Dynamics of stochastically perturbed SIS epidemic model with vaccination

Abstract and Applied Analysis

Volumn 2013, Issue , 2013, Pages

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

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b CHANGCHUN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84884866242     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/517439     Document Type: Article

References (30)

1. Chen F. H., A susceptible-infected epidemic model with voluntary vaccinations. Journal of Mathematical Biology 2006 53 2 253 272 10.1007/s00285-006-0006-1 MR2235540 ZBL1098.92044 (Pubitemid 44126176)
2. Shim E., Feng Z., Martcheva M., Castillo-Chavez C., An age-structured epidemic model of rotavirus with vaccination. Journal of Mathematical Biology 2006 53 4 719 746 10.1007/s00285-006-0023-0 MR2487364 ZBL1113.92045 (Pubitemid 44326898)
3. Moneim I., Greenhalgh D., Threshold and stability results for an sirs epidemic model with ageneral periodic vaccination strategy. Journal of Biological Systems 2005 13 131 150 10.1142/S0218339005001446 (Pubitemid 40717617)
4. Greenhalgh D., Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity. Mathematical and Computer Modelling 1997 25 2 85 107 10.1016/S0895-7177(97)00009-5 MR1434405 ZBL0877.92023 (Pubitemid 27126605)
5. Greenhalgh D., Some results for an SEIR epidemic model with density dependence in the death rate. IMA Journal of Mathematics Applied in Medicine and Biology 1992 9 2 67 106 MR1181797 10.1093/imammb/9.2.67 ZBL0805.92025
6. Li J., Ma Z., Qualitative analyses of SIS epidemic model with vaccination and varying total population size. Mathematical and Computer Modelling 2002 35 11-12 1235 1243 10.1016/S0895-7177(02)00082-1 MR1910450 ZBL1045.92039 (Pubitemid 34623159)
7. Li J., Ma Z., Global analysis of SIS epidemic models with variable total population size. Mathematical and Computer Modelling 2004 39 11-12 1231 1242 10.1016/j.mcm.2004.06.004 MR2078424 ZBL1065.92047 (Pubitemid 39350865)
8. Arnold L., Horsthemke W., Stucki J. W., The influence of external real and white noise on the Lotka-Volterra model. Biometrical Journal 1979 21 5 451 471 10.1002/bimj.4710210507 MR554250 ZBL0433.92019 (Pubitemid 10217727)
9. Bahar A., Mao X., Stochastic delay Lotka-Volterra model. Journal of Mathematical Analysis and Applications 2004 292 2 364 380 10.1016/j.jmaa.2003. 12.004 MR2047618 ZBL1043.92034 (Pubitemid 38521622)
10. Gard T. C., Persistence in stochastic food web models. Bulletin of Mathematical Biology 1984 46 3 357 370 10.1016/S0092-8240(84)80044-0 MR748544 ZBL0533.92028
11. Imhof L., Walcher S., Exclusion and persistence in deterministic and stochastic chemostat models. Journal of Differential Equations 2005 217 1 26 53 10.1016/j.jde.2005.06.017 MR2170527 ZBL1089.34041 (Pubitemid 41283325)
12. Ji C., Jiang D., Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. Journal of Mathematical Analysis and Applications 2011 381 1 441 453 10.1016/j.jmaa.2011.02.037 MR2796222 ZBL1232.34072
13. Ji C., Jiang D., Shi N., Multigroup SIR epidemic model with stochastic perturbation. Physica A 2011 390 1747 1762 10.1016/j.physa.2010.12.042
14. Jiang D., Ji C., Shi N., Yu J., The long time behavior of DI SIR epidemic model with stochastic perturbation. Journal of Mathematical Analysis and Applications 2010 372 1 162 180 10.1016/j.jmaa.2010.06.003 MR2672517 ZBL1194.92053
15. Khasminskii R. Z., Klebaner F. C., Long term behavior of solutions of the Lotka-Volterra system under small random perturbations. The Annals of Applied Probability 2001 11 3 952 963 10.1214/aoap/1015345354 MR1865029 ZBL1061.34513 (Pubitemid 33396635)
16. Mao X., Sabanis S., Renshaw E., Asymptotic behaviour of the stochastic Lotka-Volterra model. Journal of Mathematical Analysis and Applications 2003 287 1 141 156 10.1016/S0022-247X(03)00539-0 MR2010262 ZBL1048.92027 (Pubitemid 37374125)
17. Mao X., Marion G., Renshaw E., Environmental Brownian noise suppresses explosions in population dynamics. Stochastic Processes and their Applications 2002 97 1 95 110 10.1016/S0304-4149(01)00126-0 MR1870962 ZBL1058.60046 (Pubitemid 40030718)
18. Mao X., Stochastic Differential Equations and Applications 1997 Chichester, UK Horwood
19. Carletti M., On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment. Mathematical Biosciences 2002 175 2 117 131 10.1016/S0025-5564(01)00089-X MR1882285 ZBL0987.92027 (Pubitemid 34171162)
20. Dalal N., Greenhalgh D., Mao X., A stochastic model of AIDS and condom use. Journal of Mathematical Analysis and Applications 2007 325 1 36 53 10.1016/j.jmaa.2006.01.055 MR2273027 ZBL1101.92037 (Pubitemid 44615330)
21. Dalal N., Greenhalgh D., Mao X., A stochastic model for internal HIV dynamics. Journal of Mathematical Analysis and Applications 2008 341 2 1084 1101 10.1016/j.jmaa.2007.11.005 MR2398271 ZBL1132.92015
22. Tornatore E., Buccellato S., Vetro P., Stability of a stochastic SIR system. Physica A 2005 354 111 126 10.1016/j.physa.2005.02.057 (Pubitemid 40752463)
23. Gray A., Greenhalgh D., Hu L., Mao X., Pan J., A stochastic differential equation SIS epidemic model. SIAM Journal on Applied Mathematics 2011 71 3 876 902 10.1137/10081856X MR2821582 ZBL1263.34068
24. Yu J., Jiang D., Shi N., Global stability of two-group SIR model with random perturbation. Journal of Mathematical Analysis and Applications 2009 360 1 235 244 10.1016/j.jmaa.2009.06.050 MR2548379 ZBL1184.34064
25. Beretta E., Kolmanovskii V., Shaikhet L., Stability of epidemic model with time delays influenced by stochastic perturbations. Mathematics and Computers in Simulation 1998 45 3-4 269 277 10.1016/S0378-4754(97)00106-7 MR1622405 ZBL1017.92504 (Pubitemid 128451281)
26. Has'minski R. Z., Stochastic Stability of Differential Equations 1980 7 Alphen aan den Rijn, The Netherlands Sijthoff & Noordhoff xvi+344 Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis MR600653
27. Higham D. J., An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Review 2001 43 3 525 546 10.1137/S0036144500378302 MR1872387 ZBL0979.65007 (Pubitemid 32991214)
28. Gard T. C., Introduction to Stochastic Differential Equations 1988 114 New York, NY, USA Marcel Dekker xiv+234 Monographs and Textbooks in Pure and Applied Mathematics MR917064
29. Strang G., Linear Algebra and Its Applications 1988 Glendale, Calif, USA Thomson Learning
30. C. Zhu and G. Yin, "Asymptotic properties of hybrid diffusion systems," SIAM Journal on Control and Optimization, vol. 46, no. 4, pp. 11551179, 2007.