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A discrete model of avian influenza with seasonal reproduction and transmission. (English) Zbl 1342.92255
Summary: In this paper, we formulate a discrete-time model with the reproductive and overwintering periods to assess the impact of avian influenza transmission in poultry. It is shown that the disease is extinct if the basic reproduction number is less than one and is persistent if the basic reproductive number is greater than one. Furthermore, the model admits a closed invariant cycle, which means that avian influenza fluctuates in poultry.

MSC:
92D30 Epidemiology
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[1] DOI: 10.1016/0025-5564(94)90025-6 · Zbl 0807.92022 · doi:10.1016/0025-5564(94)90025-6
[2] DOI: 10.1016/S0362-546X(01)00587-9 · Zbl 1042.37544 · doi:10.1016/S0362-546X(01)00587-9
[3] DOI: 10.1080/1023619021000042216 · Zbl 1060.39012 · doi:10.1080/1023619021000042216
[4] DOI: 10.1016/S0025-5564(02)00108-6 · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6
[5] DOI: 10.1080/10236190410001654151 · Zbl 1067.92052 · doi:10.1080/10236190410001654151
[6] DOI: 10.1137/050638345 · Zbl 1108.37303 · doi:10.1137/050638345
[7] Guckenheimer J., Nonlinear Oscillations, Dynamical System and Bifurcation of Vector Fields (1983) · Zbl 0515.34001 · doi:10.1007/978-1-4612-1140-2
[8] DOI: 10.1016/j.mbs.2006.08.001 · Zbl 1114.92058 · doi:10.1016/j.mbs.2006.08.001
[9] Iwami S., J. Theor. Biol. 257 pp 1– (2008)
[10] DOI: 10.1016/j.jtbi.2008.02.020 · Zbl 1398.92240 · doi:10.1016/j.jtbi.2008.02.020
[11] LaSalle J. P., The Stability of Dynamical Systems (1976) · Zbl 0364.93002
[12] DOI: 10.1016/j.chaos.2005.01.063 · Zbl 1066.92045 · doi:10.1016/j.chaos.2005.01.063
[13] DOI: 10.1016/S1473-3099(07)70186-X · doi:10.1016/S1473-3099(07)70186-X
[14] DOI: 10.1016/j.envsoft.2008.06.011 · doi:10.1016/j.envsoft.2008.06.011
[15] DOI: 10.3934/dcdsb.2009.12.187 · Zbl 1175.34067 · doi:10.3934/dcdsb.2009.12.187
[16] DOI: 10.1142/S1793524508000035 · Zbl 1158.39009 · doi:10.1142/S1793524508000035
[17] World Health Organization,Avian Influenza: Assessing the Pandemic Threat, 2007. Available athttp://www.who.int/entity/csr/disease/influenza/H5N1-9 reduit.pdf
[18] World Health Organization,The Disease in Birds, 2006. Available athttp://www.who.int/mediacentre/factsheets/avian-influenza/en/
[19] Update on Avian Influenza in Animals (type H5) (2009)
[20] World Organisation for Animal Health,Avian Influenza. 2009. Available athttp://www.oie.int/eng/ressources/AI-EN-dc.pdf
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