Catastrophe Modelling for Time Series of Reported Cases of COVID-19: Workload Effects in the Health Care System

The COVID-19 pandemic exhibited some interesting temporal dynamics that were not accounted for by the traditional susceptible-infectious-recovered (SIR) family of epidemic time series models. The recorded number of positive tests increased and declined in waves from March 2020 to October 2021. Additional variability appeared around the peak of the waves. The present study examined the time series of positive medical tests reported by the public health system for one U.S. State. The wave patterns were consistent with the probability density function associated with the swallowtail catastrophe model. The excess variability was hypothesized to be indicative of workload stress in the health care system. The analysis of residuals from the swallowtail model was consistent with the probability density function of the cusp catastrophe model, which is known as a viable model for changes in system performance under conditions of changing workload. The two functions together accounted for 96% of the variance in daily positive test reports. A chaotic model was also tested as an alternative to the cusp. Although it contained some informative dynamics, it was not as accurate as the cusp interpretation. Implications for modeling and forecasting future epidemics are discussed.