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.
Human seasonal influenza viruses evolve rapidly, enabling the virus population to evade immunity and re-infect previously infected individuals. Antigenic properties are largely determined by the surface glycoprotein hemagglutinin (HA) and amino acid substitutions at exposed epitope sites in HA mediate loss of recognition by antibodies. Here, we show that antigenic differences measured through serological assay data are well described by a sum of antigenic changes along the path connecting viruses in a phylogenetic tree. This mapping onto the tree allows prediction of antigenicity from HA seque…
The evolutionary dynamics of human Influenza A virus presents a challenging theoretical problem. An extremely high mutation rate allows the virus to escape, at each epidemic season, the host immune protection elicited by previous infections. At the same time, at each given epidemic season a single quasi-species, that is a set of closely related strains, is observed. A non-trivial relation between the genetic (i.e., at the sequence level) and the antigenic (i.e., related to the host immune response) distances can shed light into this puzzle. In this paper we introduce a model in which, in accor…
In this paper, we carry out a computational study using the spectral decomposition of the fluctuations of a two-pathogen epidemic model around its deterministic attractor, i.e., steady state or limit cycle, to examine the role of partial vaccination and between-host pathogen interaction on early pathogen replacement during seasonal epidemics of influenza and respiratory syncytial virus.
Many viruses evolve rapidly. For example, hemagglutinin of the H3N2 influenza A virus evolves to escape antibody binding. This evolution of the H3N2 virus means that people who have previously been exposed to an influenza strain may be infected by a newly emerged virus. In this paper, we use Shannon entropy and relative entropy to measure the diversity and selection pressure by antibody in each amino acid site of H3 hemagglutinin between the 1992-1993 season and the 2009-2010 season. Shannon entropy and relative entropy are two independent state variables that we use to characterize H3N2 evolu…
In March and early April 2013, a new avian-origin influenza A (H7N9) virus (A-OIV) emerged in the eastern China. During the first week of April, the 18 infection cases have been confirmed and 6 people have died since March. This virus has caused global concern as a potential pandemic threat. Here we use evolutionary analysis to reconstruct the origins and early development of the A-OIV viruses. We found that A-OIV was derived from a reassortment of three avian flu virus strains, and substantial mutations have been detected. Our results highlight the need for systematic surveillance of influenz…
Consider a birth and death chain to model the number of types of a given virus. Each type gives birth to a new type at rate $λ$ and dies at rate 1. Each type is also assigned a fitness. When a death occurs either the least fit type dies (with probability $1-r$) or we kill a type at random (with probability $r$). We show that this random killing has a large effect (for any $r>0$) on the behavior of the model when $λ<1$. The behavior of the model with $r>0$ and $λ<1$ is consistent with features of the phylogenetic tree of influenza.
The aftermath of influenza infection is determined by a complex set of host-pathogen interactions, where genomic variability on both viral and host sides influences the final outcome. Although there exists large body of literature describing influenza virus variability, only a very small fraction covers the issue of host variance. The goal of this review is to explore the variability of host genes responsible for host-pathogen interactions, paying particular attention to genes responsible for the presence of sialylated glycans in the host endothelial membrane, mucus, genes used by viral immune…
Under the hypothesis that both influenza and respiratory syncytial virus (RSV) are the two leading causes of acute respiratory infections (ARI), in this paper we have used a standard two-pathogen epidemic model as a regressor to explain, on a yearly basis, high season ARI data in terms of the contact rates and initial conditions of the mathematical model. The rationale is that ARI high season is a transient regime of a noisy system, e.g., the system is driven away from equilibrium every year by fluctuations in variables such as humidity, temperature, viral mutations and human behavior. Using t…
Influenza is a contagious respiratory illness that causes significant human morbidity and mortality, affecting 5-15% of the population in a typical epidemic season. Human influenza epidemics are caused by types A and B, with roughly 25% of human cases due to influenza B. Influenza B is a single-stranded RNA virus with a high mutation rate, and both prior immune history and vaccination put significant pressure on the virus to evolve. Due to the high rate of viral evolution, the influenza B vaccine component of the annual influenza vaccine is updated, roughly every other year in recent years. To…
Determining phenotype from genetic data is a fundamental challenge. Influenza A viruses undergo rapid antigenic drift and identification of emerging antigenic variants is critical to the vaccine selection process. Using former seasonal influenza A(H1N1) viruses, hemagglutinin sequence and corresponding antigenic data were analyzed in combination with 3-D structural information. We attributed variation in hemagglutination inhibition to individual amino acid substitutions and quantified their antigenic impact, validating a subset experimentally using reverse genetics. Substitutions identified as…
We predict vaccine efficacy with a measure of antigenic distance between influenza A(H3N2) and candidate vaccine viruses based on amino acid substitutions in the dominant epitopes. In 2016-2017, our model predicts 19% efficacy compared to 20% observed. This tool assists candidate vaccine selection by predicting human protection against circulating strains.
Influenza viruses undergo continual antigenic evolution allowing mutant viruses to evade host immunity acquired to previous virus strains. Antigenic phenotype is often assessed through pairwise measurement of cross-reactivity between influenza strains using the hemagglutination inhibition (HI) assay. Here, we extend previous approaches to antigenic cartography, and simultaneously characterize antigenic and genetic evolution by modeling the diffusion of antigenic phenotype over a shared virus phylogeny. Using HI data from influenza lineages A/H3N2, A/H1N1, B/Victoria and B/Yamagata, we determin…
Viruses are incapable of autonomous energy production. Although many experimental studies make it clear that viruses are parasitic entities that hijack the host's molecular resources, a detailed estimate for the energetic cost of viral synthesis is largely lacking. To quantify the energetic cost of viruses to their hosts, we enumerated the costs associated with two very distinct but representative DNA and RNA viruses, namely T4 and influenza. We found that for these viruses, translation of viral proteins is the most energetically expensive process. Interestingly, the cost of building a T4 phag…
Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature include the effectively one-dimensional escape characteristic of influenza A and the prolonged coexistence of lineages in influenza B. Here we use an evolutionary model for viruses in the presence of immune host systems with finite memory to delineate parameter regimes of these patterns in a in two-dimensional antigenic space. We find that for small effective mut…
This paper develops a deterministic differential equations model that captures the H7N9 virus transmission from live poultry to human via poultry-human contacts in live poultry markets (LPMs). The virus circulation among live poultry, which happens but is hard to be detected (since contaminated live poultry appear to be asymptomatic), is also incorporated in the model. The time-dependent contact rate between human and live poultry based on LPMs closing information can be estimated. From data of LPMs closing news, the contact rate function can be easily estimated. This model could serve as a ra…
Background: There is uncertainty about the burden of severe outcomes associated with RSV and influenza in children. Methods: We have applied previously developed methodology to estimate the rates of influenza and RSV-associated hospitalizations with different diagnoses in different age subgroups of US children between the 2003-04 through the 2009-10 seasons. Results: The average annual rates (per 100,000) of influenza and RSV-associated hospitalizations for any cause excluding asthma (ICD-9 code 493) in the principal diagnosis with a respiratory cause (ICD-9 codes 460-519) in the diagnosis (ei…
The evolution of many microbes and pathogens, including circulating viruses such as seasonal influenza, is driven by immune pressure from the host population. In turn, the immune systems of infected populations get updated, chasing viruses even further away. Quantitatively understanding how these dynamics result in observed patterns of rapid pathogen and immune adaptation is instrumental to epidemiological and evolutionary forecasting. Here we present a mathematical theory of co-evolution between immune systems and viruses in a finite-dimensional antigenic space, which describes the cross-reac…
The evolution of the hemagglutinin amino acids sequences of Influenza A virus is studied by a method based on an informational metrics, originally introduced by Rohlin for partitions in abstract probability spaces. This metrics does not require any previous functional or syntactic knowledge about the sequences and it is sensitive to the correlated variations in the characters disposition. Its efficiency is improved by algorithmic tools, designed to enhance the detection of the novelty and to reduce the noise of useless mutations. We focus on the USA data from 1993/94 to 2010/2011 for A/H3N2 an…
Given a sample of genome sequences from an asexual population, can one predict its evolutionary future? Here we demonstrate that the branching patterns of reconstructed genealogical trees contains information about the relative fitness of the sampled sequences and that this information can be used to predict successful strains. Our approach is based on the assumption that evolution proceeds by accumulation of small effect mutations, does not require species specific input and can be applied to any asexual population under persistent selection pressure. We demonstrate its performance using hist…
One important feature of the mammalian immune system is the highly specific binding of antigens to antibodies. Antibodies generated in response to one infection may also provide some level of cross immunity to other infections. One model to describe this cross immunity is the notion of antigenic space, which assigns each antibody and each virus a point in $\mathbb{R}^n$. Past studies have suggested the dimensionality of antigenic space, $n$, may be small. In this study we show that data from hemagglutination assays suggest a high dimensional random walk (or self avoiding random random walk). T…
Analyses and visualizations by the ISSCOR method of influenza virus hemagglutinin genes of different A-subtypes revealed some rather striking temporal relationships between groups of individual gene subsets. Based on these findings we consider application of the ISSCOR-PCA method for analyses of large sets of homologous genes to be a worthwhile addition to a toolbox of genomics - allowing for a rapid diagnostics of trends, and ultimately even aiding an early warning of newly emerging epidemiological threats.
H1N1 influenza causes substantial seasonal illness and was the subtype of the 2009 influenza pandemic. Precise measures of antigenic distance between the vaccine and circulating virus strains help researchers design influenza vaccines with high vaccine effectiveness. We here introduce a sequence-based method to predict vaccine effectiveness in humans. Historical epidemiological data show that this sequence-based method is as predictive of vaccine effectiveness as hemagglutination inhibition (HI) assay data from ferret animal model studies. Interestingly, the expected vaccine effectiveness is g…
Epidemiological models for the spread of pathogens in a population are usually only able to describe a single pathogen. This makes their application unrealistic in cases where multiple pathogens with similar symptoms are spreading concurrently within the same population. Here we describe a method which makes possible the application of multiple single-strain models under minimal conditions. As such, our method provides a bridge between theoretical models of epidemiology and data-driven approaches for modeling of influenza and other similar viruses. Our model extends the Susceptible-Infected-Re…
Understanding the origin of infectious diseases provides scientifically based rationales for implementing public health measures that may help to avoid or mitigate future epidemics. The recent ancestors of a pandemic virus provide invaluable information about the set of minimal genomic alterations that transformed a zoonotic agent into a full human pandemic. Since the first confirmed cases of the H1N1 pandemic virus in the spring of 2009, several hypotheses about the strain's origins have been proposed. However, how, where, and when it first infected humans is still far from clear. The only wa…
Emergenet: A Digital Twin of Sequence Evolution for Scalable Emergence Risk Assessment of Animal Influenza A Strains
University of Chicago（芝加哥大学）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普利兹克分子工程学院）；Committee on Immunology, University of Chicago（芝加哥大学免疫学委员会）；Committee on Quantitative Methods in Social, Behavioral, and Health Sciences, University of Chicago（芝加哥大学社会、行为与健康科学定量方法委员会）
RNA virus populations will undergo processes of mutation and selection resulting in a mixed population of viral particles. High throughput sequencing of a viral population subsequently contains a mixed signal of the underlying clones. We would like to identify the underlying evolutionary structures. We utilize two sources of information to attempt this; within segment linkage information, and mutation prevalence. We demonstrate that clone haplotypes, their prevalence, and maximum parsimony reticulate evolutionary structures can be identified, although the solutions may not be unique, even for …
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 d…
The COVID-19 pandemic has been a great catastrophe that upended human lives and caused millions of deaths all over the world. The rapid spread of the virus, with its early-stage exponential growth and subsequent 'waves', caught many medical professionals and decision-makers unprepared. Even though epidemiological models have been known for almost a century (since the 'Spanish Influenza' pandemic of 1918-20), the real-life spread of the SARS-CoV-2 virus often confounded the modelers. While the general framework of epidemiological models like SEIR (susceptible-exposed-infected-recovered) or SIR …
Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains, preventing a build up of immunity in the host population. In this paper, a parsimonious epidemic model is defined that attempts to capture the dynamics of evolving strains within a host population. The `evolving strains' epidemic model has many properties that lie in-between the Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models…
Rapidly evolving pathogens like influenza viruses can persist by accumulating antigenic novelty fast enough to evade the adaptive immunity of the host population, yet without continuous accumulation of genetic diversity. This dynamical state is often compared to the Red Queen evolving as fast as it can just to maintain its foothold in the host population: Accumulation of antigenic novelty is balanced by the build-up of host immunity. Such Red Queen States (RQS) of continuous adaptation in large rapidly mutating populations are well understood in terms of Traveling Wave (TW) theories of populat…
Genotype networks drive oscillating endemicity and epidemic trajectories in viral evolution
University of Zaragoza（萨拉戈萨大学）；Institute of Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza（萨拉戈萨大学复杂系统生物计算与物理研究所 (BIFI)）；Universitat Rovira i Virgili（罗维拉-伊-维尔吉利大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of Kobe（神户大学）
