On the asymptotic distribution of the maximum number of infectives in epidemic models with immigration

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/235065

Title: On the asymptotic distribution of the maximum number of infectives in epidemic models with immigration
Author(s): Abramov, V. M.
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.
Publication type: Journal article
Source: Journal of Applied Probability, Vol. 31, no. 3 (Sep 1994), pp. 606-613
Publication year: 1994
FOR Code(s): 0102 Applied Mathematics; 0104 Statistics
Keyword(s): Birth-and-death process; Gambler's ruin problem; Martingales; Maximum number of infectives
Publisher: Applied Probability Trust
ISSN: 0021-9002
Publisher URL: http://www.jstor.org/stable/3215141
Peer reviewed