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Extracting the timedependent transmission rate from infection data via solution of an inverse ODE problem
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Pollicott, Mark, Wang, Hao and Weiss, Howard. (2012) Extracting the timedependent transmission rate from infection data via solution of an inverse ODE problem. Journal of Biological Dynamics, Vol.6 (No.2). pp. 509523. ISSN 17513758

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Official URL: http://dx.doi.org/10.1080/17513758.2011.645510
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 timedependent 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 SIRtype 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:  17513758 
Date:  2012 
Volume:  Vol.6 
Number:  No.2 
Page Range:  pp. 509523 
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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