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A Bayesian framework for parameter estimation in dynamical models.

Coelho FC, Codeço CT, Gomes MG - PLoS ONE (2011)

Bottom Line: Mathematical models in biology are powerful tools for the study and exploration of complex dynamics.This problem has been addressed over the years by many tools for model calibration and parameter estimation.In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used.

View Article: PubMed Central - PubMed

Affiliation: Instituto Gulbenkian de Ciência, Oeiras, Portugal. fccoelho@fgv.br

ABSTRACT
Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.

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Belgian incidence data and model fit.Incidence median curve (black line) and 95% credible intervals (shaded area) for the model-generated incidence series. The model was fitted simultaneously to Influenzanet data (green circles) and EISN data (red triangles).
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pone-0019616-g001: Belgian incidence data and model fit.Incidence median curve (black line) and 95% credible intervals (shaded area) for the model-generated incidence series. The model was fitted simultaneously to Influenzanet data (green circles) and EISN data (red triangles).

Mentions: Figures 1, 2 and 3 show the fit of the model against data from both Influenzanet and EISN for the three countries. The model was able attain a good fit to the data, allowing for reasonably precise estimate of the parameters (table 1). We have performed some consistency checks on the estimates obtained (not shown). In particular we have found a positive correlation between the fraction of infections that are symptomatic in a given season () and the time of the epidemic peak (measured from September 1st), suggesting a role of weather factors in the performance of influenza surveillance systems, which is further explored in van Noort et al. [24] by combining data from other sources. Although here we chose the simplest model formulation for the purpose of illustration of the parameter estimation method, the results are compatible with other studies. Moreover, the procedure is readily applicable to more elaborate models.


A Bayesian framework for parameter estimation in dynamical models.

Coelho FC, Codeço CT, Gomes MG - PLoS ONE (2011)

Belgian incidence data and model fit.Incidence median curve (black line) and 95% credible intervals (shaded area) for the model-generated incidence series. The model was fitted simultaneously to Influenzanet data (green circles) and EISN data (red triangles).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3101204&req=5

pone-0019616-g001: Belgian incidence data and model fit.Incidence median curve (black line) and 95% credible intervals (shaded area) for the model-generated incidence series. The model was fitted simultaneously to Influenzanet data (green circles) and EISN data (red triangles).
Mentions: Figures 1, 2 and 3 show the fit of the model against data from both Influenzanet and EISN for the three countries. The model was able attain a good fit to the data, allowing for reasonably precise estimate of the parameters (table 1). We have performed some consistency checks on the estimates obtained (not shown). In particular we have found a positive correlation between the fraction of infections that are symptomatic in a given season () and the time of the epidemic peak (measured from September 1st), suggesting a role of weather factors in the performance of influenza surveillance systems, which is further explored in van Noort et al. [24] by combining data from other sources. Although here we chose the simplest model formulation for the purpose of illustration of the parameter estimation method, the results are compatible with other studies. Moreover, the procedure is readily applicable to more elaborate models.

Bottom Line: Mathematical models in biology are powerful tools for the study and exploration of complex dynamics.This problem has been addressed over the years by many tools for model calibration and parameter estimation.In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used.

View Article: PubMed Central - PubMed

Affiliation: Instituto Gulbenkian de Ciência, Oeiras, Portugal. fccoelho@fgv.br

ABSTRACT
Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.

Show MeSH
Related in: MedlinePlus