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On the asymptotic distribution of the maximum number of infectives in epidemic models by immigration
- Source :
- Journal of Applied Probability. 31:606-613
- Publication Year :
- 1994
- Publisher :
- Cambridge University Press (CUP), 1994.
-
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. MAXIMUM NUMBER OF INFECTIVES; GAMBLER'S RUIN PROBLEM; MARTINGALE; BIRTH AND DEATH PROCESS AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 92D30 SECONDARY 60J20; 60G42; 60G40; 60J80
- Subjects :
- Birth and death process
Statistics and Probability
Limit distribution
General Mathematics
010102 general mathematics
Asymptotic distribution
Limiting
01 natural sciences
Birth–death process
010104 statistics & probability
Statistics
Applied mathematics
Almost surely
0101 mathematics
Statistics, Probability and Uncertainty
Martingale (probability theory)
Epidemic model
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 31
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....6445d18908c1ad6e1bc5e89591289521