  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
taken roughly twice a week for 19 months. Fitting our model to data is
challenging due to the large state space of our model. We develop an efficient
SMC$^2$ 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, which means we can define and fit our model for a population on the
order of tens of thousands of individuals rather than millions. Our motivating
application focuses on the dynamics of community-acquired Extended-Spectrum
Beta-Lactamase-producing Escherichia coli (E. coli) and Klebsiella pneumoniae
(K. 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.
