Dynamic behavior of a delayed impulsive SEIRS model in epidemiology

Rocky Mountain Journal of Mathematics

Volumn 38, Issue 5, 2008, Pages 1841-1862

  Zhang, Tailei ^a   Teng, Zhidong ^a  

^a XINJIANG UNIVERSITY   (China)

Author keywords

Krasnoselskii's fixed point theorem; Pulse vaccination; Threshold value; Time delay

Indexed keywords

EID: 58049151187     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/RMJ-2008-38-5-1841     Document Type: Conference Paper

References (26)

1. F. Brauer, Epidemic models in populations of varying size, in Mathematical approaches to problems in resource management and epidemiology, C.C. Carlos, S.A. Levin and C. Shoemaker, eds., Lecture Notes Biomath. 81, Springer, Berlin, 1989.
2. F. Brauer and P. Van den Driessche, Models for transmission of disease with immigration of infectives, Math. Biosci. 171 (2001), 143-154.
3. H. Bremermann and H. Thieme, A competitive exclusion principle for pathogen virulence, J. Math. Biol. 27 (1989), 179-190.
4. T. Burton, A fixed-point theorem of Krasnoselskii, Appl. Math. Lett. 11 (1998), 85-88.
5. T. Burton and T. Furumochi, Krasnoselskii's fixed point theorem and stability, Nonlinear Anal. 49 (2002), 445-454.
6. O. Diekmann and J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation, John Wiley & Sons, LTD, Chichester, New York, 2000.
7. S. Gakkhar and K. Negi, Pulse vaccination SIRS epidemic model with non monotonic incidence rate, Chaos, Solitons Fractals 35 (2008), 626-638.
8. S. Gao, L. Chen and Z. Teng, Impulsive vaccination of an SEIRS model with time delay and varying total population size, Bull. Math. Biol. 69 (2007), 731-745.
9. -, Pulse vaccination of an SEIR epidemic model with time delay, Nonlinear Analysis: Real World Appl. 9 (2008), 599-607.
10. L. Gao and H. Hethcote, Disease transmission models with density-dependent demographics, J. Math. Biol. 30 (1992), 717-731.
11. D. Greenhalgh, Some threshold and stability results for epidemic models with a density dependent death rate, Theoret. Pop. Biol. 42 (1992), 130-151.
12. H. Hethcote and P. Van den Driessche, Some epidemiological models with nonlinear incidence, J. Math. Biol. 29 (1991), 271-287.
13. M. Kermark and A. Mckendrick, Contributions to the mathematical theory of epidemics, Part I, Proc. Royal Soc. 115 (1927), 700-721.
14. Y. Kuang, Delay differential equation with application in population dynamics, Academic Press, New York, 1993.
15. G. Li and Z. Jin, Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period, Chaos, Solitons Fractals 25 (2005), 1177-1184.
16. -, Global stability of an SEI epidemic model with general contact rate, Chaos, Solitons Fractals 23 (2005), 997-1004.
17. Z. Ma, Y. Zhou, W. Wang and Z. Jin, Mathematical modelling and research of epidemic dynamaical systems, Science Press, Beijing, 2004 (in Chinese).
18. J. Mena-Lorca and H. Hethcote, Dynamic models of infectious diseases as regulators of population biology, J. Math. Biol. 30 (1992), 693-716.
19. X. Meng, L. Chen and H. Chen, Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination, Appl. Math. Comput. 186 (2007), 516-529.
20. G. Pang and L. Chen, A delayed SIRS epidemic model with pulse vaccination, Chaos, Solitons Fractals 34 (2007), 1629-1635.
21. B. Shulgin, L. Stone and Z. Agur, Pulse vaccination strategy in the SIR epidemic model, Bull. Math. Biol. 60 (1998), 1123-1148.
22. D. Smart, Fixed point theorems, Cambridge University Press, Cambridge, 1980.
23. L. Stone, B. Shulgin and Z. Agur, Theoretical examination of the pulse vaccination policy in the SIR epidemic model, J. Math. Comp. Modelling 31 (2000), 207-215.
24. H. Thieme, Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations, Math. Biosci. 111 (1992), 99-130.
25. W. Wang and S. Ruan, Bifurcations in an epidemic model with constant removal rate of the infectives, J. Math. Anal. Appl. 291 (2004), 774-793.
26. T. Zhang and Z. Teng, Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence, Chaos, Solitons Fractals 37 (2008), 1456-1468.