 Strong approximations for epidemic modelsFrank Ball and Peter Donnelly Stochastic Processes and their Applications, 1995, vol. 55, issue 1, 1-21 Abstract: This paper is concerned with the approximation of early stages of epidemic processes by branching processes. A general model for an epidemic in a closed, homogeneously mixing population is presented. A construction of a sequence of such epidemics, indexed by the initial number of susceptibles N, from the limiting branching process is described. Strong convergence of the epidemic processes to the branching process is shown when the latter goes extinct. When the branching process does not go extinct, necessary and sufficient conditions on the sequence (tN) for strong convergence over the time interval [0, tN] are provided. Convergence of a wide variety of functionals of the epidemic process to corresponding functionals of the branching process is shown, and bounds are provided on the total variation distance for given N. The theory is illustrated by reference to the general stochastic epidemic. Generalisations to, for example, multipopulation epidemics are described briefly. Keywords: Coupling; Total; variation; distance; General; branching; process; General; stochastic; epidemic (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:55:y:1995:i:1:p:1-21 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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