The Library
Simple approximations for epidemics with exponential and fixed infectious periods
Tools
Fowler, A. C. and Hollingsworth, T. Déirdre (2015) Simple approximations for epidemics with exponential and fixed infectious periods. Bulletin of mathematical biology, 77 (8). pp. 1539-1555. doi:10.1007/s11538-015-0095-3 ISSN 0092-8240.
|
PDF
WRAP_Simple_approximations_epidemics..pdf - Accepted Version - Requires a PDF viewer. Download (473Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s11538-015-0095-3
Abstract
Analytical approximations have generated many insights into the dynamics of epidemics, but there is only one well-known approximation which describes the dynamics of the whole epidemic. In addition, most of the well-known approximations for different aspects of the dynamics are for the classic susceptible–infected–recovered model, in which the infectious period is exponentially distributed. Whilst this assumption is useful, it is somewhat unrealistic. Equally reasonable assumptions are that the infectious period is finite and fixed or that there is a distribution of infectious periods centred round a nonzero mean. We investigate the effect of these different assumptions on the dynamics of the epidemic by deriving approximations to the whole epidemic curve. We show how the well-known sech-squared approximation for the infective population in ‘weak’ epidemics (where the basic reproduction rate R0≈1) can be extended to the case of an arbitrary distribution of infectious periods having finite second moment, including as examples fixed and gamma-distributed infectious periods. Further, we show how to approximate the time course of a ‘strong’ epidemic, where R0≫1, demonstrating the importance of estimating the infectious period distribution early in an epidemic.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | R Medicine > RA Public aspects of medicine | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Life Sciences (2010- ) Faculty of Science, Engineering and Medicine > Science > Mathematics |
||||||||
Library of Congress Subject Headings (LCSH): | Epidemics, Communicable diseases -- Transmission | ||||||||
Journal or Publication Title: | Bulletin of mathematical biology | ||||||||
Publisher: | Springer New York LLC | ||||||||
ISSN: | 0092-8240 | ||||||||
Official Date: | 3 September 2015 | ||||||||
Dates: |
|
||||||||
Volume: | 77 | ||||||||
Number: | 8 | ||||||||
Number of Pages: | 18 | ||||||||
Page Range: | pp. 1539-1555 | ||||||||
DOI: | 10.1007/s11538-015-0095-3 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 28 July 2016 | ||||||||
Date of first compliant Open Access: | 3 September 2016 | ||||||||
Funder: | Science Foundation Ireland (SFI), Imperial College, London | ||||||||
Grant number: | 12/1A/1683 (SFI) |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year