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Limiting results for carrier-borne epidemics

Published online by Cambridge University Press:  14 July 2016

Roy Saunders
Roy Saunders*
Affiliation:
State University of New York at Buffalo
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Abstract

In this article we examine the behavior of Mm(τ), the number of susceptibles remaining uninfected at time τ in a carrier-borne epidemic as the initial number of susceptibles m tends to infinity for fixed initial number of carriers n. We show that as m → ∞ the proportion of susceptibles process {Mm(τ)/m : ≧ 0} converges weakly to a limiting process. The limiting process has sample functions almost surely of the form exp (– h(τ)), where the form of h(τ) is determined by the removal times of the carriers.

Keywords

CARRIER-BORNE EPIDEMICPROPORTION OF SUSCEPTIBLESLIMITING PROCESSSAMPLE PATHWEAK CONVERGENCE
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 793 - 799
Copyright
Copyright © Applied Probability Trust 1975 

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References

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