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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