Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays

Applied Mathematics and Computation

Volumn 214, Issue 2, 2009, Pages 381-390

  Song, Xinyu ^a   Jiang, Yu ^b   Wei, Huiming ^c  

^a XINYANG NORMAL UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Epidemic model; Globally attractive; Permanence; Pulse vaccination; Saturation incidence; Time delay

Indexed keywords

EPIDEMIC MODEL; GLOBALLY ATTRACTIVE; PERMANENCE; PULSE VACCINATION; SATURATION INCIDENCE;

EPIDEMIOLOGY; INTEGRODIFFERENTIAL EQUATIONS;

TIME DELAY;

EID: 67649224128     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.04.005     Document Type: Article

References (27)

1. Agur Z., Cojocaru L., Mazor G., Anderson R.M., and Danon Y.L. Pulse mass measles vaccination across age cohorts. Proc. Nat. Acad. Sci. USA 90 (1993) 11698-11702
2. Anderson R.M., and May R.M. Infectious diseases of humans. Dynamics and Control (1992), Oxford University Press, Oxford
3. Bainov D.D., and Simeonov P.S. Impulsive Differential Equations: Periodic Solutions and Applications (1993), Longman Scientific and Technical, New York
4. Cooke K.L., and van Den Driessche P. Analysis of an SEIRS epidemic model with two delays. J. Math. Biol. 35 (1996) 240-260
5. de Quadros C.A., Andrus J.K., and Oliv J.M. Eradication of Poliomyelitis: Progress. Am. Ped. Inf. Dis. J. 10 3 (1991) 222-229
6. D'Onofrio A. Stability properties of pulse vaccination strategy in SEIR epidemic model. Math. Biosci. 179 (2002) 57-72
7. D'Onofrio A. Pulse vaccination strategy in SIR epidemic model. Math. Comp. Mod. 13 1 (2002) 15-26
8. D'Onofrio A. Mixed pulse vaccination strategy in epidemic model with realistic distributed infectious and latent times. Appl. Math. Comput. 151 (2004) 181-187
9. Hersh B.S., Tambini G., Norgueira A.C., Carrasco P., and de Quadros C.A. Review of regional measles surveillance data in the Americas 1996-1999. Lancet 355 (2000) 1943-1948
10. Hethcote H.W., and van den Driessche P. Some epidemiological models with nonlinear incidence. J. Math. Biol. 29 (1991) 271-287
11. Hui J., and Chen L. Impulsive vaccination of SIR epidemic models with nonlinear incidence rates. Discrete Contin. Dyn. Syst.: Series B 4 (2004) 595-605
12. Jin Z., Haque M., and Liu Q.X. Pulse vaccination in the periodic infection rate SIR epidemic model. Int. J. Biomath. 1 4 (2008) 409-432
13. Kuang Y. Delay Differential Equation with Application in Population Dynamics (1993), Academic Press, New York pp. 67-70
14. Lakshmikantham V., Bainov D., and Simeonov P. Theory of impulsive differential equations (1989), World Scientific, Singapore
15. May R.M., and Anderson R.M. Regulation and stability of host-parasite population interactions II: Destabilizing process. J. Anim. Ecol. 47 (1978) 219-267
16. Meng X.Z., and Zhang T.Q. Global dynamic behaviors of a two-dimensional integral-differential almost periodic system with infinite delays and discrete delays. Int. J. Biomath. 1 4 (2008) 487-502
17. Nokes D.J., and Swinton J. The control of childhood viral infections by pulse vaccination. IMA J. Math. Appl. Med. Biol. 12 (1995) 29-53
18. Nokes D.J., and Swinton J. Vaccination in pulses: A strategy for global eradication of measles and polio?. Trends. Microbiol. 5 (1997) 14-19
19. Ramsay M., Gay N., and Miller E. The epidemiology of measles in England and Wales: Rationale for 1994 National Vaccination Campaign. Commun. Dis. Rep. 4 (1994) 141-146
20. Ruan S., and Wang W. Dynamical behavior of an epidemic model with nonlinear incidence rate. J. Differ. Equat. 188 (2003) 135-163
21. Sabin A.B. Measles, killer of millions in developing countries: Strategies of elimination and continuing control. Eur. J. Epidemiol. 7 (1991) 1-22
22. Shulgin B., Stone L., and Agur Z. Theoretical examination of pulse vaccination policy in the sir epidemic model. Math. Comp. Mod. 31 4/5 (2000) 207-215
23. Shulgin B., Stone L., and Agur Z. Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol. 60 (1998) 1123-1148
24. Shulgin B., Stone L., and Agur Z. Theoretical examinations of pulse vaccination policy in the SIR epidemic model. Math. Comput. Modell. 30 (2000) 207-215
25. Xiao Y., and Chen L. Modelling and analysis of a predator-prey model with disease in the prey. Math. Biosci. 171 (2001) 59-82
26. Song Y., and Wei J. Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system. J. Math. Anal. Appl. 301 (2005) 1-21
27. Wang W. Global behavior of an SEIRS epidemic model with time delays. Appl. Math. Lett. 15 (2002) 423-428