# Real-time inference of the end of an outbreak: Temporally aggregated disease incidence data and under-reporting

## TL;DR

This paper uses a mathematical model to determine when it is safe to stop public health interventions during the end of an infectious disease outbreak, considering under-reporting of cases.

## Contribution

A method to account for under-reporting in real-time decisions about ending outbreak interventions using a renewal equation transmission model.

## Key findings

- Daily and weekly case reports yield similar estimates for the probability of future cases.
- Lower case reporting requires waiting longer before safely ending interventions.
- Uncertainty in case reporting can be incorporated into probability estimates.

## Abstract

Professor Pierre Magal made important contributions to the field of mathematical biology before his death on February 20, 2024, including research in which epidemiological models were used to study the ends of infectious disease outbreaks. In related work, there has been interest in inferring (in real-time) when outbreaks have ended and control interventions can be relaxed. Here, we analyse data from the 2018 Ebola outbreak in Équateur Province, Democratic Republic of the Congo, during which an Ebola Response Team (ERT) was deployed to implement public health measures. We use a renewal equation transmission model to perform a quasi real-time investigation into when the ERT could be withdrawn safely at the tail end of the outbreak. Specifically, each week following the arrival of the ERT, we calculate the probability of future cases if the ERT is withdrawn. First, we show that similar estimates of the probability of future cases can be obtained from either daily or weekly case reports. This demonstrates that high temporal resolution case reporting may not always be necessary to determine when interventions can be relaxed. Second, we demonstrate how case under-reporting can be accounted for rigorously when estimating the probability of future cases. We find that, the lower the level of case reporting, the longer it is necessary to wait after the apparent final case before interventions can be removed safely (with only a small probability of additional cases). Finally, we show how uncertainty in the extent of case reporting can be included in estimates of the probability of future cases. Our research highlights the importance of accounting for under-reporting in deciding when to remove interventions at the tail ends of infectious disease outbreaks.