The effect of impulsive vaccination on an SIR epidemic model

Applied Mathematics and Computation

Volumn 212, Issue 2, 2009, Pages 305-311

  Shi, Ruiqing ^a,b   Jiang, Xiaowu ^c   Chen, Lansun ^b  

^a SHANXI NORMAL UNIVERSITY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^c XINYANG NORMAL UNIVERSITY   (China)

Author keywords

Disease eradication periodic solution; Epidemic; Impulsive; SIR model

Indexed keywords

EPIDEMIC; GLOBAL ASYMPTOTICAL STABILITIES; IMPULSIVE; ORIGINAL SYSTEMS; SIR EPIDEMIC MODELS; SIR MODEL; SUFFICIENT CONDITIONS; THEORETICAL RESULTS;

EPIDEMIOLOGY;

EID: 67349167681     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.02.017     Document Type: Article

References (25)

1. Kermack W.O., and McKendrick A.G. Contributions to the mathematical theory of epidemics. Proc. Roy. Soc. A 115 (1927) 700-721
2. Bailey N.T.J. The Mathematical Theory of Infectious Disease (1975), Hafner, New York
3. Mollison D. Simplifying simple epidemic models. Nature 310 (1984) 224-225
4. Mollison D. Sensitivity analysis of simple endemic models. In: Bacon P.J. (Ed). Population Dynamics of Rabies in Wildlife (1985), Academic, London 223-234
5. d'Onofrio A. Stability properties of pulse vaccination strategy in SEIR epidemic model. Math. Biosci. 179 1 (2002) 57-72
6. Hui J., and Chen L. Impulsive vaccination of SIR epidemic models with nonlinear incidence rates. DCDS - B 4 (2004) 595-605
7. Beretta E., and Takeuchi Y. Convergence results in SIR epidemic model with varying total population size. Nonl. Anal. TMA 160 (1999) 191-213
8. Li M., Graef J., Wang L., and Karsai J. Global dynamics of a SEIR model with varying total population size. Math. Biosic. 160 (1999) 191-213
9. Beretta E., Hara T., Ma W., and Takeuchi Y. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonl. Anal. TMA 47 (2001) 4107-4115
10. Roberts M.G., and Kao R.R. The dynamics of an infectious disease in a population with birth pules. Math. Biosci. 149 (2002) 257-264
11. In: Lakshmikantham V., Bainov D.D., and Simeonov P. (Eds). Theory of impulsive differential equations (1989), World scientific, Singapore
12. D. Bainov, P. Simeonov (Eds.), Impulsive Differential Equations: Periodic Solutions and Applications, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 66, 1993.
13. Gao L.Q., Mena-Lorca J., and Hethcote H.W. Four SEI endemic models with periodicity and separatrices. Math. Biosci. 128 (1995) 157-184
14. Anderson R.M., Jackson H.C., May R.M., and Smith A.D.M. Population dynamics of fox rabies in Europe. Nature 289 (1981) 765-777
15. De JOng M.C.M., Dikemann O., and Heesterbeek J.A.P. How does transmission depend on population size. In: Isham V., and Medley G. (Eds). Proceedings of Human Infectious Disease, March 1993 Conference at the Isaac Newton Institute for Mathematical Sciences (1995), Cambridge University Press
16. Hethcote H.W. A thousand and one epidemic models. In: Levin S.A. (Ed). Frontiers in Mathematical Biology. Lect. Notes Biomath. vol. 100 (1995), Springer-Verlag, New York
17. Mena-Lorca J., and Hethcote H.W. Dynamic models of infectious diseases as regulators of population sizes. J. Math. Biol. 30 (1992) 693-716
18. Zhou J., and Hethcote H.W. Population size dependent incidence in models for diseases without immunity. J. Math. Biol. 32 (1994) 809-834
19. Stone L., Shulgin B., and Agur Z. Theoretical examination of the pulse vaccination policy in the SIR epidemic model. Math. Comput. Mod. 31 (2000) 207-215
20. Shulgin B., Stone L., and Agur Z. Pulse vaccination strategy in the SIR endemic model. Bull. Math. Biol. 60 (1998) 1123-1148
21. Meng X.Z., and Chen L.S. The dynamics of a new SIR epidemic model concerning pulse vaccination strategy. Appl. Math. Comput. 197 2 (2008) 582-597
22. Meng X.Z., and Chen L.S. Global dynamical behaviors for an SIR epidemic model with time delay and pulse vaccination. Taiwanese J. Math. 12 5 (2008) 1107-1122
23. Meng X.Z., and Chen L.S. A stage-structured SI eco-epidemiological model with time delay and impulsive controlling. J. Sys. Sci. Compl. 21 3 (2008) 427-440
24. Gao S., Xie D., and Chen L. Pulse vaccination strategy in a delayed SIR epidemic model with vertical transmission. DCDS - B 7 1 (2007) 77-86
25. Zhang T., and Teng Z. Global behavior and permanence of SIRS epidemic model with time delay. Nonlinear Anal.: Real World Appl. 9 (2008) 1409-1424