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Avian-human influenza epidemic model. (English) Zbl 1114.92058
Summary: A mathematical model is proposed to interpret the spread of avian influenza from the bird world to the human world. Our mathematical model warns that two types of the outbreak of avian influenza may occur if the humans do not prevent the spread of avian influenza. Moreover, it suggests that we cannot feel relieved although the total infected humans are kept at low level. In order to prevent spread of avian influenza in the human world, we must take the measures not only for the birds infected with avian influenza to exterminate but also for the humans infected with mutant avian influenza to quarantine when mutant avian influenza has already occurred. In particular, the latter measure is shown to be important to stop the second pandemic of avian influenza.

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
Full Text: DOI
[1] Burton, T.; Hutson, V., Repellers in systems with infinite delay, J. math. anal. appl., 137, 1, 240, (1989) · Zbl 0677.92016
[2] Hethcote, H.W.; van den Driessche, P., Two SIS epidemiologic models with delays, J. math. biol., 3, (2000) · Zbl 0959.92025
[3] Hutson, V., A theorem on average Liapunov functions, Monatsh. math., 267, (1984) · Zbl 0542.34043
[4] Smith, H.L.; Waltman, P., The theory of the chemostat. dynamics of microbial competition, (1995), Cambridge University · Zbl 0860.92031
[5] Muldowney, J.S., Compound matrices and ordinary differential equations, Rocky mt. J. math., 20, 857, (1990) · Zbl 0725.34049
[6] Wang, K.; Wang, W.; Liu, X., Viral infection model with periodic lytic immune response, chaos soliton fract., 28, 90, (2006) · Zbl 1079.92048
[7] Li, M.Y.; Muldowney, J.S., A geometric approach to the global-stability problems, SIAM J. math. anal., 27, 1070, (1996) · Zbl 0873.34041
[8] M.Y. Li, L. Wang, Global stability in some SEIR models, mathematical approaches for emerging and reemerging infectious diseases part II: models, methods and theory, in: Castillo-Chavez et al. (Ed.), IMA Volumes in Mathematics and its Applications, 2002, p. 126.
[9] Fiedler, M., Additive compound matrices and inequality for eigenvalues of stochastic matrices, Czech. math. J., 99, 392, (1974) · Zbl 0345.15013
[10] Kon, R.; Takeuchi, Y., Permanence of 2-host 1-parasitoid systems, Dyn. contin. discret. I. syst. ser. B appl. algorithms, 10, 389, (2003) · Zbl 1021.92041
[11] Hara, T., On the asymptotic behavior of solutions of certain non-autonomous differential equations, Osaka J. math., 267, (1975) · Zbl 0357.34049
[12] Coppel, W.A., Stability and asymptotic behavior of differential equations, health, (1965), Springer-Verlag Boston, 295-311 · Zbl 0154.09301
[13] Jeffery K. Taubenberger, Ann H. Reid, Thomas G. Fanning, Capturing a Killer Flu Virus, SCIENTIFIC AMERICAN, 2005.
[14] W. Wayt Gibbs, Christine Soares, Preparing for a Pandemic, SCIENTIFIC AMERICAN, 2005.
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