The threshold of a stochastic SIS epidemic model with vaccination

Applied Mathematics and Computation

Volumn 243, Issue , 2014, Pages 718-727

  Zhao, Yanan ^a,b,c   Jiang, Daqing ^a,c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b CHANGCHUN UNIVERSITY   (China)

^c CHINA UNIVERSITY OF PETROLEUM   (China)

Author keywords

Extinction; Persistence; SIS VS epidemic model; Threshold

Indexed keywords

EPIDEMIOLOGY; LIGHT EXTINCTION; VACCINES;

EPIDEMIC MODELING; EXTINCTION AND PERSISTENCE; LONG TIME BEHAVIOR; PERSISTENCE; THRESHOLD;

STOCHASTIC SYSTEMS;

EID: 84903978036     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.05.124     Document Type: Article

References (22)

1. F. Chen A susceptible-infected epidemic model with voluntary vaccinations J. Math. Biol. 53 2006 253 272 (Pubitemid 44126176)
2. A. Gray, D. Greenhalgh, L. Hu, X. Mao, and J. Pan A stochastic differential equation SIS epidemic model SIAM J. Appl. Math. 71 2011 876 902
3. S. Gao, H. Ouyang, and J. Nieto Mixed vaccination strategy in SIRS epidemic model with seasonal variability on infection Int. J. Biomath. 4 4 2011 473 491
4. D. Higham An algorithmic introduction to numerical simulation of stochastic differential equations SIAM Rev. 43 2001 525 546 (Pubitemid 32991214)
5. L. Imhof, and S. Walcher Exclusion and persistence in deterministic and stochastic chemostat models J. Differ. Equ. 217 2005 26 53 (Pubitemid 41283325)
6. C. Ji, D. Jiang, and N. Shi Multigroup SIR epidemic model with stochastic perturbation Physica A 390 2011 1747 1762
7. D. Jiang, C. Ji, N. Shi, and J. Yu The long time behavior of DI SIR epidemic model with stochastic perturbation J. Math. Anal. Appl. 372 2010 162 180
8. A. Lahrouz, and L. Omari Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence Stat. Probab. Lett. 83 2013 960 968
9. J. Li, and Z. Ma Global analysis of SIS epidemic models with variable total population size Math. Comput. Model. 39 2004 1231 1242
10. J. Li, and Z. Ma Qualitative analyses of SIS epidemic model with vaccination and varying total population size Math. Comput. Model. 35 2002 1235 1243 (Pubitemid 34623159)
11. X. Liu, and L. Yang Stability analysis of an SEIQV epidemic model with saturated incidence rate Nonlinear Anal.: Real World Appl. 13 6 2012 2671 2679
12. X. Mao, G. Marion, and E. Renshaw Environmental noise suppresses explosion in population dynamics Stochastic Process. Appl. 97 2002 95 110 (Pubitemid 40030718)
13. X. Mao Stochastic Differential Equations and Applications second ed. 2008 Horwood Chichester, UK
14. E. Shim, Z. Feng, M. Martcheva, and C. Castillo-Chavez An age-structured epidemic model for rotavirus with vaccination J. Math. Biol. 53 2006 719 749
15. E. Tornatore, P. Vetro, and S.M. Buccellato SIVR epidemic model with stochastic perturbation Neural Comput. Appl. 24 2 2014 309 315
16. E. Tornatore, S. Buccellato, and P. Vetro Stability of a stochastic SIR system Physica A 354 2005 111 126 (Pubitemid 40752463)
17. R. Xu Global stability of a delayed epidemic model with latent period and vaccination strategy Appl. Math. Model. 36 11 2012 5293 5300
18. J. Yu, D. Jiang, and N. Shi Global stability of two-group SIR model with random perturbation J. Math. Anal. Appl. 360 2009 235 244
19. Q. Yang, D. Jiang, N. Shi, and C. Ji The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence J. Math. Anal. Appl. 388 2012 248 271
20. Y. Zhao, and D. Jiang Dynamics of stochastically perturbed SIS epidemic model with vaccination Abstr. Appl. Anal. 2013 2013 1 12
21. Y. Zhao, D. Jiang, and D. O'Regan The extinction and persistence of the stochastic SIS epidemic model with vaccination Physica A: Stat. Mech. Appl. 392 2013 4916 4927
22. Y. Zhao, and D. Jiang The threshold of a stochastic SIRS epidemic model with saturated incidence Appl. Math. Lett. 34 2014 90 93