Approximation of epidemics by inhomogeneous birth-and-death processes

Approximation of epidemics by inhomogeneous birth-and-death processes

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Article ID: iaor19992716
Country: Netherlands
Volume: 73
Issue: 2
Start Page Number: 233
End Page Number: 245
Publication Date: Mar 1998
Journal: Stochastic Processes and Their Applications
Authors: ,
Keywords: epidemiology
Abstract:

This paper is concerned with the approximation of a class of open population epidemic models by time-inhomogeneous birth-and-death processes. In particular, we consider models in which the population of susceptibles behaves in the absence of infection as a general branching process. It is shown that for a large initial number of susceptibles, the process of infectives behaves approximately as a time-inhomogeneous birth-and-death process. Strong convergence results are obtained over an increasing sequence of time intervals [0, tN], where N is the initial number of susceptibles and tN → ∞ as N → ∞.

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