 The great circle epidemic modelFrank Ball and Peter Neal Stochastic Processes and their Applications, 2003, vol. 107, issue 2, 233-268 Abstract: We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n-->[infinity] is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n-->[infinity] by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution. Keywords: Branching; process; Central; limit; theorems; Coupling; Epidemic; process; Small-world; models; Weak; convergence (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:107:y:2003:i:2:p:233-268 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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