Effects of memory on the shapes of simple outbreak trees

Genomic tools, including phylogenetic trees derived from sequence data, are increasingly used to understand outbreaks of infectious diseases. One challenge is to link phylogenetic trees to patterns of transmission. Particularly in bacteria that cause chronic infections, this inference is affected by variable infectious periods and infectivity over time. It is known that non-exponential infectious periods can have substantial effects on pathogens’ transmission dynamics. Here we ask how this non-Markovian nature of an outbreak process affects the branching trees describing that process, with particular focus on tree shapes. We simulate Crump-Mode-Jagers branching processes and compare different patterns of infectivity over time. We find that memory (non-Markovian-ness) in the process can have a pronounced effect on the shapes of the outbreak’s branching pattern. However, memory also has a pronounced effect on the sizes of the trees, even when the duration of the simulation is fixed. When the sizes of the trees are constrained to a constant value, memory in our processes has little direct effect on tree shapes, but can bias inference of the birth rate from trees. We compare simulated branching trees to phylogenetic trees from an outbreak of tuberculosis in Canada, and discuss the relevance of memory to this dataset

Canalization of the evolutionary trajectory of the human influenza virus

Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. Antigenic evolution occurs in the context of a two-dimensional 'antigenic map', while genetic evolution shows a characteristic ladder-like genealogical tree. Here, we use a large-scale individual-based model to show that evolution in a Euclidean antigenic space provides a remarkable correspondence between model behavior and the epidemiological, antigenic, genealogical and geographic patterns observed in influenza virus. We find that evolution away from existing human immunity results in rapid population turnover in the influenza virus and that this population turnover occurs primarily along a single antigenic axis. Thus, selective dynamics induce a canalized evolutionary trajectory, in which the evolutionary fate of the influenza population is surprisingly repeatable and hence, in theory, predictable.Comment: 29 pages, 5 figures, 10 supporting figure

Fitting stochastic epidemic models to gene genealogies using linear noise approximation

Phylodynamics is a set of population genetics tools that aim at reconstructing demographic history of a population based on molecular sequences of individuals sampled from the population of interest. One important task in phylodynamics is to estimate changes in (effective) population size. When applied to infectious disease sequences such estimation of population size trajectories can provide information about changes in the number of infections. To model changes in the number of infected individuals, current phylodynamic methods use non-parametric approaches, parametric approaches, and stochastic modeling in conjunction with likelihood-free Bayesian methods. The first class of methods yields results that are hard-to-interpret epidemiologically. The second class of methods provides estimates of important epidemiological parameters, such as infection and removal/recovery rates, but ignores variation in the dynamics of infectious disease spread. The third class of methods is the most advantageous statistically, but relies on computationally intensive particle filtering techniques that limits its applications. We propose a Bayesian model that combines phylodynamic inference and stochastic epidemic models, and achieves computational tractability by using a linear noise approximation (LNA) --- a technique that allows us to approximate probability densities of stochastic epidemic model trajectories. LNA opens the door for using modern Markov chain Monte Carlo tools to approximate the joint posterior distribution of the disease transmission parameters and of high dimensional vectors describing unobserved changes in the stochastic epidemic model compartment sizes (e.g., numbers of infectious and susceptible individuals). We apply our estimation technique to Ebola genealogies estimated using viral genetic data from the 2014 epidemic in Sierra Leone and Liberia.Comment: 43 pages, 6 figures in the main tex

Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing

Many of the pathogens perceived to pose the greatest risk to humans are viral zoonoses, responsible for a range of emerging and endemic infectious diseases. Phylogeography is a useful tool to understand the processes that give rise to spatial patterns and drive dynamics in virus populations. Increasingly, whole-genome information is being used to uncover these patterns, but the limits of phylogenetic resolution that can be achieved with this are unclear. Here, whole-genome variation was used to uncover fine-scale population structure in endemic canine rabies virus circulating in Tanzania. This is the first whole-genome population study of rabies virus and the first comprehensive phylogenetic analysis of rabies virus in East Africa, providing important insights into rabies transmission in an endemic system. In addition, sub-continental scale patterns of population structure were identified using partial gene data and used to determine population structure at larger spatial scales in Africa. While rabies virus has a defined spatial structure at large scales, increasingly frequent levels of admixture were observed at regional and local levels. Discrete phylogeographic analysis revealed long-distance dispersal within Tanzania, which could be attributed to human-mediated movement, and we found evidence of multiple persistent, co-circulating lineages at a very local scale in a single district, despite on-going mass dog vaccination campaigns. This may reflect the wider endemic circulation of these lineages over several decades alongside increased admixture due to human-mediated introductions. These data indicate that successful rabies control in Tanzania could be established at a national level, since most dispersal appears to be restricted within the confines of country borders but some coordination with neighbouring countries may be required to limit transboundary movements. Evidence of complex patterns of rabies circulation within Tanzania necessitates the use of whole-genome sequencing to delineate finer scale population structure that can that can guide interventions, such as the spatial scale and design of dog vaccination campaigns and dog movement controls to achieve and maintain freedom from disease

Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model

The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our Birth-Death SIR method (BDSIR) to two viral data sets. First, five human immunodeficiency virus type 1 clusters sampled in the United Kingdom between 1999 and 2003 are analyzed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 90's. The analysis of a hepatitis C virus (HCV) genotype 2c data set shows that the local epidemic in the C\'ordoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880--1920. The estimated time of epidemic peak is around 1970.Comment: Journal link: http://rsif.royalsocietypublishing.org/content/11/94/20131106.ful

Integrating genealogical and dynamical modelling to infer escape and reversion rates in HIV epitopes

The rates of escape and reversion in response to selection pressure arising from the host immune system, notably the cytotoxic T-lymphocyte (CTL) response, are key factors determining the evolution of HIV. Existing methods for estimating these parameters from cross-sectional population data using ordinary differential equations (ODE) ignore information about the genealogy of sampled HIV sequences, which has the potential to cause systematic bias and over-estimate certainty. Here, we describe an integrated approach, validated through extensive simulations, which combines genealogical inference and epidemiological modelling, to estimate rates of CTL escape and reversion in HIV epitopes. We show that there is substantial uncertainty about rates of viral escape and reversion from cross-sectional data, which arises from the inherent stochasticity in the evolutionary process. By application to empirical data, we find that point estimates of rates from a previously published ODE model and the integrated approach presented here are often similar, but can also differ several-fold depending on the structure of the genealogy. The model-based approach we apply provides a framework for the statistical analysis of escape and reversion in population data and highlights the need for longitudinal and denser cross-sectional sampling to enable accurate estimate of these key parameters

Discovering the Phylodynamics of RNA Viruses

The advent of extremely high throughput DNA sequencing ensures that genomic data from microbial organisms can be acquired in unprecedented quantities and with remarkable rapidity. Although this genomic revolution will affect all microbes alike, our focus here is on RNA viruses, as the rapidity of their evolution, which is observable over the time scale of human observation, allows phylodynamic inferences to be made with great precision. In the foreseeable future it is likely that complete genome sequencing will become the standard method of viral characterization, providing the highest possible resolution for phylogenetic studies. The rapidity with which genome sequence data were generated from the ongoing epidemic of swine-origin H1N1 influenza A virus [1] is testament to the power of this technology