An example of the estimation and display of a smoothly varying function of time and space—The incidence of the disease mumps

We consider any quantity which varies as a smooth function of space and time but is measured as the average value over a region in space‐time. As a particular example, we consider the incidence rate of the disease mumps; the reported data are given on a state‐by‐month basis (for the period 1968–1988). By using animation techniques together with various smoothing methods we make a sequence of successively smoother dynamic maps which enable us to see the development of the disease in both space and time dimensions. We find that a smooth function (of the incidence rates) is the best way to convey the behavior of the spread of the disease. We consider various scaling techniques, ways to smooth the data, ways to estimate a smooth function of the incidence rates, and how to choose an appropriate color scale. This article also includes the description of algorithms to produce this kind of animation and a detailed description of the example concerning mumps disease in the United States. © 1994 John Wiley & Sons, Inc.