Global dynamics of a two-strain avian influenza model

International Journal of Computer Mathematics

Volumn 86, Issue 1, 2009, Pages 85-108

  Gumel, A B ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Avian influenza; Equilibria; Lyapunov function; Reproduction number; Stability

Indexed keywords

AVIAN INFLUENZA; DETERMINISTIC MODELING; DISEASE-FREE EQUILIBRIUM; EQUILIBRIA; GLOBALLY ASYMPTOTICALLY STABLE; LASALLE INVARIANCE PRINCIPLE; REPRODUCTION NUMBERS; TRANSMISSION DYNAMICS;

CONVERGENCE OF NUMERICAL METHODS; LYAPUNOV FUNCTIONS;

STRAIN RATE;

EID: 55849087998     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160701769625     Document Type: Article

References (28)

1. R.M. Anderson and R.M. May, Infectious Diseases of Humans, Oxford University Press, New York, 1991.
2. S.G. Blitz, Developments on the care of influenza patients: priorities and perspectives, JCOM 7(2) (2000), pp. 63-72.
3. C. Bowman et al., A mathematical model for assessing control strategies against West Nile virus, Bull. Math. Biol. 67 (2005), pp. 1107-1133.
4. D. Butler, Disease surveillance needs a revolution. Nature 440 (7080) (2006), pp. 6-7.
5. Center for Disease Control and Preventio, Prevention and control of influenza: recommendations of the Advisory Committee on Immunization Practices (ACIP), MMWR 52 (2003), (No. RR-8), pp. 1-34.
6. 0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), pp. 365-382.
7. N.M. Ferguson et al., Strategies for containing an emerging influenza pandemic in Southeast Asia, Nature 437(7056) (2005), pp. 209-214.
8. H.I. Freedman and J.W.-H. So, Global stability and persistence of simple food chains, Math. Biosci. 76 (1985), pp. 69-86.
9. R. Gani et al., Potential impact of antiviral drug use during influenza pandemic, Emerg. Inf. Dis. 11(9) (2005), pp. 1355-1362.
10. T.C. Germann et al., Mitigation strategies for pandemic influenza in the United States, Proc. Natl. Acad. Sci. 103(15) (2006), pp. 5935-5940.
11. A.B. Gumel, M. Nuno, and G. Chowell, Mathematical assessment of Canada's pandemic influenza preparedness plan, Can. J. Infect. Dis. Med. Microbiol. 19 (2008), pp. 185-192.
12. H. Guo and M.Y. Li, Global dynamics of a staged progression model for infectious diseases, Math. Biosci. and Engrg. 1(1) (2004), pp. 1-13.
13. J.K. Hale, Ordinary Differential Equations, John Wiley & Sons, New York, 1969.
14. H.W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42(4) (2000), pp. 599-653.
15. S. Iwami, Y. Takeuchi, and X. Liu, Avian-human influenza epidemic model, Math. Biosci. 207(1) (2007), pp. 1-25.
16. A. Korobinikov and P.K. Maini, A Lyapunov function and some properties for SEIR, SIS epidemic models, Math. Biosci. Eng. 1 (2004), pp. 157-160.
17. J.P. LaSalle, The Stability of Dynamical Systems, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 25, SIAM, Philadelphia, 1976.
18. V. Lakshmikantham, S. Leela, and A.A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, Inc., New York and Basel, 1989.
19. M.Y. Li and J.S. Muldowney, A geometric approach to the global stability problems, SIAM J. Math. Anal. 27 (1996), pp. 1070-1083.
20. I.M. Longini et al., Containing the pandemic influenza with antiviral agents, Am. J. Epidemiol. 159(7) (2004), pp. 623-633.
21. I.M. Longini and M.E. Halloran, Strategy for distribution of influenza vaccine to high-risk groups and children, Am. J. Epidemiol. 161(4) (2005), pp. 303-306.
22. M.I. Meltzer, N.J. Cox, and K. Fukuda, The economic impact of pandemic influenza in the United States: priorities for intervention, Emerg. Infec. Dis. 5(5) (1999), pp. 659-671.
23. K.G. Nicholson, R.G. Webster, and A.J. Hay, Textbook of Influenza, Blackwell Science Ltd, 1998.
24. M. Nuno, G. Chowell, and A.B. Gumel, Assessing the role of basic control measures, antivirals and vaccine in curtailling pandemic infleunza: scenarios for the US, UK and the Netherlands, J. Roy. Soc. Interface. 4 (2007), pp. 505-521.
25. O. Sharomi et al., Role of incidence function in vaccine-induced backward bifurcation in some HIV models, Math. Biosci. 210 (2007), pp. 43663.
26. C. Stuart-Harris, Epidemiology of Influenza in man, Br. Med. Bull. 35(1) (1979), pp. 3-8.
27. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Bios. 180 (2002), pp. 29-48.
28. M.L. van Genugten, M.L. Heijnen, and J.C. Jager, Pandemic influenza and healthcare demand in the Netherlands: Scenario analysis, Emerg. Infec. Dis. 9(5) (2003), pp. 531-538.