The threshold behaviour of epidemic models
- 1 June 1983
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (2) , 227-241
- https://doi.org/10.2307/3213797
Abstract
We provide a method of constructing a sequence of general stochastic epidemics, indexed by the initial number of susceptiblesN, from a time-homogeneous birth-and-death process. The construction is used to show strong convergence of the general stochastic epidemic to a birth-and-death process, over any finite time interval [0,t], and almost sure convergence of the total size of the general stochastic epidemic to that of a birth-and-death process. The latter result furnishes us with a new proof of the threshold theorem of Williams (1971). These methods are quite general and in the remainder of the paper we develop similar results for a wide variety of epidemics, including chain-binomial, host-vector and geographical spread models.Keywords
This publication has 14 references indexed in Scilit:
- A threshold theorem for the Reed-Frost chain-binomial epidemicJournal of Applied Probability, 1983
- Simpler proofs of two threshold theorems for a general stochastic epidemicJournal of Applied Probability, 1981
- Threshold limit theorems for some epidemic processesAdvances in Applied Probability, 1980
- On the spread of a disease with gamma distributed latent and infectious periodsBiometrika, 1980
- On the size distribution for some epidemic modelsJournal of Applied Probability, 1980
- Spatial Contact Models for Ecological and Epidemic SpreadJournal of the Royal Statistical Society Series B: Statistical Methodology, 1977
- An algebraic proof of the threshold theorem for the general stochastic epidemicAdvances in Applied Probability, 1971
- Some Stochastic Models for Small Epidemics in Large PopulationsJournal of the Royal Statistical Society Series C: Applied Statistics, 1964
- The Theory of Branching ProcessesPublished by Springer Nature ,1963
- DETERMINISTIC AND STOCHASTIC EPIDEMICS IN CLOSED POPULATIONSPublished by University of California Press ,1956