Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19.

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

Long-ranged correlations in large deviations of local clustering.

In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realize large-deviation events. The bias acts on a single particle, but elicits a response that spans the whole system. We analyze this effect through the lens of macroscopic fluctuation theory, focusing on the coupling of the bias to hydrodynamic modes. This explains that the dynamical free energy has nontrivial scaling relationships with the system size, in 1 and 2 spatial dimensions. We show that the long-ranged response to a bias on one particle also has consequences when biasing two particles.

Predicting the dynamics of bacterial growth inhibition by ribosome-targeting antibiotics.

Understanding how antibiotics inhibit bacteria can help to reduce antibiotic use and hence avoid antimicrobial resistance-yet few theoretical models exist for bacterial growth inhibition by a clinically relevant antibiotic treatment regimen. In particular, in the clinic, antibiotic treatment is time-dependent. Here, we use a theoretical model, previously applied to steady-state bacterial growth, to predict the dynamical response of a bacterial cell to a time-dependent dose of ribosome-targeting antibiotic. Our results depend strongly on whether the antibiotic shows reversible transport and/or low-affinity ribosome binding ('low-affinity antibiotic') or, in contrast, irreversible transport and/or high affinity ribosome binding ('high-affinity antibiotic'). For low-affinity antibiotics, our model predicts that growth inhibition depends on the duration of the antibiotic pulse, and can show a transient period of very fast growth following removal of the antibiotic. For high-affinity antibiotics, growth inhibition depends on peak dosage rather than dose duration, and the model predicts a pronounced post-antibiotic effect, due to hysteresis, in which growth can be suppressed for long times after the antibiotic dose has ended. These predictions are experimentally testable and may be of clinical significance.