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November, 1995 The Asymptotic Evolution of the General Stochastic Epidemic
Gesine Reinert
Ann. Appl. Probab. 5(4): 1061-1086 (November, 1995). DOI: 10.1214/aoap/1177004606


Generalizing Sellke's construction, a general stochastic epidemic with non-Markovian transition behavior is considered. At time $t = 0$, the population of total size $K$ consists of $aK$ individuals that are infected by a certain disease (and infectious); the remaining $bK$ individuals are susceptible with respect to that disease. An initially susceptible individual $i$, when infected (call $A^K_i$ its time of infection), stays infectious for a period of length $r_i$, until it is removed. An initially infected individual $i$ stays infected for a period of length $\hat{r}_i$ until it is removed. Removed individuals can no longer be affected by the disease. A deterministic approximation as (as $K \rightarrow \infty$) to the empirical measure $\xi_K = \frac{1}{K} \sum^{aK}_{i=1} \delta_{(0,\hat{r}_i)} + \frac{1}{K} \sum^{bK}_{i=1} \delta_{(A^K_i, A^K_i + r_i)}$, describing the average path behavior, is established using Stein's method.


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Gesine Reinert. "The Asymptotic Evolution of the General Stochastic Epidemic." Ann. Appl. Probab. 5 (4) 1061 - 1086, November, 1995.


Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0851.60093
MathSciNet: MR1384366
Digital Object Identifier: 10.1214/aoap/1177004606

Primary: 60K30
Secondary: 60G57 , 92D30

Keywords: empirical measures , general stochastic epidemic , Stein's method

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 4 • November, 1995
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