Journal article
Approximating the epidemic curve
AD Barbour, G Reinerty
Electronic Journal of Probability | INST MATHEMATICAL STATISTICS-IMS | Published : 2013
DOI: 10.1214/EJP.v18-2557
Abstract
Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susceptible follows a more or less deterministic course. In this paper, we show that both of these features are consequences of assuming a locally branching structure in the models, and that the deterministic course can itself be determined from the distribution of the limiting random variable associated with the backward, susceptibility branching process. Examples considered include a stochastic version of the Kermack & McKendrick model, the Reed-Fro..
View full abstractRelated Projects (2)
Grants
Awarded by Engineering and Physical Sciences Research Council
Funding Acknowledgements
This work was carried out in part while ADB was Saw Swee Hock Professor of Statistics at the National University of Singapore. ADB was supported in part by Australian Research Council Grants Nos DP120102728 and DP120102398. We are grateful to Peter Jagers, Hans Heesterbeek and Odo Diekmann for a number of helpful discussions, and to the referees for their pertinent comments. ADB thanks the mathematics departments of the University of Melbourne, Monash University and the University of Queensland, and the Department of Statistics and Applied Probability and the Institute for Mathematical Sciences at the National University of Singapore, for their kind hospitality while part of the work was undertaken. GDR thanks EPSRC, the BBSRC and the Oxford Martin School for their support.