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Global asymptotic stable eradication for the SIV epidemic model with impulsive vaccination and infection-age. (English) Zbl 1114.35031

Summary: We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion \(p\). We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.

MSC:

35B41 Attractors
92D30 Epidemiology
35R12 Impulsive partial differential equations
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[1] R. M. Ander and R. M. May, Infectious Diseases of Humans, Oxford University Press, 1991.
[2] M.Martcheva and H. R. Thieme, Progression age enhanced backward bifurcation in an epidemic model with super-infection, J. Math. Biol., 2003, 46: 385–424. · Zbl 1097.92046 · doi:10.1007/s00285-002-0181-7
[3] Z. Feng, M. Iannelli, and F. A. Milner, A two-strain tuberculosis model with age of infection, SIAM. Appl. Math., 2002, 62 (5): 1634–1656. · Zbl 1017.35066
[4] Z. Agur, L. Cojocaru, R. M. Anderson, and Y. L. Danon, Pulse mass measles vaccination across age cohorts, Proc. Nat. Acad. Sci. (USA), 1993, 90: 11698–11702.
[5] B. Shulgin, L. Ston, and Z. Agur, Theoretical examination of pulse vaccination policy in the SIR epidemic model, Math. Comput. Modelling, 2000, 31(4–5): 207–215. · Zbl 1043.92527
[6] A. D’Onofri, Stability properties of pulse vaccination strategy in SEIR epidemic model, Math. Biosci., 2002, 179: 57–72. · Zbl 0991.92025 · doi:10.1016/S0025-5564(02)00095-0
[7] Y. Zhou and H. Liu, Stability of periodic solutions for an SIS model with pulse vaccination, Math. Comput. Modelling, 2003, 38: 229–308. · Zbl 1045.92042 · doi:10.1016/S0895-7177(03)90088-4
[8] B. Shulgin, L. Stone, and Z. Agur, Pulse vaccination strategy in the SIR epidemic model, Bull. Math. Biol., 1998, 60: 1123–1148. · Zbl 0941.92026 · doi:10.1016/S0092-8240(98)90005-2
[9] A. D’Onofri, Pulse vaccination strategy in the SIR epidemic model: Global asymptotic stable eradication in presence of vaccine failures, Math. Comput. Modelling, 2002, 36: 473–489. · Zbl 1025.92011 · doi:10.1016/S0895-7177(02)00177-2
[10] C. A. de Quadros, J. K. Andrus, and J. M. Olive, Eradication of poliomyelitis: progress in the Americas, Pediat. Inf. Dis. J., 1991, 10(3): 222–229.
[11] A. B. Sabin, Measlles: Killer of millions in developing countries: strategies of elimination and continuing control, Eur. J. Epid., 1991, 7: 1–022.
[12] M. Ramsay and E. Miller, The epidemiology of measles in England and Wales Rationale for 1994 national vaccination campaign, Eur. J. Epid., 1991, 7: 1–22.
[13] S. Busenberg and P. van der Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol., 1990, 28: 257–270. · Zbl 0725.92021 · doi:10.1007/BF00178776
[14] M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, Global dynamics of an SEIR model with varying population size, Math. Biosc., 1999, 160: 191–213. · Zbl 0974.92029 · doi:10.1016/S0025-5564(99)00030-9
[15] L. Esteva and C. Vargas, A model for Dengue disease with variable human population, J. Math. Biol., 1999, 38: 220–240. · Zbl 0981.92016 · doi:10.1007/s002850050147
[16] G. F. Webb, Theory of Nonlinear Age-dependent Population Dynamics, Marcel Dekker, New York, 1985. · Zbl 0555.92014
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