Abstract
Most of the growing prospective analytic methods in space-time disease surveillance and intended functions of disease surveillance systems focus on earlier detection of disease outbreaks, disease clusters, or increased incidence. The spread of the virus such as SARS-CoV-2 has not been spatially and temporally uniform in an outbreak. With the identification of an infectious disease outbreak, recognizing and evaluating anomalies (excess and decline) of disease incidence spread at the time of occurrence during the course of an outbreak is a logical next step. We propose and formulate a hypergeometric probability model that investigates anomalies of infectious disease incidence spread at the time of occurrence in the timeline for many geographically described populations (e.g., hospitals, towns, counties) in an ongoing daily monitoring process. It is structured to determine whether the incidence grows or declines more rapidly in a region on the single current day or the most recent few days compared to the occurrence of the incidence during the previous few days relative to elsewhere in the surveillance period. The new method uses a time-varying baseline risk model, accounting for regularly (e.g., daily) updated information on disease incidence at the time of occurrence, and evaluates the probability of the deviation of particular frequencies to be attributed to sampling fluctuations, accounting for the unequal variances of the rates due to different population bases in geographical units. We attempt to present and illustrate a new model to advance the investigation of anomalies of infectious disease incidence spread by analyzing subsamples of spatiotemporal disease surveillance data from Taiwan on dengue and COVID-19 incidence which are mosquito-borne and contagious infectious diseases, respectively. Efficient R programs for computation are available to implement the two approximate formulae of the hypergeometric probability model for large numbers of events.