that determines extinction and persistence epidemic. Compared corresponding deterministic system, value affected by white noise, which less than basic reproduction number system. On other hand, obtain large will also suppress to prevail, never happens in These results are illustrated computer simulations.

参考文章(33)
A. Gray, D. Greenhalgh, L. Hu, X. Mao, J. Pan, A Stochastic Differential Equation SIS Epidemic Model Siam Journal on Applied Mathematics. ,vol. 71, pp. 876- 902 ,(2011) , 10.1137/10081856X
Andrea Franceschetti, Andrea Pugliese, Threshold behaviour of a SIR epidemic model with age structure and immigration. Journal of Mathematical Biology. ,vol. 57, pp. 1- 27 ,(2008) , 10.1007/S00285-007-0143-1
Elisabetta Tornatore, Stefania Maria Buccellato, Pasquale Vetro, Stability of a stochastic SIR system Physica A: Statistical Mechanics and its Applications. ,vol. 354, pp. 111- 126 ,(2005) , 10.1016/J.PHYSA.2005.02.057
Margherita Carletti, Mean-square stability of a stochastic model for bacteriophage infection with time delays Bellman Prize in Mathematical Biosciences. ,vol. 210, pp. 395- 414 ,(2007) , 10.1016/J.MBS.2007.05.009
Gul Zaman, Yong Han Kang, Il Hyo Jung, Stability analysis and optimal vaccination of an SIR epidemic model BioSystems. ,vol. 93, pp. 240- 249 ,(2008) , 10.1016/J.BIOSYSTEMS.2008.05.004
Herbert W. Hethcote, P. van den Driessche, An SIS epidemic model with variable population size and a delay Journal of Mathematical Biology. ,vol. 34, pp. 177- 194 ,(1995) , 10.1007/BF00178772
Miljana Jovanović, Marija Krstić, Stochastically perturbed vector-borne disease models with direct transmission Applied Mathematical Modelling. ,vol. 36, pp. 5214- 5228 ,(2012) , 10.1016/J.APM.2011.11.087
Mimmo Iannelli, Mi-Young Kim, Eun-Jae Park, Asymptotic behavior for an SIS epidemic model and its approximation Nonlinear Analysis-theory Methods & Applications. ,vol. 35, pp. 797- 814 ,(1999) , 10.1016/S0362-546X(97)00597-X