The importance of vaccinated individuals to population-level evolution of pathogens.

Virus evolution shapes the epidemiological patterns of infectious disease, particularly via evasion of population immunity. At the individual level, host immunity itself may drive viral evolution towards antigenic escape. Using compartmental SIR-style models with imperfect vaccination, we allow the probability of immune escape to differ in vaccinated and unvaccinated hosts. As the relative contribution to selection in these different hosts varies, the overall effect of vaccination on the antigenic escape pressure at the population level changes. We find that this relative contribution to escape is important for understanding the effects of vaccination on the escape pressure and we draw out some fairly general patterns. If vaccinated hosts do not contribute much more than unvaccinated hosts to the escape pressure, then increasing vaccination always reduces the overall escape pressure. In contrast, if vaccinated hosts contribute significantly more than unvaccinated hosts to the population level escape pressure, then the escape pressure is maximised for intermediate vaccination levels. Past studies find only that the escape pressure is maximal for intermediate levels with fixed extreme assumptions about this relative contribution. Here we show that this result does not hold across the range of plausible assumptions for the relative contribution to escape from vaccinated and unvaccinated hosts. We also find that these results depend on the vaccine efficacy against transmission, particularly through the partial protection against infection. This work highlights the potential value of understanding better how the contribution to antigenic escape pressure depends on individual host immunity.

Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK.

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Key questions for modelling COVID-19 exit strategies.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

A scale-free analysis of the HIV-1 genome demonstrates multiple conserved regions of structural and functional importance.

HIV-1 replicates via a low-fidelity polymerase with a high mutation rate; strong conservation of individual nucleotides is highly indicative of the presence of critical structural or functional properties. Identifying such conservation can reveal novel insights into viral behaviour. We analysed 3651 publicly available sequences for the presence of nucleic acid conservation beyond that required by amino acid constraints, using a novel scale-free method that identifies regions of outlying score together with a codon scoring algorithm. Sequences with outlying score were further analysed using an algorithm for producing local RNA folds whilst accounting for alignment properties. 11 different conserved regions were identified, some corresponding to well-known cis-acting functions of the HIV-1 genome but also others whose conservation has not previously been noted. We identify rational causes for many of these, including cis functions, possible additional reading frame usage, a plausible mechanism by which the central polypurine tract primes second-strand DNA synthesis and a conformational stabilising function of a region at the 5' end of env.

Human mobility and the spatial transmission of influenza in the United States.

Seasonal influenza epidemics offer unique opportunities to study the invasion and re-invasion waves of a pathogen in a partially immune population. Detailed patterns of spread remain elusive, however, due to lack of granular disease data. Here we model high-volume city-level medical claims data and human mobility proxies to explore the drivers of influenza spread in the US during 2002-2010. Although the speed and pathways of spread varied across seasons, seven of eight epidemics likely originated in the Southern US. Each epidemic was associated with 1-5 early long-range transmission events, half of which sparked onward transmission. Gravity model estimates indicate a sharp decay in influenza transmission with the distance between infectious and susceptible cities, consistent with spread dominated by work commutes rather than air traffic. Two early-onset seasons associated with antigenic novelty had particularly localized modes of spread, suggesting that novel strains may spread in a more localized fashion than previously anticipated.

Infectious Disease Surveillance in the Big Data Era: Towards Faster and Locally Relevant Systems.

While big data have proven immensely useful in fields such as marketing and earth sciences, public health is still relying on more traditional surveillance systems and awaiting the fruits of a big data revolution. A new generation of big data surveillance systems is needed to achieve rapid, flexible, and local tracking of infectious diseases, especially for emerging pathogens. In this opinion piece, we reflect on the long and distinguished history of disease surveillance and discuss recent developments related to use of big data. We start with a brief review of traditional systems relying on clinical and laboratory reports. We then examine how large-volume medical claims data can, with great spatiotemporal resolution, help elucidate local disease patterns. Finally, we review efforts to develop surveillance systems based on digital and social data streams, including the recent rise and fall of Google Flu Trends. We conclude by advocating for increased use of hybrid systems combining information from traditional surveillance and big data sources, which seems the most promising option moving forward. Throughout the article, we use influenza as an exemplar of an emerging and reemerging infection which has traditionally been considered a model system for surveillance and modeling.

Capturing the dynamics of pathogens with many strains.

Pathogens that consist of multiple antigenic variants are a serious public health concern. These infections, which include dengue virus, influenza and malaria, generate substantial morbidity and mortality. However, there are considerable theoretical challenges involved in modelling such infections. As well as describing the interaction between strains that occurs as a result cross-immunity and evolution, models must balance biological realism with mathematical and computational tractability. Here we review different modelling approaches, and suggest a number of biological problems that are potential candidates for study with these methods. We provide a comprehensive outline of the benefits and disadvantages of available frameworks, and describe what biological information is preserved and lost under different modelling assumptions. We also consider the emergence of new disease strains, and discuss how models of pathogens with multiple strains could be developed further in future. This includes extending the flexibility and biological realism of current approaches, as well as interface with data.

Spatial Transmission of 2009 Pandemic Influenza in the US.

The 2009 H1N1 influenza pandemic provides a unique opportunity for detailed examination of the spatial dynamics of an emerging pathogen. In the US, the pandemic was characterized by substantial geographical heterogeneity: the 2009 spring wave was limited mainly to northeastern cities while the larger fall wave affected the whole country. Here we use finely resolved spatial and temporal influenza disease data based on electronic medical claims to explore the spread of the fall pandemic wave across 271 US cities and associated suburban areas. We document a clear spatial pattern in the timing of onset of the fall wave, starting in southeastern cities and spreading outwards over a period of three months. We use mechanistic models to tease apart the external factors associated with the timing of the fall wave arrival: differential seeding events linked to demographic factors, school opening dates, absolute humidity, prior immunity from the spring wave, spatial diffusion, and their interactions. Although the onset of the fall wave was correlated with school openings as previously reported, models including spatial spread alone resulted in better fit. The best model had a combination of the two. Absolute humidity or prior exposure during the spring wave did not improve the fit and population size only played a weak role. In conclusion, the protracted spread of pandemic influenza in fall 2009 in the US was dominated by short-distance spatial spread partially catalysed by school openings rather than long-distance transmission events. This is in contrast to the rapid hierarchical transmission patterns previously described for seasonal influenza. The findings underline the critical role that school-age children play in facilitating the geographic spread of pandemic influenza and highlight the need for further information on the movement and mixing patterns of this age group.

Identification of a novel splice variant form of the influenza A virus M2 ion channel with an antigenically distinct ectodomain.

Segment 7 of influenza A virus produces up to four mRNAs. Unspliced transcripts encode M1, spliced mRNA2 encodes the M2 ion channel, while protein products from spliced mRNAs 3 and 4 have not previously been identified. The M2 protein plays important roles in virus entry and assembly, and is a target for antiviral drugs and vaccination. Surprisingly, M2 is not essential for virus replication in a laboratory setting, although its loss attenuates the virus. To better understand how IAV might replicate without M2, we studied the reversion mechanism of an M2-null virus. Serial passage of a virus lacking the mRNA2 splice donor site identified a single nucleotide pseudoreverting mutation, which restored growth in cell culture and virulence in mice by upregulating mRNA4 synthesis rather than by reinstating mRNA2 production. We show that mRNA4 encodes a novel M2-related protein (designated M42) with an antigenically distinct ectodomain that can functionally replace M2 despite showing clear differences in intracellular localisation, being largely retained in the Golgi compartment. We also show that the expression of two distinct ion channel proteins is not unique to laboratory-adapted viruses but, most notably, was also a feature of the 1983 North American outbreak of H5N2 highly pathogenic avian influenza virus. In identifying a 14th influenza A polypeptide, our data reinforce the unexpectedly high coding capacity of the viral genome and have implications for virus evolution, as well as for understanding the role of M2 in the virus life cycle.

Waning immunity can drive repeated waves of infections.

In infectious disease models, it is known that mechanisms such as births, seasonality in transmission and pathogen evolution can generate oscillations in infection numbers. We show how waning immunity is also a mechanism that is sufficient on its own to enable sustained oscillations. When previously infected or vaccinated individuals lose full protective immunity, they become partially susceptible to reinfections. This partial immunity subsequently wanes over time, making individuals more susceptible to reinfections and potentially more infectious if infected. Losses of full and partial immunity lead to a surge in infections, which is the precursor of oscillations. We present a discrete-time Susceptible-Infectious-Immune-Waned-Infectious (SIRWY) model that features the waning of fully immune individuals (as a distribution of time at which individuals lose fully immunity) and the gradual loss of partial immunity (as increases in susceptibility and potential infectiousness over time). A special case of SIRWY is the discrete-time SIRS model with geometric distributions for waning and recovery. Its continuous-time analogue is the classic SIRS with exponential distributions, which does not produce sustained oscillations for any choice of parameters. We show that the discrete-time version can produce sustained oscillations and that the oscillatory regime disappears as discrete-time tends to continuous-time. A different special case of SIRWY is one with fixed times for waning and recovery. We show that this simpler model can also produce sustained oscillations. In conclusion, under certain feature and parameter choices relating to how exactly immunity wanes, fluctuations in infection numbers can be sustained without the need for any additional mechanisms.

The role of social contacts and original antigenic sin in shaping the age pattern of immunity to seasonal influenza.

Recent serological studies of seasonal influenza A in humans suggest a striking characteristic profile of immunity against age, which holds across different countries and against different subtypes of influenza. For both H1N1 and H3N2, the proportion of the population seropositive to recently circulated strains peaks in school-age children, reaches a minimum between ages 35-65, then rises again in the older ages. This pattern is little understood. Variable mixing between different age classes can have a profound effect on disease dynamics, and is hence the obvious candidate explanation for the profile, but using a mathematical model of multiple influenza strains, we see that age dependent transmission based on mixing data from social contact surveys cannot on its own explain the observed pattern. Instead, the number of seropositive individuals in a population may be a consequence of 'original antigenic sin'; if the first infection of a lifetime dominates subsequent immune responses, we demonstrate that it is possible to reproduce the observed relationship between age and seroprevalence. We propose a candidate mechanism for this relationship, by which original antigenic sin, along with antigenic drift and vaccination, results in the age profile of immunity seen in empirical studies.

Overlapping signals for translational regulation and packaging of influenza A virus segment 2.

Influenza A virus segment 2 mRNA expresses three polypeptides: PB1, PB1-F2 and PB1-N40, from AUGs 1, 4 and 5 respectively. Two short open reading frames (sORFs) initiated by AUGs 2 and 3 are also present. To understand translational regulation in this system, we systematically mutated AUGs 1-4 and monitored polypeptide synthesis from plasmids and recombinant viruses. This identified sORF2 as a key regulatory element with opposing effects on PB1-F2 and PB1-N40 expression. We propose a model in which AUGs 1-4 are accessed by leaky ribosomal scanning, with sORF2 repressing synthesis of downstream PB1-F2. However, sORF2 also up-regulates PB1-N40 expression, most likely by a reinitiation mechanism that permits skipping of AUG4. Surprisingly, we also found that in contrast to plasmid-driven expression, viruses with improved AUG1 initiation contexts produced less PB1 in infected cells and replicated poorly, producing virions with elevated particle:PFU ratios. Analysis of the genome content of virus particles showed reduced packaging of the mutant segment 2 vRNAs. Overall, we conclude that segment 2 mRNA translation is regulated by a combination of leaky ribosomal scanning and reinitiation, and that the sequences surrounding the PB1 AUG codon are multifunctional, containing overlapping signals for translation initiation and for segment-specific packaging.

A novel approach to finding conserved features in low-variability gene alignments characterises RNA motifs in SARS-CoV and SARS-CoV-2.

Collections of genetic sequences belonging to related organisms contain information on the evolutionary constraints to which the organisms have been subjected. Heavily constrained regions can be investigated to understand their roles in an organism's life cycle, and drugs can be sought to disrupt these roles. In organisms with low genetic diversity, such as newly-emerged pathogens, it is key to obtain this information early to develop new treatments. Here, we present methods that ensure we can leverage all the information available in a low-signal, low-noise set of sequences, to find contiguous regions of relatively conserved nucleic acid. We demonstrate the application of these methods by analysing over 5 million genome sequences of the recently-emerged RNA virus SARS-CoV-2 and correlating these results with an analysis of 119 genome sequences of SARS-CoV. We propose the precise location of a previously described packaging signal, and discuss explanations for other regions of high conservation.

Coughs, colds and "freshers' flu" survey in the University of Cambridge, 2007-2008.

Universities provide many opportunities for the spread of infectious respiratory illnesses. Students are brought together into close proximity from all across the world and interact with one another in their accommodation, through lectures and small group teaching and in social settings. The COVID-19 global pandemic has highlighted the need for sufficient data to help determine which of these factors are important for infectious disease transmission in universities and hence control university morbidity as well as community spillover. We describe the data from a previously unpublished self-reported university survey of coughs, colds and influenza-like symptoms collected in Cambridge, UK, during winter 2007-2008. The online survey collected information on symptoms and socio-demographic, academic and lifestyle factors. There were 1076 responses, 97% from University of Cambridge students (5.7% of the total university student population), 3% from staff and <1% from other participants, reporting onset of symptoms between September 2007 and March 2008. Undergraduates are seen to report symptoms earlier in the term than postgraduates; differences in reported date of symptoms are also seen between subjects and accommodation types, although these descriptive results could be confounded by survey biases. Despite the historical and exploratory nature of the study, this is one of few recent detailed datasets of influenza-like infection in a university context and is especially valuable to share now to improve understanding of potential transmission dynamics in universities during the current COVID-19 pandemic.

Influenza emergence in the face of evolutionary constraints.

Different influenza subtypes can evolve at very different rates, but the causes are not well understood. In this paper, we explore whether differences in transmissibility between subtypes can play a role if there are fitness constraints on antigenic evolution. We investigate the problem using a mathematical model that separates the interaction of strains through cross-immunity from the process of emergence for new antigenic variants. Evolutionary constraints are also included with antigenic mutation incurring a fitness cost. We show that the transmissibility of a strain can become disproportionately important in dictating the rate of antigenic drift: strains that spread only slightly more easily can have a much higher rate of emergence. Further, we see that the effect continues when vaccination is considered; a small increase in the rate of transmission can make it much harder to control the frequency at which new strains emerge. Our results not only highlight the importance of considering both transmission and fitness constraints when modelling influenza evolution, but may also help in understanding the differences between the emergence of H1N1 and H3N2 subtypes.

Age profile of immunity to influenza: effect of original antigenic sin.

When multiple infections are possible during an individual's lifetime, as with influenza, a host's history of infection and immunity will determine the result of future exposures. In turn, the suite of varying individual infection histories will shape the population level dynamics of the disease. Exploring the consequences of precisely how immunity is acquired using mathematical models has proven challenging though: if n strains have circulated previously, there are 2(n) combinations of past infection to consider. However, by using an age-structured mathematical model of a disease with multiple strains, we can examine the population immune profile without explicitly keeping track of all possible infection histories. This framework allows previously unknown consequences of assumptions about immune acquisition to be observed. In particular, we see that 'original antigenic sin' can reduce immunity in some age groups: these immune blind spots could be responsible for the unexpectedly high severity of certain past influenza epidemics.

A Bayesian approach to analyse genetic variation within RNA viral populations.

The development of modern and affordable sequencing technologies has allowed the study of viral populations to an unprecedented depth. This is of particular interest for the study of within-host RNA viral populations, where variation due to error-prone polymerases can lead to immune escape, antiviral resistance and adaptation to new host species. Methods to sequence RNA virus genomes include reverse transcription (RT) and polymerase chain reaction (PCR). RT-PCR is a molecular biology technique widely used to amplify DNA from an RNA template. The method itself relies on the in vitro synthesis of copy DNA from RNA followed by multiple cycles of DNA amplification. However, this method introduces artefactual errors that can act as confounding factors when the sequence data are analysed. Although there are a growing number of published studies exploring the intra- and inter-host evolutionary dynamics of RNA viruses, the complexity of the methods used to generate sequences makes it difficult to produce probabilistic statements about the likely sources of observed sequence variants. This complexity is further compounded as both the depth of sequencing and the length of the genome segment of interest increase. Here we develop a bayesian method to characterise and differentiate between likely structures for the background viral population. This approach can then be used to identify nucleotide sites that show evidence of change in the within-host viral population structure, either over time or relative to a reference sequence (e.g. an inoculum or another source of infection), or both, without having to build complex evolutionary models. Identification of these sites can help to inform the design of more focussed experiments using molecular biology tools, such as site-directed mutagenesis, to assess the function of specific amino acids. We illustrate the method by applying to datasets from experimental transmission of equine influenza, and a pre-clinical vaccine trial for HIV-1.

Genomic analysis of codon, sequence and structural conservation with selective biochemical-structure mapping reveals highly conserved and dynamic structures in rotavirus RNAs with potential cis-acting functions.

Rotaviruses are a major cause of acute, often fatal, gastroenteritis in infants and young children world-wide. Virions contain an 11 segment double-stranded RNA genome. Little is known about the cis-acting sequences and structural elements of the viral RNAs. Using a database of 1621 full-length sequences of mammalian group A rotavirus RNA segments, we evaluated the codon, sequence and RNA structural conservation of the complete genome. Codon conservation regions were found in eight ORFs, suggesting the presence of functional RNA elements. Using ConStruct and RNAz programmes, we identified conserved secondary structures in the positive-sense RNAs including long-range interactions (LRIs) at the 5' and 3' terminal regions of all segments. In RNA9, two mutually exclusive structures were observed suggesting a switch mechanism between a conserved terminal LRI and an independent 3' stem-loop structure. In RNA6, a conserved stem-loop was found in a region previously reported to have translation enhancement activity. Biochemical structural analysis of RNA11 confirmed the presence of terminal LRIs and two internal helices with high codon and sequence conservation. These extensive in silico and in vitro analyses provide evidence of the conservation, complexity, multi-functionality and dynamics of rotavirus RNA structures which likely influence RNA replication, translation and genome packaging.

Commentary on the use of the reproduction number R during the COVID-19 pandemic.

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.