Inference on extended-spectrum beta-lactamase Escherichia coli and Klebsiella pneumoniae data through SMC²

We propose a novel stochastic model for the spread of antimicrobial-resistant bacteria in a population, together with an efficient algorithm for fitting such a model to sample data. We introduce an individual-based model for the epidemic, with the state of the model determining which individuals are colonised by the bacteria. The transmission rate of the epidemic takes into account both individuals' locations, individuals' covariates, seasonality, and environmental effects. The state of our model is only partially observed, with data consisting of test results from individuals from a sample of households. Fitting our model to data is challenging due to the large state space of our model. We develop an efficient SMC2 algorithm to estimate parameters and compare models for the transmission rate. We implement this algorithm in a computationally efficient manner by using the scale invariance properties of the underlying epidemic model. Our motivating application focuses on the dynamics of community-acquired extended-spectrum beta-lactamase-producing Escherichia coli and Klebsiella pneumoniae, using data collected as part of the Drivers of Resistance in Uganda and Malawi project. We infer the parameters of the model and learn key epidemic quantities such as the effective reproduction number, spatial distribution of prevalence, household cluster dynamics, and seasonality.