Susceptibility sets and the final outcome of collective Reed–Frost epidemics

Ball, Frank

Abstract

This paper is concerned with exact results for the final outcome of stochastic SIR (susceptible → infective → recovered) epidemics among a closed, finite and homogeneously mixing population. The factorial moments of the number of initial susceptibles who ultimately avoid infection by such an epidemic are shown to be intimately related to the concept of a susceptibility set. This connection leads to simple, probabilistically illuminating proofs of exact results concerning the total size and severity of collective Reed–Frost epidemic processes, in terms of Gontcharoff polynomials, first obtained in a series of papers by Claude Lef`evre and Philippe Picard. The proofs extend easily to include general final state random variables defined on SIR epidemics, and also to multitype epidemics.

Citation

Ball, F. (2019). Susceptibility sets and the final outcome of collective Reed–Frost epidemics. Methodology and Computing in Applied Probability, 21(2), 401–421. https://doi.org/10.1007/s11009-018-9631-6

• Journal Article Type: Article
• Acceptance Date: Mar 19, 2018
• Online Publication Date: Apr 4, 2018
• Publication Date: 2019-06
• Deposit Date: Mar 20, 2018
• Publicly Available Date: Apr 4, 2018
• Journal: Methodology and Computing in Applied Probability
• Print ISSN: 1387-5841
• Electronic ISSN: 1573-7713
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 2
• Pages: 401–421
• DOI: https://doi.org/10.1007/s11009-018-9631-6
• Keywords: Total size; Severity; Susceptibility set; Symmetric sampling procedure; Gontcharoff polynomial; General final state random variables
• Public URL: https://nottingham-repository.worktribe.com/output/923801
• Publisher URL: https://link.springer.com/article/10.1007/s11009-018-9631-6