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Home List of Titles On the asymptotic distribution of the maximum number of infectives in epidemic models with immigration
Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/235065
- On the asymptotic distribution of the maximum number of infectives in epidemic models with immigration
- Abramov, V. M.
- 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
- Journal of Applied Probability, Vol. 31, no. 3 (Sep 1994), pp. 606-613
- Publication year
- FOR Code(s)
- 0102 Applied Mathematics; 0104 Statistics
- Birth-and-death process; Gambler's ruin problem; Martingales; Maximum number of infectives
- Applied Probability Trust
- Publisher URL
- Copyright © Applied Probability Trust 1994.
- Peer reviewed