A discrete model of avian influenza with seasonal reproduction and transmission

Journal of Biological Dynamics

Volumn 4, Issue 3, 2010, Pages 296-314

  Ma, Xinling ^a   Wang, Wendi ^a  

^a SOUTHWEST UNIVERSITY   (China)

Author keywords

Global stability; Hopf bifurcation; Permanence; Poultry; Reproduction number

Indexed keywords

ANIMAL; ARTICLE; AVIAN INFLUENZA; BIOLOGICAL MODEL; COMPUTER SIMULATION; DISEASE TRANSMISSION; PHYSIOLOGY; POPULATION DENSITY; POULTRY; REPRODUCTION; SEASON; VIROLOGY;

ANIMALS; COMPUTER SIMULATION; INFLUENZA IN BIRDS; MODELS, BIOLOGICAL; POPULATION DENSITY; POULTRY; REPRODUCTION; SEASONS;

AVES;

EID: 79960528739     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513751003793009     Document Type: Article

References (20)

1. L.J.S. Allen, Some discrete-time SI, SIR, and SIS epidemic models, Math. Biosci. 124 (1994), pp. 83-105.
2. C. Castillo-Chavez and A-A.Yakubu, Discrete-time SIS models with complex dynamics, Nonlinear Anal. 47 (2001), pp. 4753-4762.
3. J.M. Cushing, Cycle chains and the LPA model, J. Differ. Equ. Appl. 9 (2003), pp. 655-670.
4. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29-48.
5. K.M. Emmert and L.J.S. Allen, Population persistence and extinction in a discrete-time, stage-structured epidemic model, J. Differ. Equ. Appl. 10 (2004), pp. 1177-1199.
6. J.E. Franke and A-A.Yakubu, Discrete-time SIS model in a seasonal environment, SIAM J. Appl. Math. 66 (2006), pp. 1563-1587.
7. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical System and Bifurcation of Vector Fields, Springer-Verlag, NewYork, 1983.
8. S. Iwami, Y. Takeuchi, and X. Liu, Avian-human influenza epidemic model, Math. Biosci. 207 (2007), pp. 1-25.
9. S. Iwami, Y. Takeuchi, and X. Liu, Avian flu pandemic: Can we prevent it? J. Theor. Biol. 257 (2008), pp. 1-27.
10. S. Iwami, Y. Takeuchi, A. Korobeinikov, and X. Liu, Prevention of avian influenza epidemic: What policy should we choose? J. Theor. Biol. 252 (2008), pp. 732-741.
11. J.P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976.
12. X. Li and W.Wang, A discrete epidemic model with stage structure, Chaos Solitons Fractals 26 (2005), pp. 947-958.
13. A.W. Park and K. Glass, Dynamic patterns of avian and human influenza in east and southeast Asia, Lancet Infect. Dis. 7 (2007), pp. 543-548.
14. D.M. Rao, A. Chernyakhovsky, and V. Rao, Modeling and analysis of global epidemiology of avian influenza, Environ. Model. Softw. 24 (2009), pp. 124-134.
15. P.L. Salceanu and H.L. Smith, Lyapunov exponents and persistence in some discrete dynamical systems, Discrete Contin. Dyn. Syst. B 12 (2009), pp. 187-203.
16. X. Wang and Z. Li, Globally dynamical behaviors for discrete Lasota-Wazewska model with several delays and almost periodic coefficients, Int. J. Biomath. 1 (2008), pp. 95-105.
17. World Health Organization, Avian Influenza: Assessing the Pandemic Threat, 2007.Available at http://www.who.int/entity/csr/disease/influenza/H5N1-9reduit.pdf
18. World Health Organization, The Disease in Birds, 2006. Available at http://www.who.int/mediacentre/factsheets/avian-influenza/en/
19. World Organisation for Animal Health, Update on Avian Influenza in Animals (type H5),World Organisation for Animal Health, Paris, 2009.Available at http://www.oie.int/downld/AVIAN%20INFLUENZA/A_AIAsia.htm (accessed 7 January 2009).
20. World Organisation for Animal Health, Avian Influenza. 2009. Available at http://www.oie.int/eng/ressources/AIEN-dc.pdf