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.
Highlights
Mathematical models have long played a key role in understanding infectious disease epidemiology [1] as well as other biological dynamical systems
Proper representation of the intrinsic uncertainty associated with dynamic models of biological systems has been under increasing scrutiny through the development of a number of methods for parameter estimation and model calibration [3,4,5,6,7,8,9,10]
In this paper we introduce a Bayesian framework for parameter estimation in dynamic models that is applicable to both deterministic and stochastic models [15]
Summary
Mathematical models have long played a key role in understanding infectious disease epidemiology [1] as well as other biological dynamical systems. The fitting process estimates the posterior probability distributions for both the model’s parameters and output series. The dynamic model, from the point of view of the inference machinery, is treated as a ‘‘black box’’ with inputs (parameters) and outputs (time-series), and the full uncertainty about each of these elements can be included in the form of prior distributions which will get updated based on observational data.
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