Pollicott, Mark, Wang, Hao and Weiss, Howard. (2012) Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem. Journal of Biological Dynamics, Vol.6 (No.2). pp. 509-523. ISSN 1751-3758

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Abstract

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > RA Public aspects of medicine
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Communicable diseases -- Transmission -- Mathematical models
Journal or Publication Title:	Journal of Biological Dynamics
Publisher:	Taylor & Francis Ltd.
ISSN:	1751-3758
Date:	2012
Volume:	Vol.6
Number:	No.2
Page Range:	pp. 509-523
Identification Number:	10.1080/17513758.2011.645510
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/52247

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