Journal ArticleDOI
Poisson approximation for some epidemic models
Frank Ball,A. D. Barbour +1 more
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In this article, the authors extended the Daniels' Poisson limit theorem for the final size of a severe general stochastic epidemic to the Martin-Lof epidemic, and an order of magnitude for the error in the approximation was also given.Abstract:
The Daniels' Poisson limit theorem for the final size of a severe general stochastic epidemic is extended to the Martin-Lof epidemic, and an order of magnitude for the error in the approximation is also given. The argument consists largely of showing that the number of survivors of a severe epidemic is essentially the same as the number of isolated vertices in a random directed graph. Poisson approximation for the latter quantity is proved using the Stein–Chen method and a suitable coupling.read more
Citations
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Book ChapterDOI
Stochastic epidemic models for S-I-R infectious diseases: a brief survey of the recent general theory
TL;DR: This survey is intended to give a brief presentation of the recently published work on the general theory of stochastic epidemic models for an S-I-R infectious disease and to omit voluntarily the statistical aspects involved, the optimal or other control problems underlying and the “associated” deterministic approach.
References
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The outcome of a stochastic epidemic-a note on
TL;DR: In this paper, it was shown that for quite a general case these same probabilities may be obtained by the solution of a set of singly recurrent relations, which provides a stochastic equivalent to Kermack & McKendrick s threshold theorem.
Journal ArticleDOI
A Unified Approach to the Distribution of Total Size and Total Area under the Trajectory of Infectives in Epidemic Models
TL;DR: In this paper, a unified probabilistic approach to the distribution of total size and total area under the trajectory of infectives for a general stochastic epidemic with any specified distribution of the infectious period is provided.
Journal ArticleDOI
On the Asymptotic Distribution of the Size of a Stochastic Epidemic.
TL;DR: For a stochastic epidemic of the type considered by Bailey and Kendall as mentioned in this paper, the distribution of the number remaining uninfected in a large epidemic has approximately the Poisson form.