Parameterizing state–space models for infectious disease dynamics by generalized profiling: measles in Ontario
- 17 November 2010
- journal article
- Published by The Royal Society in Journal of The Royal Society Interface
- Vol. 8 (60), 961-974
- https://doi.org/10.1098/rsif.2010.0412
Abstract
Parameter estimation for infectious disease models is important for basic understanding (e.g. to identify major transmission pathways), for forecasting emerging epidemics, and for designing control measures. Differential equation models are often used, but statistical inference for differential equations suffers from numerical challenges and poor agreement between observational data and deterministic models. Accounting for these departures via stochastic model terms requires full specification of the probabilistic dynamics, and computationally demanding estimation methods. Here, we demonstrate the utility of an alternative approach, generalized profiling, which provides robustness to violations of a deterministic model without needing to specify a complete probabilistic model. We introduce novel means for estimating the robustness parameters and for statistical inference in this framework. The methods are applied to a model for pre-vaccination measles incidence in Ontario, and we demonstrate the statistical validity of our inference through extensive simulation. The results confirm that school term versus summer drives seasonality of transmission, but we find no effects of short school breaks and the estimated basic reproductive ratio ℛ 0 greatly exceeds previous estimates. The approach applies naturally to any system for which candidate differential equations are available, and avoids many challenges that have limited Monte Carlo inference for state–space models.Keywords
This publication has 52 references indexed in Scilit:
- Optimizing infectious disease interventions during an emerging epidemicProceedings of the National Academy of Sciences of the United States of America, 2009
- Reconstructing influenza incidence by deconvolution of daily mortality time seriesProceedings of the National Academy of Sciences of the United States of America, 2009
- Seasonality and comparative dynamics of six childhood infections in pre-vaccination CopenhagenProceedings. Biological sciences, 2009
- Plug-and-play inference for disease dynamics: measles in large and small populations as a case studyJournal of The Royal Society Interface, 2009
- Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in LondonJournal of The Royal Society Interface, 2008
- Parameter Estimation for Differential Equations: a Generalized Smoothing ApproachJournal of the Royal Statistical Society Series B: Statistical Methodology, 2007
- Inference for nonlinear dynamical systemsProceedings of the National Academy of Sciences of the United States of America, 2006
- Ecological and immunological determinants of dengue epidemicsProceedings of the National Academy of Sciences of the United States of America, 2006
- Strategies for mitigating an influenza pandemicNature, 2006
- Classic flea-borne transmission does not drive plague epizootics in prairie dogsProceedings of the National Academy of Sciences of the United States of America, 2006