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On the Asymptotic Distribution of the Maximum Number of Infectives in Epidemic Models with Immigration

V. M. Abramov
Journal of Applied Probability
Vol. 31, No. 3 (Sep., 1994), pp. 606-613
DOI: 10.2307/3215141
Stable URL: http://www.jstor.org/stable/3215141
Page Count: 8
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On the Asymptotic Distribution of the Maximum Number of Infectives in Epidemic Models with Immigration
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Abstract

This paper considers the asymptotic distribution of the maximum number of infectives in an epidemic model by showing that, as the initial number of susceptibles converges to infinity, the process of infectives converges almost surely to a birth and death process. The model studied here is more general than usual (see e.g. Bailey (1975), Bharucha-Reid (1960), Keilson (1979)) in that it incorporates immigration and the limiting birth and death process is non-linear. The main novelty of the present paper is the martingale approach used to prove the above-mentioned convergence.

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