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Singular perturbations of epidemic models involving a threshold

Part 3 Research Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 985)

Abstract

This paper deals with the mathematical model of an epidemic with a small number of initial infectives I0. The time development of the epidemic, satisfying an integro-differential equation, is approximated with singular perturbation techniques. The asymptotic result for I0 → 0 shows that when the number of infectives exceeds a fixed small value (independent of I0) the time course of the epidemic is fixated; the time needed to pass this value is of the order 0(-log I0).

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© 1983 Springer-Verlag

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Grasman, J., Matkowsky, B.J. (1983). Singular perturbations of epidemic models involving a threshold. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062378

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  • DOI: https://doi.org/10.1007/BFb0062378

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12286-9

  • Online ISBN: 978-3-540-39612-3

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