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The exact and asymptotic formulas for the state probabilities in simple epidemics with m kinds of susceptibles

Published online by Cambridge University Press:  14 July 2016

H. Lacayo  and
Naftali A. Langberg
H. Lacayo*
Affiliation:
Bureau of Labor Statistics
Naftali A. Langberg*
Affiliation:
University of Haifa
*
∗Postal address: Bureau of Labor Statistics, G.A.O. Building, Room 2146, 441 G St N.W., Washington, DC 20212, U.S.A.
∗∗Postal address: Department of Statistics, University of Haifa, Mount Carmel, Haifa 31 999, Israel.
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Abstract

A population of susceptible individuals partitioned into m groups and exposed to a contagious disease is considered.

The progress of this simple epidemic is modeled by an m -dimensional stochastic process, whose components are the number of infective individuals in the respective groups at time t. Exact and approximate formulas for the joint and marginal state probabilities are obtained.

Keywords

SIMPLE EPIDEMICSDIFFERENT LEVELS OF SUSCEPTIBILITYCONVERGENCE IN DISTRIBUTIONEXPONENTIALNEGATIVE BINOMIALMULTINOMIAL DISTRIBUTIONS
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 1 - 9
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research sponsored by the National Institute of Environmental Health Sciences, under Grant 5-T32-HS007011.

Research supported by the United States Army Research Office, Durham, under Grant No. DAAG29-79 C0158.

References

Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases. Hafner, New York.Google Scholar
Billard, L., Lacayo, H. and Langberg, N. A. (1980) Generalizations of the simple epidemic process. J. Appl. Prob. 17, 1072–1078.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Gart, J. J. (1968) The mathematical analysis of an epidemic with two kinds of susceptibles. Biometrics 24, 557–566.CrossRefGoogle ScholarPubMed
Gart, J. J. (1972) The statistical analysis of chain-binomial epidemic models with several kinds of susceptibles. Biometrics 28, 921–930.CrossRefGoogle Scholar
Langberg, N. A. (1980) The convergence in distribution of some simple epidemics. Math. Biosci. 50, 275–284.CrossRefGoogle Scholar
Loève, ?. (1963) Probability Theory. Van Nostrand, Princeton, NJ.Google Scholar
Mcneil, D. R. (1972) On the simple stochastic epidemic. Biometrika 59, 494–497.CrossRefGoogle Scholar
Severo, N. C. (1969) Generalizations of some stochastic epidemic models. Math. Biosci. 4, 395–402.CrossRefGoogle Scholar