zbMATH — the first resource for mathematics

Approximating the Reed-Frost epidemic process. (English) Zbl 1113.92054
Summary: The paper is concerned with refining two well-known approximations to the Reed-Frost epidemic process. The first is the branching process approximation in the early stages of the epidemic; we extend its range of validity, and sharpen the estimates of the error incurred. The second is the normal approximation to the distribution of the final size of a large epidemic, which we complement with a detailed local limit approximation. The latter, in particular, is relevant if the approximations are to be used for statistical inference.

92D30 Epidemiology
60J85 Applications of branching processes
60F05 Central limit and other weak theorems
PDF BibTeX Cite
Full Text: DOI
[1] Ball, F.G.; Donnelly, P., Strong approximations for epidemic models, Stochastic. process. appl., 55, 1-21, (1995) · Zbl 0823.92024
[2] F. Ball, O. Lyne, Parameter estimation for SIR epidemics in households, Bulletin of the International Statistical Institution, 52nd Session Contributed Papers, Vol. LVIII, Book 2, 1999, pp. 251-252.
[3] Barraez, D.; Boucheron, S.; Fernandez de la Vega, W., On the fluctuations of the giant component, Combin. probab. comput., 9, 287-304, (2000) · Zbl 0969.05054
[4] Britton, T.; Becker, N.G., Design issues for studies of infectious diseases, J. statist. plan. inference, 96, 41-66, (2001) · Zbl 0972.62102
[5] Lefèvre, Cl.; Utev, S., Poisson approximation for the final state of a generalized epidemic process, Ann. probab., 23, 1139-1162, (1995) · Zbl 0833.60023
[6] Lefèvre, Cl.; Utev, S., Branching approximation for the collective epidemic model, Method. comput. appl. probab., 1, 211-228, (1999) · Zbl 0966.92023
[7] Martin-Löf, A., Symmetric sampling procedures, general epidemic processes and their threshold limit theorems, J. appl. probab., 23, 265-282, (1986) · Zbl 0605.92009
[8] Pollard, D., Convergence of stochastic processes, (1984), Springer New York · Zbl 0544.60045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.