Dynamical behavior of epidemiological models with nonlinear incidence rates

Journal of Mathematical Biology - Tập 25 Số 4 - Trang 359-380 - 1987
Weimin Liu1, Herbert W. Hethcote2, Simon A. Levin1
1Center for Applied Mathematics, 14853, Ithaca, NY, USA
2Department of Mathematics, University of Iowa, 52242, Iowa City, IA, USA

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Tài liệu tham khảo

Bailey, N. T. J.: The mathematical theory of infectious diseases and its applications 2nd edn. London: Griffin 1975

Capasso, V., Serio, G.: A generalization of the Kermack-McKendrick deterministic epidemic model. Math. Biosci. 42, 41?61 (1978)

Carr, J.: Applications of centre manifold theory. Berlin Heidelberg New York: Springer 1981

Cunningham, J.: A deterministic model for measles. Z. Naturforsch. 34c, 647?648 (1979)

Guckenheimer, J., Holmes, P.: Nonlinear oscillations, dynamical systems and bifurcations of vector fields, pp. 150?156. Berlin Heidelberg New York Tokyo: Springer 1983

Hale, J. K.: Ordinary differential equations. New York: Wiley-Interscience 1969

Hethcote, H. W.: Qualitative analyses of communicable disease models. Math. Biosci. 28, 335?356 (1976)

Hethcote, H. W., Stech, H. W., Van den Driessche, P.: Stability analysis for models of diseases without immunity. J. Math. Biol. 13, 185?198 (1981a)

Hethcote, H. W., Stech, H. W., Van den Driessche, P.: Periodicity and stability in epidemic models: a survey. In: Cooke, K. L. (ed.) Differential equations and applications in ecology, epidemics, and population problems, pp. 65?82. New York London Toronto Sydney San Francisco: Academic Press 1981b

Liu, W. M., Levin, S. A.: Influenza and some related mathematical models. In: Levin, S. A., Hallam, T., Gross, L. (eds.) Applied mathematical ecology. Berlin Heidelberg New York: Springer

Liu, W. M., Levin, S. A., Iwasa, Y.: Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23, 187?204 (1986)

Liu, W. M.: Dynamics of epidemiological models-recurrent outbreaks in autonomous systems. Ph.D. Thesis, Cornell University (1987)

Marsden, J. E., McCracken, M.: The Hopf bifurcation and its applications. Berlin Heidelberg New York: Springer 1976

Saunders, I. W.: A model for myxomatosis. Math. Biosci. 48, 1?15 (1980)

Wang, F. J. S.: Asymptotic behavior of some deterministic epidemic models. SIAM J. Math. Anal. 9, 529?534 (1978)

Wilson, E. B., Worcester, J.: The law of mass action in epidemiology. Proc. Natl. Acad. Sci. USA 31, 24?34 (1945)

Wilson, E. B., Worcester, J.: The law of mass action in epidemiology II. Proc. Natl. Acad. Sci. USA 31, 109?116 (1945)