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A nonlinear programming approach for estimation of transmission parameters in childhood infectious disease using a continuous time model

Word, DP and Cummings, DAT and Burke, DS and Iamsirithaworn, S and Laird, CD (2012) A nonlinear programming approach for estimation of transmission parameters in childhood infectious disease using a continuous time model. Journal of the Royal Society Interface, 9 (73). 1983 - 1987. ISSN 1742-5689

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Abstract

Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches. © 2012 The Royal Society.


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Details

Item Type: Article
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Word, DP
Cummings, DAT
Burke, DSdonburke@pitt.eduDONBURKE
Iamsirithaworn, S
Laird, CD
Centers: Other Centers, Institutes, or Units > Center for Vaccine Research
Date: 7 August 2012
Date Type: Publication
Journal or Publication Title: Journal of the Royal Society Interface
Volume: 9
Number: 73
Page Range: 1983 - 1987
DOI or Unique Handle: 10.1098/rsif.2011.0829
Schools and Programs: Graduate School of Public Health > Epidemiology
Refereed: Yes
ISSN: 1742-5689
Date Deposited: 07 May 2015 19:06
Last Modified: 13 Oct 2017 18:55
URI: http://d-scholarship.pitt.edu/id/eprint/24606

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