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On periodic solutions of a delay integral equation modelling epidemics. (English) Zbl 0354.92035

MSC:
92D25 Population dynamics (general)
45Mxx Qualitative behavior of solutions to integral equations
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[1] Cooke, K. L., Kaplan, J. L.: A periodicity threshold theorem for epidemics and population growth. J. Math. Biosciences (to appear). · Zbl 0341.92012
[2] Cooke, K. L., Yorke, J. A.: Some equations modelling growth processes and gonorrhea epidemics. Math. Biosci. 16, 75-101 (1973). · Zbl 0251.92011
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[4] Hethcote, H. W.: Asymptotic behavior in a deterministic epidemic model. Bull. Math. Biology 35, 607-614 (1973). · Zbl 0279.92011
[5] Hoppensteadt, F., Waltman, P.: A problem in the theory of epidemics. Math. Biosci. 9, 71-91 (1970). · Zbl 0212.52105
[6] Hoppensteadt, F., Waltman, P.: A problem in the theory of epidemics II. Math. Biosci. 12, 133-145 (1971). · Zbl 0226.92011
[7] Krasnosel’skii, M. A.: Positive solutions of operator equations. Groningen: Noordhoff 1964.
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[9] London, W. P., Yorke, J. A.: Recurrent outbreaks of measles, chickenpox, and mumps I: seasonal variation in contact rates. Amer. J. Epidemics 98, 453-468 (1973).
[10] Nussbaum, R.: A periodicity threshold theorem for some nonlinear integral equations (to appear). · Zbl 0385.45007
[11] Rogers, F. B.: Epidemiology and Communicable Disease Control. New York: Grune & Stratton1963.
[12] Rudin, W.: Functional Analysis. New York: McGraw-Hill 1973. · Zbl 0253.46001
[13] Yorke, J. A., London, W. P.: Recurrent outbreaks of measles, chickenpox, and mumps II: systematic differences in contact rates and stochastic effects. Amer. J. Epidemics 98, 469-482 (1973).
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