Understanding the impact of numerical solvers on inference for differential equation models.

Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers that seem sufficiently accurate for the forward problem, i.e. for obtaining an accurate simulation, might not be sufficiently accurate for the inverse problem, i.e. for inferring the model parameters from data. We show that for both fixed step and adaptive step ODE solvers, solving the forward problem with insufficient accuracy can distort likelihood surfaces, which might become jagged, causing inference algorithms to get stuck in local 'phantom' optima. We demonstrate that biases in inference arising from numerical approximation of ODEs are potentially most severe in systems involving low noise and rapid nonlinear dynamics. We reanalyse an ODE change point model previously fit to the COVID-19 outbreak in Germany and show the effect of the step size on simulation and inference results. We then fit a more complicated rainfall run-off model to hydrological data and illustrate the importance of tuning solver tolerances to avoid distorted likelihood surfaces. Our results indicate that, when performing inference for ODE model parameters, adaptive step size solver tolerances must be set cautiously and likelihood surfaces should be inspected for characteristic signs of numerical issues.

A Bayesian nonparametric method for detecting rapid changes in disease transmission.

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number, Rt. Real-time or retrospective identification of changes in Rt following the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts in Rt within a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman-Yor process. We assume that Rt is piecewise-constant, and the incidence data and priors determine when or whether Rt should change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty in Rt and its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where the Rt profile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Learning transmission dynamics modelling of COVID-19 using comomodels.

The COVID-19 epidemic continues to rage in many parts of the world. In the UK alone, an array of mathematical models have played a prominent role in guiding policymaking. Whilst considerable pedagogical material exists for understanding the basics of transmission dynamics modelling, there is a substantial gap between the relatively simple models used for exposition of the theory and those used in practice to model the transmission dynamics of COVID-19. Understanding these models requires considerable prerequisite knowledge and presents challenges to those new to the field of epidemiological modelling. In this paper, we introduce an open-source R package, comomodels, which can be used to understand the complexities of modelling the transmission dynamics of COVID-19 through a series of differential equation models. Alongside the base package, we describe a host of learning resources, including detailed tutorials and an interactive web-based interface allowing dynamic investigation of the model properties. We then use comomodels to illustrate three key lessons in the transmission of COVID-19 within R Markdown vignettes.

Innate and adaptive immune mechanisms regulating central nervous system remyelination.

Neuroinflammation is a hallmark of many neurodegenerative diseases and is considered their underlying cause. However, certain aspects of neuroinflammation favour beneficial outcomes after damage including the regeneration of myelin (remyelination). Both innate and adaptive immune mechanisms have been recognised as central to remyelination success. In particular, central nervous system (CNS) microglia and macrophages are established as key regulators of remyelination in the injured CNS with recently discovered novel mechanisms that underpin remyelination. How the adaptive immune system contributes to and regulates remyelination, however, is less established. Owing to their immunomodulatory and recently discovered proregenerative functions including in the CNS, regulatory T cells were identified as key for successful remyelination, but many gaps in the underlying mechanisms remain. As there are no therapies yet that enhance remyelination after damage, harnessing the beneficial aspects of neuroinflammation could underpin proregenerative CNS therapies of the future.

High-resolution temporal profiling of the human gut microbiome reveals consistent and cascading alterations in response to dietary glycans.

BACKGROUND: Dietary glycans, widely used as food ingredients and not directly digested by humans, are of intense interest for their beneficial roles in human health through shaping the microbiome. Characterizing the consistency and temporal responses of the gut microbiome to glycans is critical for rationally developing and deploying these compounds as therapeutics. METHODS: We investigated the effect of two chemically distinct glycans (fructooligosaccharides and polydextrose) through three clinical studies conducted with 80 healthy volunteers. Stool samples, collected at dense temporal resolution (~ 4 times per week over 10 weeks) and analyzed using shotgun metagenomic sequencing, enabled detailed characterization of participants' microbiomes. For analyzing the microbiome time-series data, we developed MC-TIMME2 (Microbial Counts Trajectories Infinite Mixture Model Engine 2.0), a purpose-built computational tool based on nonparametric Bayesian methods that infer temporal patterns induced by perturbations and groups of microbes sharing these patterns. RESULTS: Overall microbiome structure as well as individual taxa showed rapid, consistent, and durable alterations across participants, regardless of compound dose or the order in which glycans were consumed. Significant changes also occurred in the abundances of microbial carbohydrate utilization genes in response to polydextrose, but not in response to fructooligosaccharides. Using MC-TIMME2, we produced detailed, high-resolution temporal maps of the microbiota in response to glycans within and across microbiomes. CONCLUSIONS: Our findings indicate that dietary glycans cause reproducible, dynamic, and differential alterations to the community structure of the human microbiome.

MITRE: inferring features from microbiota time-series data linked to host status.

Longitudinal studies are crucial for discovering causal relationships between the microbiome and human disease. We present MITRE, the Microbiome Interpretable Temporal Rule Engine, a supervised machine learning method for microbiome time-series analysis that infers human-interpretable rules linking changes in abundance of clades of microbes over time windows to binary descriptions of host status, such as the presence/absence of disease. We validate MITRE's performance on semi-synthetic data and five real datasets. MITRE performs on par or outperforms conventional difficult-to-interpret machine learning approaches, providing a powerful new tool enabling the discovery of biologically interpretable relationships between microbiome and human host ( https://github.com/gerberlab/mitre/ ).