The effects of pulse vaccination on SEIR model with two time delays

Applied Mathematics and Computation

Volumn 201, Issue 1-2, 2008, Pages 282-292

  Gao, Shujing ^a,b   Teng, Zhidong ^b   Xie, Dehui ^a  

^a GANNAN NORMAL UNIVERSITY   (China)

^b XINJIANG UNIVERSITY   (China)

Author keywords

Global attractivity; Permanence; Pulse vaccination; SEIR epidemic model; Time delay

Indexed keywords

MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING; TIME DELAY; VACCINES;

GLOBAL ATTRACTIVITY; PERMANENCE; PULSE VACCINATION; SEIR EPIDEMIC MODELS;

DISEASE CONTROL;

EID: 44649122225     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.12.019     Document Type: Article

References (24)

1. d'Onofrio A. Mixed pulse vaccination strategy in epidemic model with realistic distributed infectious and latent times. Appl. Math. Comput. 151 (2004) 181-187
2. Shulgin B., Stone L., and Agur Z. Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol. 60 (1998) 1123-1148
3. Stone L., Shulgin B., and Agur Z. Theoretical examination of the pulse vaccination policy in the SIR epidemic model. Math. Comput. Modell. 31 (2000) 207-215
4. Gumel A.B., and Moghadas S.M. A qualitative study of a vaccination model with nonlinear incidence. Appl. Math. Comput. 143 (2003) 409-419
5. Hui J., and Chen L. Impulsive vaccination of SIR epidemic models with nonlinear incidence rates. Discrete Continuous Dyn. Syst. Ser. B 4 (2004) 595-605
6. Nokes D.J., and Swinton J. The control of a childhood viral infections by pulse vaccination. IMA J. Math. Appl. Med. Biol. 12 (1995) 29-53
7. Sabin A.B. Measles: killer of millions in developing countries: strategies of elimination and continuing control. Eur. J. Epid. 7 (1991) 1-22
8. De Quadros C.A., Andrus J.K., and Olivé J.M. Eradication of poliomyelitis: progress. Am. Pediatr. Inf. Dis. J. 10 (1991) 222-229
9. Bainov D.D., and Simeonov P.S. Impulsive Differential Equations: Asymptotic Properties of the Solutions (1995), World Scientific, Singapore
10. Bainov D.D., and Simeonov P.S. Impulsive Differential Equations: Periodic Solutions and Applications (1993), Longman, Harlow
11. Bainov D.D., and Simeonov P.S. Systems with Impulse Effect: Stability, Theory, and Applications (1989), Ellis Horwood, Chichester
12. Yang T. Impulsive Control. IEEE Trans. Automat. Control AC-44 5 (1999) 1081-1083
13. Li X.Z., Gupur G., and Zhu G.T. Threshold and stability results for an age-structured SEIR epidemic model. Comput. Math. Appl. 42 (2001) 883-907
14. Wang W. Global behavior of an SEIRS epidemic model with time delays. Appl. Math. Lett. 15 (2002) 423-428
15. d'Onofrio A. Stability properties of pulse vaccination strategy in SEIR epidemic model. Math. Biosci. 179 (2002) 57-72
16. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
17. Cull P. Global stability for population models. Bull. Math. Bio. 43 (1981) 47-58
18. Kuang Y. Delay Differential Equation with Application in Population Dynamics (1993), Academic Press, New York
19. Xiao Y., and Chen L. Modelling and analysis of a predator-prey model with disease in the prey. Math. Bios. 171 (2001) 59-82
20. Zhang C., Liu M., and Zheng B. Hopf bifurcation in numerical approximation of a class delay differential equations. Appl. Math. Comput. 146 (2003) 335-349
21. Busenberg S., and Cooke K.L. Vertically transmitted diseases. Biomathematics 23 (1993), Springer-Verlag, Berlin
22. Hethcote H.W., Stech H.W., and van den Driessche P. Nonlinear oscillations in epidemic models. SIAM J. Appl. Math. 40 (1981) 1-9
23. Schwartz I.B. Small amplitude, long period outbreaks in seasonally driven epidemics. J. Math. Biol. 30 (1992) 473-491
24. Schwartz I.B., and Smith H.L. Infinite subharmonic bifurcation in an SEIR epidemic model. J. Math. Biol. 18 (1983) 233-253