On the application of integer-valued time series models for the analysis of disease incidence

Statistical time series models are practical tools in public health surveil lance. Their capacity to forecast future disease incidence values exemplifi es their usefulness. Using these forecasts, one can develop strategies to t rigger alerts to public health officials when irregular disease incidence v alues have occurred. Clearly, the better the forecasting performance of the model class used in the time series analysis, the more realistic are the a lerts triggered. The time series analysis of disease incidence values has o ften entailed the Box and Jenkins model class. However, this class was desi gned to model real-valued variables whereas disease incidences are integer- valued variables. A new class of time series models, called integer-valued autoregressive models, has been developed and studied over the past decade. The objective of this paper is to introduce this new class of models to th e application of time series analysis of infectious disease incidence, and to demonstrate its advantages over the class of real-valued Box and Jenkins models. The paper also presents a bootstrap method developed for the calcu lation of forecast interval limits. Copyright (C) 1999 John Wiley & Sons, L td.