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Note that there are many data points out in front of the modelled front: this model was actually fit using data of the form (xi,yi,ti), where ti is the date of the first confirmed case in town i. This is an important source of bias: by the time a case is confirmed, several months may have gone by with rabies existing in the town.
Note also the voids in the wake of the front: the hypothesized reason is that the epidemic decimates the local raccoon population, so the number of reported cases is consequently very low. After many months, the raccoon population rebounds somewhat, but rabies continues to exact a toll. After the front has passed, rabies "percolates" about the state.