An efficient moments-based inference method for within-host bacterial infection dynamics

Abstract

Over the last ten years, isogenic tagging (IT) has revolutionised the study of bacterial infection dynamics in laboratory animal models. However, quantitative analysis of IT data has been hindered by the piecemeal development of relevant statistical models. The most promising approach relies on stochastic Markovian models of bacterial population dynamics within and among organs. Here we present an efficient numerical method to fit such stochastic dynamic models to in vivo experimental IT data. A common approach to statistical inference with stochastic dynamic models relies on producing large numbers of simulations, but this remains a slow and inefficient method for all but simple problems, especially when tracking bacteria in multiple locations simultaneously. Instead, we derive and solve the systems of ordinary differential equations for the two lower-order moments of the stochastic variables (mean, variance and covariance). For any given model structure, and assuming linear dynamic rates, we demonstrate how the model parameters can be efficiently and accurately estimated by divergence minimisation. We then apply our method to an experimental dataset and compare the estimates and goodness-of-fit to those obtained by maximum likelihood estimation. While both sets of parameter estimates had overlapping confidence regions, the new method produced lower values for the division and death rates of bacteria: these improved the goodness-of-fit at the second time point at the expense of that of the first time point. This flexible framework can easily be applied to a range of experimental systems. Its computational efficiency paves the way for model comparison and optimal experimental design.

Death and population dynamics affect mutation rate estimates and evolvability under stress in bacteria

“…The birth and death dynamics can be obtained by several methods. We used plasmid segregation, but other methods may be possible, such as segregation of engineered self-assembling fluorescent particles [ 59 ], isogenic strain tagging [ 60 ], Carboxyfluorescein succinimidyl ester (CFSE) membrane staining [ 61 ], or direct microscopic observations at single-cell resolution. Microscopic observations with cell tracking may give much more precise and less noisy information than other methods but are only suitable when the death rate is sufficiently low, because only a limited number of cells can be tracked.…”

A data-based mathematical modelling study to quantify the effects of ciprofloxacin and ampicillin on the within-host dynamics of Salmonella enterica during treatment and relapse

“…To avoid the step of solving the probability density function characterising the multivariate bacterial distribution, we use summary statistics to capture the necessary features of interest. Our models only incorporate zero-order dynamics, thus the first-(mean numbers of bacteria in each organ) and second-order (variance-covariance matrix of bacterial numbers in all organs) moments suffice to describe the distribution [44].…”

Dose–response and transmission: the nexus between reservoir hosts, environment and recipient hosts

“…B 374: 20190016 dose -response relationships for different combinations of pathogen, host and dead-end species and individual traits. A compartmental model, where transmission is modelled as a spatial process within and between hosts, could provide a more flexible modelling framework for the integration of such heterogeneities [35,36]. As a first approximation, hosts could be modelled as a network of tissues (e.g.…”