We can invert either the dispersion model alone or a combined model that includes the dispersion model and a model of the effects of aerosol cloud of biological agent (Figure 19.5). We refer to the former inversion as two-stage inversion because we must invert the aerosol effects model and the dispersion model separately. The inverted aerosol-effects model— using biosurveillance data as input—estimates downwind concentrations for input into the inverted dispersion model. We refer to the inversion of the combined model (that includes a dispersion model) as one-stage inversion. It does not require computing downwind concentrations, but instead involves estimation of release parameters directly from biosurveillance data.
There are two possible approaches to inverting a model, whether it is the dispersion model, the aerosol effects (or disease) model, or a model that is a combination of the two. The first—to invert them algebraically by solving a system of equations with release parameters as unknowns—is usually not possible. Another method of inversion is to employ a search: try thousands of combinations of values for the release parameters and output the parameters that best explain either downwind concentrations or the biosurveillance data. This device requires a measurement of how well a set of parameters explain downwind concentrations or biosurveillance data. All but one of the approaches we describe in this section use probability as a measurement.
We next describe examples of two-stage and one-stage inverted models. The work is preliminary and the improvement in outbreak detection performance (if any) that the models provide over other outbreak detection algorithms is not yet known.
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