Estimating transmission heterogeneity and case ascertainment from variations in case counts in surveillance data

Introduction: The reported numbers of infectious disease case counts in surveillance data typically show considerable variation. This variation is a result of the process and observation noise. The process noise stems from the stochastic element of transmission at the individual level, i.e., the overdispersion of secondary cases. The observation noise results from variations in testing uptake and the sampling error. Our objective was to better understand how the process and observation noise shape the observed variation in infectious disease case counts in surveillance data. Methods: We derived a mechanistic model of the data generating process of infectious disease case counts in surveillance data that incorporates a negative binomial offspring distribution for individual cases and the binomial sampling error from the observation process. We validated the model using data from stochastic simulations of SARS-CoV-2 transmission and case ascertainment. Finally, we applied the model to SARS-CoV-2 surveillance data from Switzerland. Results: Assuming a constant observation probability, we showed that the daily numbers of reported cases in surveillance data are expected to follow a quasi Poisson distribution. The overdispersion in reported cases is a function of the expected number of cases, the effective reproduction number, the overdispersion in secondary cases k, and the observation probability. Using simulated data, we found that one can estimate the overdispersion in secondary cases when the observation probability is known, or vice versa. We illustrated this property with data from the SARS-CoV-2 epidemic in Switzerland from 2020 to 2022. Using previous estimates for the overdispersion in secondary cases, we were able to estimate and track the upper bound of the observation probability of SARS-CoV-2 over time. Discussion: We showed how the process noise at the individual level of transmission and the observation noise result in the observed variation in infectious disease case counts in surveillance data. Conclusion: Our model has the potential to continuously monitor either the transmission heterogeneity or the case ascertainment for various infectious diseases from routine surveillance data.