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A carrier-borne epidemic with multiple stages of infection

Published online by Cambridge University Press:  14 July 2016

J. Gani  and
Gy. Michaletzky
J. Gani*
Affiliation:
University of California, Santa Barbara
Gy. Michaletzky*
Affiliation:
University Eötvös L.
*
∗Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA.
∗∗Postal address: University Eötvös L., Department of Probability Theory and Statistics, 1088 Museum Krt 6–8, Budapest, VIII ker, Hungary.
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Abstract

This paper considers a carrier-borne epidemic in continuous time with m + 1 > 2 stages of infection. The carriers U(t) follow a pure death process, mixing homogeneously with susceptibles X0(t), and infectives Xi(t) in stages 1≦i≦m of infection. The infectives progress through consecutive stages of infection after each contact with the carriers. It is shown that under certain conditions {X0(t), X1(t), · ··, Xm(t) U(t); t≧0} is an (m + 2)-variate Markov chain, and the partial differential equation for its probability generating function derived. This can be solved after a transfomation of variables, and the probability of survivors at the end of the epidemic found.

Keywords

CARRIERSUSCEPTIBLESTAGE i INFECTIVEPROBABILITY OF SURVIVAL
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 1 - 8
Copyright
Copyright © Applied Probability Trust 1991 

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