Parameterization and Model Validation

The usefulness of any model and the reliability of its predictions depend on its veracity. Thus, models need to be carefully based on ground truths, a process that is made particularly challenging for high-dimensional age-structured models because a fundamental challenge to the effective parameterization of age-specific models is determination of the appropriate patterns of contact by age. It is fortunate that recent studies have addressed this problem, and detailed information on the typically age-stratified patterns of contact in the United States (Del Valle et al., 2007) and a number of European countries (Mossong et al., 2008) is now available. Synthesis of this information together with historical incidence data to formulate validated transmission models is made possible by the use of modern inference techniques, including sequential Monte Carlo methods for hypothesis testing (Ionides et al., 2006). An example is the age-structured pertussis model developed by Rohani et al. (2010) and parameterized with data from incidence reports from Sweden.

Data Needs

The production of fully validated transmission models requires access to age-specific incidence reports. This is often a critical bottleneck in such an endeavor, as public health agencies (e.g., CDC) do not routinely provide such complete data via, for instance, the National Notifiable Diseases Surveillance System (Goldwyn and Rohani, 2012). When detailed incidence reports, stratified by age, county, and immunization status (e.g., through the Supplementary Pertussis Surveillance System), do become available, requests for access to such data are not always granted in a timely manner, and may be answered with the provision of data that was not obtained using the best-available methods (Thacker et al., 2012).

Quantifying Uncertainty and Sensitivity

The predictions of any formal modeling analyses need to be evaluated within the context of their inherent variability and should be subject to extensive sensitivity analyses (Blower, 2000). Uncertainty in predictions can be quantified by use of a wide array of rigorous probabilistic approaches to model execution, whereby the system of equations is translated into a Markov chain process (Gibson and Bruck, 2000; Gillespie, 1977; Keeling and Rohani, 2008). Such an approach would permit a detailed situational analysis, whereby the model could provide policy makers with information on the most likely (i.e., the median) outcome, for example, the size of the focal vaccine-preventable disease outbreak given a specific change in the



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