Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

Mark Pollicott, Hao Wang, Howard Weiss

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)509-523
Number of pages15
JournalJournal of Biological Dynamics
Volume6
Issue number2
DOIs
StatePublished - Mar 2012

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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