iPAR: A framework for modelling and inferring information about disease spread when the populations at risk are unknown

We introduce the inference for populations at risk (iPAR) framework which enables modelling and estimation of spatial disease dynamics in scenarios where the population at risk is unknown or poorly quantified. This framework addresses a gap in spatial infectious disease modelling approaches, with current methods typically requiring knowledge of the spatial distribution of the population at risk or making simplifying assumptions that are not supported in many real-world outbreaks where only case-report data are available. The principles for iPAR are demonstrated in the context of a susceptible-infected disease dynamics model coupled with Bayesian inference implemented via data-augmentation Markov chain Monte Carlo (MCMC). This implementation of iPAR is tested for a range of scenarios using simulated outbreak data. Results indicate that the method can effectively estimate key properties of disease spread from spatio-temporal case reports and make useful predictions of future spread. The method is then applied to a case study exploring the 2015-2019 Estonian outbreak of African Swine Fever (ASF) in wild boar. Estimates of epidemiological parameters reveal evidence for long distance transmission, as well as disease control via reduction of the wild boar population in Estonia.