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 an d time but is measured as the average value over a region in space-tim e. As a particular example, we consider the incidence rate of the dise ase mumps; the reported data are given on a state-by-month basis (for the period 1968-1988). By using animation techniques together with var ious smoothing methods we make a sequence of successively smoother dyn amic maps which enable us to see the development of the disease in bot h space and time dimensions. We find that a smooth function (of the in cidence rates) is the best way to convey the behavior of the spread of the disease. We consider various scaling techniques, ways to smooth t he data, ways to estimate a smooth function of the incidence rates, an d 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 U nited States.