Infectious Disease Dynamics Inferred from Genetic Data via Sequential Monte Carlo

Phylodynamic assessment of SNP distances from whole genome sequencing for determining Mycobacterium tuberculosis transmission

The global tuberculosis (TB) epidemic is driven by primary transmission. Pathogen genome sequencing is increasingly used in molecular epidemiology and outbreak investigations. Based on contact tracing and epidemiological links, Single Nucleotide Polymorphism (SNP) cut-offs, ranging from 3 to 12 SNPs, identify probable transmission clusters or exclude direct transmission. However, contact tracing can be limited by recall bias and inconsistent methodologies across TB settings. We propose phylodynamic models, i.e. methods to infer transmission processes from pathogen genomes and associated epidemiological data, as an alternative reference to infer transmission events. We analyzed 2,008 whole-genome sequences from Dutch TB patients collected from 2015 to 2019. Genetic clusters were defined within a 20-SNP range, and the phylodynamic model phybreak was employed to infer transmission. Probable transmission SNP cut-offs were assessed by the proportion of inferred transmission events with a SNP distance below these cut-offs. A total of 79 clusters were identified, with a median size of 4 isolates (IQR = 3-8). A SNP cut-off of 4 captured 98% of inferred transmission events while reducing pairs without transmission links. A cut-off beyond 12 SNPs effectively excluded transmission. Phylodynamic approaches provide a valuable alternative to contact tracing for defining SNP cut-offs, allowing for a more precise assessment of transmission events.

Early detection of highly transmissible viral variants using phylogenomics

As demonstrated by the SARS-CoV-2 pandemic, the emergence of novel viral strains with increased transmission rates poses a serious threat to global health. Statistical models of genome sequence evolution may provide a critical tool for early detection of these strains. Using a novel stochastic model that links transmission rates to the entire viral genome sequence, we study the utility of phylogenetic methods that use a phylogenetic tree relating viral samples versus count-based methods that use case counts of variants over time exclusively to detect increased transmission rates and identify candidate causative mutations. We find that phylogenies in particular can detect novel transmission-enhancing variants very soon after their origin and may facilitate the development of early detection systems for outbreak surveillance.

Immuno-epidemiology and the predictability of viral evolution

Understanding viral evolution depends on a synthesis of evolutionary biology and immuno-epidemiology.

Markov genealogy processes

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.

Particle Gibbs sampling for Bayesian phylogenetic inference

MOTIVATION

The combinatorial sequential Monte Carlo (CSMC) has been demonstrated to be an efficient complementary method to the standard Markov chain Monte Carlo (MCMC) for Bayesian phylogenetic tree inference using biological sequences. It is appealing to combine the CSMC and MCMC in the framework of the particle Gibbs (PG) sampler to jointly estimate the phylogenetic trees and evolutionary parameters. However, the Markov chain of the PG may mix poorly for high dimensional problems (e.g. phylogenetic trees). Some remedies, including the PG with ancestor sampling and the interacting particle MCMC, have been proposed to improve the PG. But they either cannot be applied to or remain inefficient for the combinatorial tree space.

RESULTS

We introduce a novel CSMC method by proposing a more efficient proposal distribution. It also can be combined into the PG sampler framework to infer parameters in the evolutionary model. The new algorithm can be easily parallelized by allocating samples over different computing cores. We validate that the developed CSMC can sample trees more efficiently in various PG samplers via numerical experiments.

AVAILABILITY AND IMPLEMENTATION

The implementation of our method and the data underlying this article are available at https://github.com/liangliangwangsfu/phyloPMCMC.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Demographic inference from multiple whole genomes using a particle filter for continuous Markov jump processes

Demographic events shape a population's genetic diversity, a process described by the coalescent-with-recombination model that relates demography and genetics by an unobserved sequence of genealogies along the genome. As the space of genealogies over genomes is large and complex, inference under this model is challenging. Formulating the coalescent-with-recombination model as a continuous-time and -space Markov jump process, we develop a particle filter for such processes, and use waypoints that under appropriate conditions allow the problem to be reduced to the discrete-time case. To improve inference, we generalise the Auxiliary Particle Filter for discrete-time models, and use Variational Bayes to model the uncertainty in parameter estimates for rare events, avoiding biases seen with Expectation Maximization. Using real and simulated genomes, we show that past population sizes can be accurately inferred over a larger range of epochs than was previously possible, opening the possibility of jointly analyzing multiple genomes under complex demographic models. Code is available at https://github.com/luntergroup/smcsmc.

Estimating Epidemic Incidence and Prevalence from Genomic Data

Modern phylodynamic methods interpret an inferred phylogenetic tree as a partial transmission chain providing information about the dynamic process of transmission and removal (where removal may be due to recovery, death, or behavior change). Birth–death and coalescent processes have been introduced to model the stochastic dynamics of epidemic spread under common epidemiological models such as the SIS and SIR models and are successfully used to infer phylogenetic trees together with transmission (birth) and removal (death) rates. These methods either integrate analytically over past incidence and prevalence to infer rate parameters, and thus cannot explicitly infer past incidence or prevalence, or allow such inference only in the coalescent limit of large population size. Here, we introduce a particle filtering framework to explicitly infer prevalence and incidence trajectories along with phylogenies and epidemiological model parameters from genomic sequences and case count data in a manner consistent with the underlying birth–death model. After demonstrating the accuracy of this method on simulated data, we use it to assess the prevalence through time of the early 2014 Ebola outbreak in Sierra Leone.

Choices and trade-offs in inference with infectious disease models

Inference using mathematical models of infectious disease dynamics can be an invaluable tool for the interpretation and analysis of epidemiological data. However, researchers wishing to use this tool are faced with a choice of models and model types, simulation methods, inference methods and software packages. Given the multitude of options, it can be challenging to decide on the best approach. Here, we delineate the choices and trade-offs involved in deciding on an approach for inference, and discuss aspects that might inform this decision. We provide examples of inference with a dataset of influenza cases using the R packages pomp and rbi.

Panel Data Analysis via Mechanistic Models

Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing down scientifically motivated equations describing the collection of dynamic systems giving rise to the observations on each unit. A defining characteristic of panel systems is that the dynamic interaction between units should be negligible. Panel models therefore consist of a collection of independent stochastic processes, generally linked through shared parameters while also having unit-specific parameters. To give the scientist flexibility in model specification, we are motivated to develop a framework for inference on panel data permitting the consideration of arbitrary nonlinear, partially observed panel models. We build on iterated filtering techniques that provide likelihood-based inference on nonlinear partially observed Markov process models for time series data. Our methodology depends on the latent Markov process only through simulation; this plug-and-play property ensures applicability to a large class of models. We demonstrate our methodology on a toy example and two epidemiological case studies. We address inferential and computational issues arising due to the combination of model complexity and dataset size. Supplementary materials for this article are available online.

An Annealed Sequential Monte Carlo Method for Bayesian Phylogenetics

We describe an “embarrassingly parallel” method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo (SMC), based on recent advances in the SMC literature such as adaptive determination of annealing parameters. The algorithm provides an approximate posterior distribution over trees and evolutionary parameters as well as an unbiased estimator for the marginal likelihood. This unbiasedness property can be used for the purpose of testing the correctness of posterior simulation software. We evaluate the performance of phylogenetic annealed SMC by reviewing and comparing with other computational Bayesian phylogenetic methods, in particular, different marginal likelihood estimation methods. Unlike previous SMC methods in phylogenetics, our annealed method can utilize standard Markov chain Monte Carlo (MCMC) tree moves and hence benefit from the large inventory of such moves available in the literature. Consequently, the annealed SMC method should be relatively easy to incorporate into existing phylogenetic software packages based on MCMC algorithms. We illustrate our method using simulation studies and real data analysis.

Bayesian phylodynamic inference with complex models

Population genetic modeling can enhance Bayesian phylogenetic inference by providing a realistic prior on the distribution of branch lengths and times of common ancestry. The parameters of a population genetic model may also have intrinsic importance, and simultaneous estimation of a phylogeny and model parameters has enabled phylodynamic inference of population growth rates, reproduction numbers, and effective population size through time. Phylodynamic inference based on pathogen genetic sequence data has emerged as useful supplement to epidemic surveillance, however commonly-used mechanistic models that are typically fitted to non-genetic surveillance data are rarely fitted to pathogen genetic data due to a dearth of software tools, and the theory required to conduct such inference has been developed only recently. We present a framework for coalescent-based phylogenetic and phylodynamic inference which enables highly-flexible modeling of demographic and epidemiological processes. This approach builds upon previous structured coalescent approaches and includes enhancements for computational speed, accuracy, and stability. A flexible markup language is described for translating parametric demographic or epidemiological models into a structured coalescent model enabling simultaneous estimation of demographic or epidemiological parameters and time-scaled phylogenies. We demonstrate the utility of these approaches by fitting compartmental epidemiological models to Ebola virus and Influenza A virus sequence data, demonstrating how important features of these epidemics, such as the reproduction number and epidemic curves, can be gleaned from genetic data. These approaches are provided as an open-source package PhyDyn for the BEAST2 phylogenetics platform.

Recent advances in computational phylodynamics

Time-stamped, trait-annotated phylogenetic trees built from virus genome data are increasingly used for outbreak investigation and monitoring ongoing epidemics. This routinely involves reconstructing the spatial and demographic processes from large data sets to help unveil the patterns and drivers of virus spread. Such phylodynamic inferences can however become quite time-consuming as the dimensions of the data increase, which has led to a myriad of approaches that aim to tackle this complexity. To elucidate the current state of the art in the field of phylodynamics, we discuss recent developments in Bayesian inference and accompanying software, highlight methods for improving computational efficiency and relevant visualisation tools. As an alternative to fully Bayesian approaches, we touch upon conditional software pipelines that compromise between statistical coherence and turn-around-time, and we highlight the available software packages. Finally, we outline future directions that may facilitate the large-scale tracking of epidemics in near real time.

Models and analyses to understand threats to polio eradication

To achieve complete polio eradication, the live oral poliovirus vaccine (OPV) currently used must be phased out after the end of wild poliovirus transmission. However, poorly understood threats may arise when OPV use is stopped. To counter these threats, better models than those currently available are needed. Two articles recently published in BMC Medicine address these issues. Mercer et al. (BMC Med 15:180, 2017) developed a statistical model analysis of polio case data and characteristics of cases occurring in several districts in Pakistan to inform resource allocation decisions. Nevertheless, despite having the potential to accelerate the elimination of polio cases, their analyses are unlikely to advance our understanding OPV cessation threats. McCarthy et al. (BMC Med 15:175, 2017) explored one such threat, namely the emergence and transmission of serotype 2 circulating vaccine derived poliovirus (cVDPV2) after OPV2 cessation, and found that the risk of persistent spread of cVDPV2 to new areas increases rapidly 1-5 years after OPV2 cessation. Thus, recently developed models and analysis methods have the potential to guide the required steps to surpass these threats. 'Big data' scientists could help with this; however, datasets covering all eradication efforts should be made readily available.Please see related articles: https://bmcmedicine.biomedcentral.com/articles/10.1186/s12916-017-0937-y and https://bmcmedicine.biomedcentral.com/articles/10.1186/s12916-017-0941-2 .

Monte Carlo profile confidence intervals for dynamic systems

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As datasets become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present examples arising in the study of infectious disease transmission, demonstrating our methodology for inference on nonlinear dynamic models using genetic sequence data and panel time-series data. We also discuss applicability to nonlinear time-series and spatio-temporal data.