Backtracking: Improved methods for identifying the source of a deliberate release of Bacillus anthracis from the temporal and spatial distribution of cases

Reverse epidemiology is a mathematical modelling tool used to ascertain information about the source of a pathogen, given the spatial and temporal distribution of cases, hospitalisations and deaths. In the context of a deliberately released pathogen, such as Bacillus anthracis (the disease-causing organism of anthrax), this can allow responders to quickly identify the location and timing of the release, as well as other factors such as the strength of the release, and the realized wind speed and direction at release. These estimates can then be used to parameterise a predictive mechanistic model, allowing for estimation of the potential scale of the release, and to optimise the distribution of prophylaxis. In this paper we present two novel approaches to reverse epidemiology, and demonstrate their utility in responding to a simulated deliberate release of B. anthracis in ten locations in the UK and compare these to the standard grid-search approach. The two methods - a modified MCMC and a Recurrent Convolutional Neural Network - are able to identify the source location and timing of the release with significantly better accuracy compared to the grid-search approach. Further, the neural network method is able to do inference on new data significantly quicker than either the grid-search or novel MCMC methods, allowing for rapid deployment in time-sensitive outbreaks. Author summary In this paper we demonstrate three methods for estimating the source location and timing of a deliberate release of Bacillus anthracis based on the temporal and spatial distribution of cases. Two of our proposed methods, a modified MCMC approach and a neural network based approach, provide significant improvements over previous methods by directly addressing the problematic parameter-likelihood surface, and, in the case of the neural network approach, addressing the slow deployment speeds of existing methods. Our results represent a major step forward in the accuracy and speed of epidemiological back-calculation.