Abstract
Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of these simplifications, the model output, of, say, new cases of a disease over time or when an epidemic will occur, may be inconsistent with the available data. In this case, we must improve the model, especially if we plan to make decisions based on it that could affect human health and safety, but direct improvements are often beyond our reach. In this work, we explore this problem through a case study of the Zika outbreak in Brazil in 2016. We propose an embedded discrepancy operator-a modification to the model equations that requires modest information about the system and is calibrated by all relevant data. We show that the new enriched model demonstrates greatly increased consistency with real data. Moreover, the method is general enough to easily apply to many other mathematical models in epidemiology.
Highlights
Mathematical models of scientific systems necessarily include simplifications about the actual system they aim to represent
We show that including the embedded discrepancy operator greatly increases the fidelity of the model so that the model output and real data are consistent
The quintessential example of this comes from the domain of classical mechanics: Newtonian mechanics ignores quantum and relativistic effects but, over a wide domain of masses and energies, provides a completely adequate model to scitation.org/journal/cha describe the motion of macroscopic objects
Summary
Mathematical models of scientific systems necessarily include simplifications about the actual system they aim to represent. Without accounting for the discrepancy, one cannot trust the model output, much less use it to make predictions or decisions In this case, there are two immediate options: (1) improve the model directly, i.e., from first principles or by including additional information and (2) represent the model discrepancy itself. A response discrepancy function builds a better interpolation to a single dataset over the range of usable data This approach provides no basis for extrapolation to, for example, make a prediction about the probability of an epidemic year. In this paper, we show how to modify equations directly to account for the model error with an embedded discrepancy operator The advantages of this approach are threefold: 1. 2. (Domain-)Consistency: Information or constraints about the system can be incorporated into the discrepancy operator
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