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Updated: May 19, 2026

Experimental Viral Infection in Adult Mosquitoes by Oral Feeding and Microinjection
Published on: July 28, 2022
Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem
Mark Pollicott1, Hao Wang, Howard Howie Weiss
1Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK. mpollic@maths.warwick.ac.uk
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.
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