The threshold behaviour of epidemic models
Keyword(s):
We provide a method of constructing a sequence of general stochastic epidemics, indexed by the initial number of susceptibles N, from a time-homogeneous birth-and-death process. The construction is used to show strong convergence of the general stochastic epidemic to a birth-and-death process, over any finite time interval [0, t], and almost sure convergence of the total size of the general stochastic epidemic to that of a birth-and-death process. The latter result furnishes us with a new proof of the threshold theorem of Williams (1971). These methods are quite general and in the remainder of the paper we develop similar results for a wide variety of epidemics, including chain-binomial, host-vector and geographical spread models.
1983 ◽
Vol 20
(02)
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pp. 227-241
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2001 ◽
Vol 38
(01)
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pp. 18-35
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1986 ◽
Vol 23
(03)
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pp. 832-836
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Keyword(s):
Keyword(s):