Mapping social distancing measures to the reproduction number for COVID-19

In the absence of a vaccine, severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) transmission has been controlled by preventing person-to-person interactions via social distancing measures. In order to re-open parts of society, policy-makers need to consider how combinations of measures will affect transmission and understand the trade-offs between them. We use age-specific social contact data, together with epidemiological data, to quantify the components of the COVID-19 reproduction number. We estimate the impact of social distancing policies on the reproduction number by turning contacts on and off based on context and age. We focus on the impact of re-opening schools against a background of wider social distancing measures. We demonstrate that pre-collected social contact data can be used to provide a time-varying estimate of the reproduction number (R). We find that following lockdown (when R= 0.7, 95% CI 0.6, 0.8), opening primary schools has a modest impact on transmission (R = 0.89, 95% CI 0.82-0.97) as long as other social interactions are not increased. Opening secondary and primary schools is predicted to have a larger impact (R = 1.22, 95% CI 1.02-1.53). Contact tracing and COVID security can be used to mitigate the impact of increased social mixing to some extent; however, social distancing measures are still required to control transmission. Our approach has been widely used by policy-makers to project the impact of social distancing measures and assess the trade-offs between them. Effective social distancing, contact tracing and COVID security are required if all age groups are to return to school while controlling transmission. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Using Serology to Anticipate Measles Post-honeymoon Period Outbreaks

Measles vaccination is a public health 'best buy', with the highest cost of illness averted of any vaccine-preventable disease (Ozawa et al., Bull. WHO 2017;95:629). In recent decades, substantial reductions have been made in the number of measles cases, with an estimated 20 million deaths averted from 2000 to 2017 (Dabbagh et al., MMWR 2018;67:1323). Yet, an important feature of epidemic dynamics is that large outbreaks can occur following years of apparently successful control (Mclean et al., Epidemiol. Infect. 1988;100:419-442). Such 'post-honeymoon period' outbreaks are a result of the nonlinear dynamics of epidemics (Mclean et al., Epidemiol. Infect. 1988;100:419-442). Anticipating post-honeymoon outbreaks could lead to substantial gains in public health, helping to guide the timing, age-range, and location of catch-up vaccination campaigns (Grais et al., J. Roy. Soc. Interface 2008003B6:67-74). Theoretical conditions for such outbreaks are well understood for measles, yet the information required to make these calculations policy-relevant is largely lacking. We propose that a major extension of serological studies to directly characterize measles susceptibility is a high priority.

Lord Robert May (1936–2020)

Pioneering ecologist and a founder of chaos theory

Mapping the drivers of within-host pathogen evolution using massive data sets

Differences among hosts, resulting from genetic variation in the immune system or heterogeneity in drug treatment, can impact within-host pathogen evolution. Genetic association studies can potentially identify such interactions. However, extensive and correlated genetic population structure in hosts and pathogens presents a substantial risk of confounding analyses. Moreover, the multiple testing burden of interaction scanning can potentially limit power. We present a Bayesian approach for detecting host influences on pathogen evolution that exploits vast existing data sets of pathogen diversity to improve power and control for stratification. The approach models key processes, including recombination and selection, and identifies regions of the pathogen genome affected by host factors. Our simulations and empirical analysis of drug-induced selection on the HIV-1 genome show that the method recovers known associations and has superior precision-recall characteristics compared to other approaches. We build a high-resolution map of HLA-induced selection in the HIV-1 genome, identifying novel epitope-allele combinations.

A restatement of the natural science evidence base on the effects of endocrine disrupting chemicals on wildlife

Endocrine disrupting chemicals (EDCs) are substances that alter the function of the endocrine system and consequently cause adverse effects to humans or wildlife. The release of particular EDCs into the environment has been shown to negatively affect certain wildlife populations and has led to restrictions on the use of some EDCs. Current chemical regulations aim to balance the industrial, agricultural and/or pharmaceutical benefits of using these substances with their demonstrated or potential harm to human health or the environment. A summary is provided of the natural science evidence base informing the regulation of chemicals released into the environment that may have endocrine disrupting effects on wildlife. This summary is in a format (a 'restatement') intended to be policy-neutral and accessible to informed, but not expert, policy-makers and stakeholders.

Increased T cell trafficking as adjunct therapy for HIV-1

Although antiretroviral drug therapy suppresses human immunodeficiency virus-type 1 (HIV-1) to undetectable levels in the blood of treated individuals, reservoirs of replication competent HIV-1 endure. Upon cessation of antiretroviral therapy, the reservoir usually allows outgrowth of virus and approaches to targeting the reservoir have had limited success. Ongoing cycles of viral replication in regions with low drug penetration contribute to this persistence. Here, we use a mathematical model to illustrate a new approach to eliminating the part of the reservoir attributable to persistent replication in drug sanctuaries. Reducing the residency time of CD4 T cells in drug sanctuaries renders ongoing replication unsustainable in those sanctuaries. We hypothesize that, in combination with antiretroviral drugs, a strategy to orchestrate CD4 T cell trafficking could contribute to a functional cure for HIV-1 infection.

Investigating the effects of age-related spatial structuring on the transmission of a tick-borne virus in a colonially breeding host

Higher pathogen and parasite transmission is considered a universal cost of colonial breeding due to the physical proximity of colony members. However, this has rarely been tested in natural colonies, which are structured entities, whose members interact with a subset of individuals and differ in their infection histories. We use a population of common guillemots, Uria aalge, infected by a tick-borne virus, Great Island virus, to explore how age-related spatial structuring can influence the infection costs borne by different members of a breeding colony. Previous work has shown that the per-susceptible risk of infection (force of infection) is different for prebreeding (immature) and breeding (adult) guillemots which occupy different areas of the colony. We developed a mathematical model which showed that this difference in infection risk can only be maintained if mixing between these age groups is low. To estimate mixing between age groups, we recorded the movements of 63 individually recognizable, prebreeding guillemots in four different parts of a major colony in the North Sea during the breeding season. Prebreeding guillemots infrequently entered breeding areas (in only 26% of watches), though with marked differences in frequency of entry among individuals and more entries toward the end of the breeding season. Once entered, the proportion of time spent in breeding areas by prebreeding guillemots also varied between different parts of the colony. Our data and model predictions indicate low levels of age-group mixing, limiting exposure of breeding guillemots to infection. However, they also suggest that prebreeding guillemots have the potential to play an important role in driving infection dynamics. This highlights the sensitivity of breeding colonies to changes in the behavior of their members-a subject of particular importance in the context of global environmental change.

A restatement of the natural science evidence base concerning the health effects of low-level ionizing radiation

Exposure to ionizing radiation is ubiquitous, and it is well established that moderate and high doses cause ill-health and can be lethal. The health effects of low doses or low dose-rates of ionizing radiation are not so clear. This paper describes a project which sets out to summarize, as a restatement, the natural science evidence base concerning the human health effects of exposure to low-level ionizing radiation. A novel feature, compared to other reviews, is that a series of statements are listed and categorized according to the nature and strength of the evidence that underpins them. The purpose of this restatement is to provide a concise entrée into this vibrant field, pointing the interested reader deeper into the literature when more detail is needed. It is not our purpose to reach conclusions on whether the legal limits on radiation exposures are too high, too low or just right. Our aim is to provide an introduction so that non-specialist individuals in this area (be they policy-makers, disputers of policy, health professionals or students) have a straightforward place to start. The summary restatement of the evidence and an extensively annotated bibliography are provided as appendices in the electronic supplementary material.

Evolution, human-microbe interactions, and life history plasticity

A bacterium was once a component of the ancestor of all eukaryotic cells, and much of the human genome originated in microorganisms. Today, all vertebrates harbour large communities of microorganisms (microbiota), particularly in the gut, and at least 20% of the small molecules in human blood are products of the microbiota. Changing human lifestyles and medical practices are disturbing the content and diversity of the microbiota, while simultaneously reducing our exposures to the so-called old infections and to organisms from the natural environment with which human beings co-evolved. Meanwhile, population growth is increasing the exposure of human beings to novel pathogens, particularly the crowd infections that were not part of our evolutionary history. Thus some microbes have co-evolved with human beings and play crucial roles in our physiology and metabolism, whereas others are entirely intrusive. Human metabolism is therefore a tug-of-war between managing beneficial microbes, excluding detrimental ones, and channelling as much energy as is available into other essential functions (eg, growth, maintenance, reproduction). This tug-of-war shapes the passage of each individual through life history decision nodes (eg, how fast to grow, when to mature, and how long to live).

The impact of antiretroviral therapy on population-level virulence evolution of HIV-1

In HIV-infected patients, an individual's set point viral load (SPVL) strongly predicts disease progression. Some think that SPVL is evolving, indicating that the virulence of the virus may be changing, but the data are not consistent. In addition, the widespread use of antiretroviral therapy (ART) has the potential to drive virulence evolution. We develop a simple deterministic model designed to answer the following questions: what are the expected patterns of virulence change in the initial decades of an epidemic? Could administration of ART drive changes in virulence evolution and, what is the potential size and direction of this effect? We find that even without ART we would not expect monotonic changes in average virulence. Transient decreases in virulence following the peak of an epidemic are not necessarily indicative of eventual evolution to avirulence. In the short term, we would expect widespread ART to cause limited downward pressure on virulence. In the long term, the direction of the effect is determined by a threshold condition, which we define. We conclude that, given the surpassing benefits of ART to the individual and in reducing onward transmission, virulence evolution considerations need have little bearing on how we treat.

A restatement of recent advances in the natural science evidence base concerning neonicotinoid insecticides and insect pollinators

A summary is provided of recent advances in the natural science evidence base concerning the effects of neonicotinoid insecticides on insect pollinators in a format (a 'restatement') intended to be accessible to informed but not expert policymakers and stakeholders. Important new studies have been published since our recent review of this field (Godfray et al. 2014 Proc. R. Soc. B 281, 20140558. (doi:10.1098/rspb.2014.0558)) and the subject continues to be an area of very active research and high policy relevance.

Structured observations reveal slow HIV-1 CTL escape

The existence of viral variants that escape from the selection pressures imposed by cytotoxic T-lymphocytes (CTLs) in HIV-1 infection is well documented, but it is unclear when they arise, with reported measures of the time to escape in individuals ranging from days to years. A study of participants enrolled in the SPARTAC (Short Pulse Anti-Retroviral Therapy at HIV Seroconversion) clinical trial allowed direct observation of the evolution of CTL escape variants in 125 adults with primary HIV-1 infection observed for up to three years. Patient HLA-type, longitudinal CD8+ T-cell responses measured by IFN-γ ELISpot and longitudinal HIV-1 gag, pol, and nef sequence data were used to study the timing and prevalence of CTL escape in the participants whilst untreated. Results showed that sequence variation within CTL epitopes at the first time point (within six months of the estimated date of seroconversion) was consistent with most mutations being transmitted in the infecting viral strain rather than with escape arising within the first few weeks of infection. Escape arose throughout the first three years of infection, but slowly and steadily. Approximately one third of patients did not drive any new escape in an HLA-restricted epitope in just under two years. Patients driving several escape mutations during these two years were rare and the median and modal numbers of new escape events in each patient were one and zero respectively. Survival analysis of time to escape found that possession of a protective HLA type significantly reduced time to first escape in a patient (p = 0.01), and epitopes escaped faster in the face of a measurable CD8+ ELISpot response (p = 0.001). However, even in an HLA matched host who mounted a measurable, specific, CD8+ response the average time before the targeted epitope evolved an escape mutation was longer than two years.

A restatement of the natural science evidence base concerning neonicotinoid insecticides and insect pollinators

There is evidence that in Europe and North America many species of pollinators are in decline, both in abundance and distribution. Although there is a long list of potential causes of this decline, there is concern that neonicotinoid insecticides, in particular through their use as seed treatments are, at least in part, responsible. This paper describes a project that set out to summarize the natural science evidence base relevant to neonicotinoid insecticides and insect pollinators in as policy-neutral terms as possible. A series of evidence statements are listed and categorized according to the nature of the underlying information. The evidence summary forms the appendix to this paper and an annotated bibliography is provided in the electronic supplementary material.

Impact of HLA-driven HIV adaptation on virulence in populations of high HIV seroprevalence

It is widely believed that epidemics in new hosts diminish in virulence over time, with natural selection favoring pathogens that cause minimal disease. However, a tradeoff frequently exists between high virulence shortening host survival on the one hand but allowing faster transmission on the other. This is the case in HIV infection, where high viral loads increase transmission risk per coital act but reduce host longevity. We here investigate the impact on HIV virulence of HIV adaptation to HLA molecules that protect against disease progression, such as HLA-B*57 and HLA-B*58:01. We analyzed cohorts in Botswana and South Africa, two countries severely affected by the HIV epidemic. In Botswana, where the epidemic started earlier and adult seroprevalence has been higher, HIV adaptation to HLA including HLA-B*57/58:01 is greater compared with South Africa (P = 7 × 10(-82)), the protective effect of HLA-B*57/58:01 is absent (P = 0.0002), and population viral replicative capacity is lower (P = 0.03). These data suggest that viral evolution is occurring relatively rapidly, and that adaptation of HIV to the most protective HLA alleles may contribute to a lowering of viral replication capacity at the population level, and a consequent reduction in HIV virulence over time. The potential role in this process played by increasing antiretroviral therapy (ART) access is also explored. Models developed here suggest distinct benefits of ART, in addition to reducing HIV disease and transmission, in driving declines in HIV virulence over the course of the epidemic, thereby accelerating the effects of HLA-mediated viral adaptation.

Positive selection and compensatory adaptation interact to stabilize non-transmissible plasmids

Plasmids are important drivers of bacterial evolution, but it is challenging to understand how plasmids persist over the long term because plasmid carriage is costly. Classical models predict that horizontal transfer is necessary for plasmid persistence, but recent work shows that almost half of plasmids are non-transmissible. Here we use a combination of mathematical modelling and experimental evolution to investigate how a costly, non-transmissible plasmid, pNUK73, can be maintained in populations of Pseudomonas aeruginosa. Compensatory adaptation increases plasmid stability by eliminating the cost of plasmid carriage. However, positive selection for plasmid-encoded antibiotic resistance is required to maintain the plasmid by offsetting reductions in plasmid frequency due to segregational loss. Crucially, we show that compensatory adaptation and positive selection reinforce each other’s effects. Our study provides a new understanding of how plasmids persist in bacterial populations, and it helps to explain why resistance can be maintained after antibiotic use is stopped.

Plasmids are important for bacterial evolution but the evolutionary mechanisms behind their maintenance are unclear. Here the authors show that the interplay between compensatory adaptation and positive selection for plasmid-encoded antibiotic resistance determines plasmid persistence in P. aeruginosa.

Seven challenges in modeling pathogen dynamics within-host and across scales

The population dynamics of infectious disease is a mature field in terms of theory and to some extent, application. However for microparasites, the theory and application of models of the dynamics within a single infected host is still an open field. Further, connecting across the scales--from cellular to host level, to population level--has potential to vastly improve our understanding of pathogen dynamics and evolution. Here, we highlight seven challenges in the following areas: transmission bottlenecks, heterogeneity within host, dynamic fitness landscapes within hosts, making use of next-generation sequencing data, capturing superinfection and when and how to model more than two scales.

Nine challenges in modelling the emergence of novel pathogens

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We summarize key challenges in modeling the emergence of novel infectious agents.

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We focus on connections to data, including epidemiologic and genetic data.

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Zoonoses are emphasized, because they are the source of most new human pathogens.

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Challenges span reservoir dynamics, cross-species spillover, and outbreak dynamics.

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Estimation of fatality rates and overall risk assessment are also addressed.

Studying the emergence of novel infectious agents involves many processes spanning host species, spatial scales, and scientific disciplines. Mathematical models play an essential role in combining insights from these investigations and drawing robust inferences from field and experimental data. We describe nine challenges in modelling the emergence of novel pathogens, emphasizing the interface between models and data.

A restatement of the natural science evidence base relevant to the control of bovine tuberculosis in Great Britain

Bovine tuberculosis (bTB) is a very important disease of cattle in Great Britain, where it has been increasing in incidence and geographical distribution. In addition to cattle, it infects other species of domestic and wild animals, in particular the European badger (Meles meles). Policy to control bTB is vigorously debated and contentious because of its implications for the livestock industry and because some policy options involve culling badgers, the most important wildlife reservoir. This paper describes a project to provide a succinct summary of the natural science evidence base relevant to the control of bTB, couched in terms that are as policy-neutral as possible. Each evidence statement is placed into one of four categories describing the nature of the underlying information. The evidence summary forms the appendix to this paper and an annotated bibliography is provided in the electronic supplementary material.

Towards the endgame and beyond: complexities and challenges for the elimination of infectious diseases

Successful control measures have interrupted the local transmission of human infectious diseases such as measles, malaria and polio, and saved and improved billions of lives. Similarly, control efforts have massively reduced the incidence of many infectious diseases of animals, such as rabies and rinderpest, with positive benefits for human health and livelihoods across the globe. However, disease elimination has proven an elusive goal, with only one human and one animal pathogen globally eradicated. As elimination targets expand to regional and even global levels, hurdles may emerge within the endgame when infections are circulating at very low levels, turning the last mile of these public health marathons into the longest mile. In this theme issue, we bring together recurring challenges that emerge as we move towards elimination, highlighting the unanticipated consequences of particular ecologies and pathologies of infection, and approaches to their management.

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 (ODEs) ignore information about the genealogy of sampled HIV sequences, which has the potential to cause systematic bias and overestimate 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 and hypothesis testing 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.

Why was the 2009 influenza pandemic in England so small?

The “Swine flu” pandemic of 2009 caused world-wide infections and deaths. Early efforts to understand its rate of spread were used to predict the probable future number of cases, but by the end of 2009 it was clear that these predictions had substantially overestimated the pandemic's eventual impact. In England, the Health Protection Agency made announcements of the number of cases of disease, which turned out to be surprisingly low for an influenza pandemic. The agency also carried out a serological survey half-way through the English epidemic. In this study, we use a mathematical model to reconcile early estimates of the rate of spread of infection, weekly data on the number of cases in the 2009 epidemic in England and the serological status of the English population at the end of the first pandemic wave. Our results reveal that if there are around 19 infections (i.e., seroconverters) for every reported case then the three data-sets are entirely consistent with each other. We go on to discuss when in the epidemic such a high ratio of seroconverters to cases of disease might have been detected, either through patterns in the case reports or through even earlier serological surveys.

Modelling the spread of HIV immune escape mutants in a vaccinated population

Because cytotoxic T-lymphocytes (CTLs) have been shown to play a role in controlling human immunodeficiency virus (HIV) infection and because CTL-based simian immunodeficiency virus (SIV) vaccines have proved effective in non-human primates, one goal of HIV vaccine design is to elicit effective CTL responses in humans. Such a vaccine could improve viral control in patients who later become infected, thereby reducing onwards transmission and enhancing life expectancy in the absence of treatment. The ability of HIV to evolve mutations that evade CTLs and the ability of these ‘escape mutants’ to spread amongst the population poses a challenge to the development of an effective and robust vaccine. We present a mathematical model of within-host evolution and between-host transmission of CTL escape mutants amongst a population receiving a vaccine that elicits CTL responses to multiple epitopes. Within-host evolution at each epitope is represented by the outgrowth of escape mutants in hosts who restrict the epitope and their reversion in hosts who do not restrict the epitope. We use this model to investigate how the evolution and spread of escape mutants could affect the impact of a vaccine. We show that in the absence of escape, such a vaccine could markedly reduce the prevalence of both infection and disease in the population. However the impact of such a vaccine could be significantly abated by CTL escape mutants, especially if their selection in hosts who restrict the epitope is rapid and their reversion in hosts who do not restrict the epitope is slow. We also use the model to address whether a vaccine should span a broad or narrow range of CTL epitopes and target epitopes restricted by rare or common HLA types. We discuss the implications and limitations of our findings.

The evolution and spread of HIV strains that evade the immune response poses a major challenge to the development of an effective and robust HIV vaccine. We present a new mathematical tool that we use to dissect the drivers of the spread of these ‘immune escape mutants’ in a vaccinated population. Our study focuses on a vaccine that can reduce infectiousness and enhance longevity but does not provide sterilizing immunity. We show that in the absence of escape such a vaccine could reduce the prevalence of both infection and disease in the population. However, vaccine impact could be significantly abated by immune escape mutants, especially if they emerge rapidly and revert very slowly after transmission to hosts in whom the original selection pressure is absent. We also discuss the effect that vaccine breadth and the frequency with which different epitopes are targeted have upon vaccine impact.

There is no safe dose of prions

Understanding the circumstances under which exposure to transmissible spongiform encephalopathies (TSEs) leads to infection is important for managing risks to public health. Based upon ideas in toxicology and radiology, it is plausible that exposure to harmful agents, including TSEs, is completely safe if the dose is low enough. However, the existence of a threshold, below which infection probability is zero has never been demonstrated experimentally. Here we explore this question by combining data and mathematical models that describe scrapie infections in mice following experimental challenge over a broad range of doses. We analyse data from 4338 mice inoculated at doses ranging over ten orders of magnitude. These data are compared to results from a within-host model in which prions accumulate according to a stochastic birth-death process. Crucially, this model assumes no threshold on the dose required for infection. Our data reveal that infection is possible at the very low dose of a 1000 fold dilution of the dose that infects half the challenged animals (ID50). Furthermore, the dose response curve closely matches that predicted by the model. These findings imply that there is no safe dose of prions and that assessments of the risk from low dose exposure are right to assume a linear relationship between dose and probability of infection. We also refine two common perceptions about TSE incubation periods: that their mean values decrease linearly with logarithmic decreases in dose and that they are highly reproducible between hosts. The model and data both show that the linear decrease in incubation period holds only for doses above the ID50. Furthermore, variability in incubation periods is greater than predicted by the model, not smaller. This result poses new questions about the sources of variability in prion incubation periods. It also provides insight into the limitations of the incubation period assay.

A mathematical framework for estimating pathogen transmission fitness and inoculum size using data from a competitive mixtures animal model

We present a method to measure the relative transmissibility (“transmission fitness”) of one strain of a pathogen compared to another. The model is applied to data from “competitive mixtures” experiments in which animals are co-infected with a mixture of two strains. We observe the mixture in each animal over time and over multiple generations of transmission. We use data from influenza experiments in ferrets to demonstrate the approach. Assessment of the relative transmissibility between two strains of influenza is important in at least three contexts: 1) Within the human population antigenically novel strains of influenza arise and compete for susceptible hosts. 2) During a pandemic event, a novel sub-type of influenza competes with the existing seasonal strain(s). The unfolding epidemiological dynamics are dependent upon both the population's susceptibility profile and the inherent transmissibility of the novel strain compared to the existing strain(s). 3) Neuraminidase inhibitors (NAIs), while providing significant potential to reduce transmission of influenza, exert selective pressure on the virus and so promote the emergence of drug-resistant strains. Any adverse outcome due to selection and subsequent spread of an NAI-resistant strain is exquisitely dependent upon the transmission fitness of that strain. Measurement of the transmission fitness of two competing strains of influenza is thus of critical importance in determining the likely time-course and epidemiology of an influenza outbreak, or the potential impact of an intervention measure such as NAI distribution. The mathematical framework introduced here also provides an estimate for the size of the transmitted inoculum. We demonstrate the framework's behaviour using data from ferret transmission studies, and through simulation suggest how to optimise experimental design for assessment of transmissibility. The method introduced here for assessment of mixed transmission events has applicability beyond influenza, to other viral and bacterial pathogens.

Determining which of two related viruses will spread from human to human more efficiently – e. g. an influenza virus that is treatable with drugs and one that is resistant to them – is important when forecasting the potential impact of an emergent novel virus or developing public health intervention strategies. However, making such measurements of relative transmissibility directly through observation, even using an animal model, is difficult. We have recently developed and published an experimental technique in which an animal is infected with both viruses of interest at once, and then allowed to mix with other animals and so transmit the infection. These experiments provide the necessary data for analysis using the novel mathematical framework that we introduce here. Our mathematical and computational results exploit the power of the experimental system, and allow us to make a quantitative estimate of the relative transmissibility of a drug-resistant influenza virus compared to its drug-sensitive counterpart. Through computer simulation, we demonstrate the wider application of our mathematical technique, and suggest design criteria for future experiments designed to measure the transmissibility of one virus (or other type of pathogen) compared to another.

Dynamic coinfection with multiple viral subtypes in acute hepatitis C

INTRODUCTION

Acute hepatitis C virus (HCV) infection is rarely studied, but virus sequence evolution and host-virus dynamics during this early stage may influence the outcome of infection. Hypervariable region 1 (HVR1) is genetically diverse and under selective pressure from the host immune response. We analyzed HVR1 evolution by frequent sampling of an acutely infected HCV cohort.

METHODS

Three or more pretreatment samples were obtained from each of 10 acutely infected subjects. Polymerase chain reaction amplification was performed with multiple primer combinations to identify the full range of sequences present. Positive samples were cloned and sequenced. Phylogenetic analyses were used to assess viral diversity.

RESULTS

Eight of the 10 subjects were coinfected with at least 2 HCV subtypes. Multiple subtypes were detected in individual samples, and their relative proportions changed through acute infection. The subjects with the most complex subtype structure also had a dynamic viral load; however, changes in viral load were not directly linked to changes in subtype.

CONCLUSIONS

This well-sampled cohort with acute HCV infection was characterized by dynamic coinfection with multiple viral subtypes, representing a highly complex virologic landscape extremely early in infection.

Insights into the evolution and emergence of a novel infectious disease

Many zoonotic, novel infectious diseases in humans appear as sporadic infections with spatially and temporally restricted outbreaks, as seen with influenza A(H5N1). Adaptation is often a key factor for successfully establishing sustained human-to-human transmission. Here we use simple mathematical models to describe different adaptation scenarios with particular reference to spatial heterogeneity within the human population. We present analytical expressions for the probability of emergence per introduction, as well as the waiting time to a successful emergence event. Furthermore, we derive general analytical results for the statistical properties of emergence events, including the probability distribution of outbreak sizes. We compare our analytical results with a stochastic model, which has previously been studied computationally. Our results suggest that, for typical connection strengths between communities, spatial heterogeneity has only a weak effect on outbreak size distributions, and on the risk of emergence per introduction. For example, if or larger, any village connected to a large city by just ten commuters a day is, effectively, just a part of the city when considering the chances of emergence and the outbreak size distribution. We present empirical data on commuting patterns and show that the vast majority of communities for which such data are available are at least this well interconnected. For plausible parameter ranges, the effects of spatial heterogeneity are likely to be dominated by the evolutionary biology of host adaptation. We conclude by discussing implications for surveillance and control of emerging infections.

Emerging infections are a continuing global public health issue, the most recent example being last year's ‘Swine flu’ influenza pandemic. However, for many zoonotic pathogens, some adaptation is required to cross the species barrier from an animal reservoir into humans and cause sustained transmission. Previous work has explored the relationship between the evolutionary biology of an adapting pathogen, and the epidemiology of cases that may arise before such a pathogen becomes pandemic-capable. Here, we extend this work to incorporate what is often an important host ecological feature, the spatial distribution of the host population. Many zoonoses occur away from large population centres. For example, HIV is thought to have entered the human population through bushmeat hunters in the sparsely populated jungles of Central Africa. We ask: when a pathogen is evolving to adapt for human transmission, under what circumstances does the spatial structure underlying the human population become important? We approach this question using mathematical models to explore regimes of connectedness between communities. Our results suggest that most communities are sufficiently interconnected to show no effect on the emergence process. We finish by discussing the implications of these findings for public health.

How fast could HIV change gene frequencies in the human population?

Infectious diseases have the potential to act as strong forces for genetic selection on the populations they affect. Human immunodeficiency virus (HIV) is a prime candidate to impose such genetic selection owing to the vast number of people it infects and the varying susceptibility of different human leucocyte antigen (HLA) types to HIV disease progression. We have constructed a model of HIV infection that differentiates between these HLA types, and have used reported estimates of the number of people infected with HIV and the different rates of progression to acquired immunodeficiency syndrome (AIDS) to provide a lower bound estimate on the length of time it would take for HIV to impose major genetic change in humans. We find that an HIV infection similar to that currently affecting sub-Saharan Africa could not yet have caused more than a 3 per cent decrease in the proportion of individuals who progress quickly to disease. Such an infection is unlikely to cause major genetic change (defined as a decrease in the proportion of quickly progressing individuals to under 50 per cent of their starting proportion) until 400 years have passed since HIV emergence. However, in very severely affected populations, there is a chance of observing such major genetic changes after another 50 years.

No evidence for competition between cytotoxic T-lymphocyte responses in HIV-1 infection

Strong competition between cytotoxic T-lymphocytes (CTLs) specific for different epitopes in human immunodeficiency virus (HIV) infection would have important implications for the design of an HIV vaccine. To investigate evidence for this type of competition, we analysed CTL response data from 97 patients with chronic HIV infection who were frequently sampled for up to 96 weeks. For each sample, CTL responses directed against a range of known epitopes in gag, pol and nef were measured using an enzyme-linked immunospot assay. The Lotka-Volterra model of competition was used to predict patterns that would be expected from these data if competitive interactions materially affect CTL numbers. In this application, the model predicts that when hosts make responses to a larger number of epitopes, they would have diminished responses to each epitope and that if one epitope-specific response becomes dramatically smaller, others would increase in size to compensate; conversely if one response grows, others would shrink. Analysis of the experimental data reveals results that are wholly inconsistent with these predictions. In hosts who respond to more epitopes, the average epitope-specific response tends to be larger, not smaller. Furthermore, responses to different epitopes almost always increase in unison or decrease in unison. Our findings are therefore inconsistent with the hypothesis that there is competition between CTL responses directed against different epitopes in HIV infection. This suggests that vaccines that elicit broad responses would be favourable because they would direct a larger total response against the virus, in addition to being more robust to the effects of CTL escape.

The effect of intrinsic stochasticity on transmitted HIV drug resistance patterns

Estimates of transmitted HIV drug-resistance prevalence vary widely among and within epidemiological surveys. Interpretation of trends from available survey data is therefore difficult. Because the emergence of drug-resistance involves small populations of infected drug-resistant individuals, the role of stochasticity (chance events) is likely to be important. The question addressed here is: how much variability in transmitted HIV drug-resistance prevalence patterns arises due to intrinsic stochasticity alone, i.e., if all starting conditions in the different epidemics surveyed were identical? This 'thought experiment' gives insight into the minimum expected variabilities within and among epidemics. A simple stochastic mathematical model was implemented. Our results show that stochasticity alone can generate a significant degree of variability and that this depends on the size and variation of the pool of new infections when drug treatment is first introduced. The variability in transmitted drug-resistance prevalence within an epidemic (i.e., the temporal variability) is large when the annual pool of all new infections is small (fewer than 200, typical of the HIV epidemics in Central European and Scandinavian countries) but diminishes rapidly as that pool grows. Epidemiological surveys involving hundreds of new infections annually are therefore needed to allow meaningful interpretation of temporal trends in transmitted drug-resistance prevalence within individual epidemics. The stochastic variability among epidemics shows a similar dependence on the pool of new infections if treatment is introduced after endemic equilibrium is established, but can persist even when there are more than 10,000 new infections annually if drug therapy is introduced earlier. Stochastic models may therefore have an important role to play in interpreting differences in transmitted drug-resistance prevalence trends among epidemiological surveys.

Evolution and emergence of novel human infections

Some zoonotic pathogens cause sporadic infection in humans but rarely propagate further, while others have succeeded in overcoming the species barrier and becoming established in the human population. Adaptation, driven by selection pressure in human hosts, can play a significant role in allowing pathogens to cross this species barrier. Here we use a simple mathematical model to study potential epidemiological markers of adaptation. We ask: under what circumstances could ongoing adaptation be signalled by large clusters of human infection? If a pathogen has caused hundreds of cases but with little transmission, does this indicate that the species barrier cannot be crossed? Finally, how can case reports be monitored to detect an imminent emergence event? We distinguish evolutionary scenarios under which adaptation is likely to be signalled by large clusters of infection and under which emergence is likely to occur without any prior warning. Moreover, we show that a lack of transmission never rules out adaptability, regardless of how many zoonoses have occurred. Indeed, after the first 100 zoonotic cases, continuing sporadic zoonotic infections without onward, human-to-human transmission offer little extra information on pathogen adaptability. Finally, we present a simple method for monitoring outbreaks for signs of emergence and discuss public health implications.

HLA-associated clinical progression correlates with epitope reversion rates in early human immunodeficiency virus infection

Human immunodeficiency virus type 1 (HIV-1) can evade immunity shortly after transmission to a new host but the clinical significance of this early viral adaptation in HIV infection is not clear. We present an analysis of sequence variation from a longitudinal cohort study of HIV adaptation in 189 acute seroconverters followed for up to 3 years. We measured the rates of variation within well-defined epitopes to determine associations with the HLA-linked hazard of disease progression. We found early reversion across both the gag and pol genes, with a 10-fold faster rate of escape in gag (2.2 versus 0.27 forward mutations/1,000 amino acid sites). For most epitopes (23/34), variation in the HLA-matched and HLA-unmatched controls was similar. For a minority of epitopes (8/34, and generally associated with HLA class I alleles that confer clinical benefit), new variants appeared early and consistently over the first 3 years of infection. Reversion occurred early at a rate which was HLA-dependent and correlated with the HLA class 1-associated relative hazard of disease progression and death (P = 0.0008), reinforcing the association between strong cytotoxic T-lymphocyte responses, viral fitness, and disease status. These data provide a comprehensive overview of viral adaptation in the first 3 years of infection. Our findings of HLA-dependent reversion suggest that costs are borne by some escape variants which may benefit the host, a finding contrary to a simple immune evasion paradigm. These epitopes, which are both strongly and frequently recognized, and for which escape involves a high cost to the virus, have the potential to optimize vaccine design.

Antiviral treatment for the control of pandemic influenza: some logistical constraints

Disease control programmes for an influenza pandemic will rely initially on the deployment of antiviral drugs such as Tamiflu, until a vaccine becomes available. However, such control programmes may be severely hampered by logistical constraints such as a finite stockpile of drugs and a limit on the distribution rate. We study the effects of such constraints using a compartmental modelling approach. We find that the most aggressive possible antiviral programme minimizes the final epidemic size, even if this should lead to premature stockpile run-out. Moreover, if the basic reproductive number R(0) is not too high, such a policy can avoid run-out altogether. However, where run-out would occur, such benefits must be weighed against the possibility of a higher epidemic peak than if a more conservative policy were followed. Where there is a maximum number of treatment courses that can be dispensed per day, reflecting a manpower limit on antiviral distribution, our results suggest that such a constraint is unlikely to have a significant impact (i.e. increasing the final epidemic size by more than 10%), as long as drug courses sufficient to treat at least 6% of the population can be dispensed per day.

Quantifying the risk from ovine BSE and the impact of control strategies

Although no naturally infected sheep with bovine spongiform encephalopathy (BSE) has ever been discovered, it remains possible that BSE once infected the UK sheep population, has been transmitted between sheep, and is still present today. We constructed a mathematical model to assess the current maximum theoretical exposure to consumers from BSE-infected ovine material and to estimate the risk reduction that could be achieved by abattoir-based control options if BSE-infected sheep were ever found in the national flock. We predict that, if present, the exposure to consumers from a single BSE-infected sheep would be high: one sheep, close to the end of its incubation period, is likely to contribute 10-1000 times more infectious material than a fully infectious cow. Furthermore, 30% of this exposure comes from infectivity residing in lymphatic and peripheral tissue that cannot be completely removed from a carcass. We are 95% confident that throughout Great Britain, no more than four sheep flocks currently harbour an ongoing BSE epidemic. However, since the exposure from a single infected sheep is high, the annual human exposure from four 'typical' BSE-infected flocks could be considerable. Small reductions in exposure could be achieved by strategies based on tissue testing, a 12-month age restriction or expanded definitions of high-risk tissues. A six-month age restriction is likely to be more effective and genotype-based strategies the most effective.

Understanding the impact of Hib conjugate vaccine on transmission, immunity and disease in the United Kingdom

A rise in invasive Haemophilus influenzae type b (Hib) infections occurred 8 years after vaccine introduction in the United Kingdom. Aspects of Hib vaccine delivery unique to the United Kingdom have been implicated. The authors developed a fully age-structured deterministic susceptible-infected-resistant-susceptible mathematical model, expressed as a set of partial differential equations, to better understand the causes of declining vaccine effectiveness. We also investigated the consequences of the vaccine's impact on reducing Hib transmission for maintenance of immunity. Our findings emphasized the importance of maintaining high post-immunization antibody titres among age groups at greatest risk of invasive infections. In keeping with UK population-based estimates, low direct efficacy of immunological memory against disease was found, cautioning against over-reliance on evidence of priming alone as a correlate of population protection. The contribution of herd immunity to disease control was reinforced. Possible intervention strategies will be explored in subsequent work.

In vivo CD8+ T cell control of immunodeficiency virus infection in humans and macaques

Forty million people are estimated to be infected with HIV-1, and only a small fraction of those have access to life-prolonging antiretroviral treatment. As the epidemic grows there is an urgent need for effective therapeutic and prophylactic vaccines. Nonhuman primate models of immunodeficiency virus infection are essential for the preclinical evaluation of candidate vaccines. To interpret the results of these trials, comparative studies of the human and macaque immune responses are needed. Despite the widespread use of macaques to evaluate vaccines designed to elicit a CD8(+) cytotoxic T lymphocyte (CTL) response, the efficiency with which CTL control immunodeficiency virus infections has not been compared between humans and macaques, largely because of difficulties in assaying the functional CTL response. We recently developed a method for estimating the rate at which CTLs kill cells productively infected with HIV-1 in humans in vivo. Here, using the same technique, we quantify the rate at which CTLs kill infected cells in macaque models of HIV infection. We show that CTLs kill productively infected cells significantly faster (P = 0.004) and that escape variants have significantly higher fitness costs (P = 0.003) in macaques compared with humans. These results suggest that it may be easier to elicit a protective CTL response in macaques than in humans and that vaccine studies conducted in macaques need to be interpreted accordingly.

Introduction

In this introductory chapter, we indicate the aims and structure of this book. We also indicate some of the ways in which the book is not synoptic in its coverage, but rather offers an interlinked account of some major developments in our understanding of the dynamics of ecological systems, from populations to communities, along with practical applications to important problems. Ecology is a young science. Theword ecology itself was coined not much more than 100 years ago, and the oldest professional society, the British Ecological Society, is less than a century old. Arguably the first published work on ecology was Gilbert White’s The Natural History of Selborne. This book, published in 1789, was ahead of its time in seeing plants and animals not as individual objects of wonder—things to be assembled in a cabinet of curiosities—but as parts of acommunity of living organisms, interacting with the environment, other organisms, and humans. The book has not merely remained in print, but has run steadily through well over 200 editions and translations, to attain the status of the fourth most published book (in the sense of separate editions) in the English language. The following excerpt captures White’s blend of detailed observation and concern for basic questions. Among the many singularities attending those amusing birds, the swifts, I am now confirmed in the opinion that we have every year the same number of pairs invariably; at least, the result of my inquiry has been exactly the same for a long time past. The swallows and martins are so numerous, and so widely distributed over the village, that it is hardly possible to recount them; while the swifts, though they do not all build in the church, yet so frequently haunt it, and play and rendezvous round it, that they are easily enumerated. The number that I constantly find are eight pairs, about half of which reside in the church, and the rest in some of the lowest and meanest thatched cottages.

Inefficient cytotoxic T lymphocyte-mediated killing of HIV-1-infected cells in vivo

Understanding the role of cytotoxic T lymphocytes (CTLs) in controlling HIV-1 infection is vital for vaccine design. However, it is difficult to assess the importance of CTLs in natural infection. Different human leukocyte antigen (HLA) class I alleles are associated with different rates of progression to AIDS, indicating that CTLs play a protective role. Yet virus clearance rates following antiretroviral therapy are not impaired in individuals with advanced HIV disease, suggesting that weakening of the CTL response is not the major underlying cause of disease progression and that CTLs do not have an important protective role. Here we reconcile these apparently conflicting studies. We estimate the selection pressure exerted by CTL responses that drive the emergence of immune escape variants, thereby directly quantifying the efficiency of HIV-1–specific CTLs in vivo. We estimate that only 2% of productively infected CD4 ⁺ cell death is attributable to CTLs recognising a single epitope. We suggest that CTLs kill a large number of infected cells (about 10 ⁷) per day but are not responsible for the majority of infected cell death.

Although cytotoxic T lymphocytes (CTLs) kill a large number of HIV-infected cells every day, they may not be responsible for the majority of infected cell death.

Quantification of the virus-host interaction in human T lymphotropic virus I infection

BACKGROUND

HTLV-I causes the disabling inflammatory disease HAM/TSP: there is no vaccine, no satisfactory treatment and no means of assessing the risk of disease or prognosis in infected people. Like many immunopathological diseases with a viral etiology the outcome of infection is thought to depend on the virus-host immunology interaction. However the dynamic virus-host interaction is complex and current models of HAM/TSP pathogenesis are conflicting. The CD8+ cell response is thought to be a determinant of both HTLV-I proviral load and disease status but its effects can obscure other factors.

RESULTS

We show here that in the absence of CD8+ cells, CD4+ lymphocytes from HAM/TSP patients expressed HTLV-I protein significantly more readily than lymphocytes from asymptomatic carriers of similar proviral load (P = 0.017). A high rate of viral protein expression was significantly associated with a large increase in the prevalence of HAM/TSP (P = 0.031, 89% of cases correctly classified). Additionally, a high rate of Tax expression and a low CD8+ cell efficiency were independently significantly associated with a high proviral load (P = 0.005, P = 0.003 respectively).

CONCLUSION

These results disentangle the complex relationship between immune surveillance, proviral load, inflammatory disease and viral protein expression and indicate that increased protein expression may play an important role in HAM/TSP pathogenesis. This has important implications for therapy since it suggests that interventions should aim to reduce Tax expression rather than proviral load per se.

What have we learnt from SARS?

With outbreaks of infectious disease emerging from animal sources, we have learnt to expect the unexpected. We were, and are, expecting a new influenza A pandemic, but no one predicted the emergence of an unknown coronavirus (CoV) as a deadly human pathogen. Thanks to the preparedness of the international network of influenza researchers and laboratories, the cause of severe acute respiratory syndrome (SARS) was rapidly identified, but there is no complacency over the global or local management of the epidemic in terms of public health logistics. The human population was lucky that only a small proportion of infected persons proved to be highly infectious to others, and that they did not become so before they felt ill. These were the features that helped to make the outbreak containable. The next outbreak of another kind of transmissible disease may well be quite different.

A scrapie epidemic in Cyprus

Scrapie is endemic in the sheep flocks of many countries, but good epidemiological information on this disease is scarce. Data on the initial stages of an epidemic are even more rare. We describe the ongoing epidemic of scrapie in Cyprus that has been tracked since it began in the mid-1980s. The early stages of the spread of scrapie from farm to farm, between 1985 and 2000, is analysed with a simple mathematical model. The flock-to-flock basic reproductive number (R0) for the spread of scrapie was estimated at between 1.4 and 1.8. The impact of interventions on the control of the epidemic are discussed from an epidemiological and economic point of view. Early identification of scrapie cases on farms can have a large impact on the number of farms affected. The long period before detection of disease in a flock means that policies based on whole-flock slaughter can be inefficient in preventing spread. Under a range of scenarios, a concentration of resources on early detection and quarantine may be more effective in terms of both the costs and control of the epidemic.

Quantifiable cytotoxic T lymphocyte responses and HLA-related risk of progression to AIDS

There are significant associations between possession of certain HLA class I alleles and rate of progression to AIDS. Immunological data provide an explanatory mechanism for this relationship. Patients with HLA types associated with rapid disease progression recognize a significantly smaller fraction of their known repertoire of viral epitopes than do patients with HLA types associated with slow progression. Population frequency of HLA types (or supertypes) and their capacity to elicit cytotoxic T lymphocyte responses are also negatively correlated. These data provide an immunological mechanism to explain HLA-related risk of progression to AIDS and emphasize the central role of viral evolution in the pathogenesis of HIV.

Introduction. Emerging infections: what have we learnt from SARS?

In the summer of 2003, as the first global severe acute respiratory syndrome (SARS) epidemic stuttered to a close, The Royal Society set about organizing a meeting that would take stock of the year's events and ask ‘what can we learn from SARS about emerging infections in general?’ Emerging infections are more than just a current biological fashion. The bitter ongoing experience of AIDS and the looming threat of an influenza pandemic teach us that the control of infectious disease is a problem we have not yet solved. It is a problem that needs to be addressed by a broad community. Scientists, policy makers and health care workers all need to be prepared, but prepared to do what? The purpose of the meeting was to use SARS as an example to enumerate the generic issues that must be considered when planning for the control of emerging infections.

Epidemiological implications of the susceptibility to BSE of putatively resistant sheep

The experimental infection of sheep with bovine spongiform encephalopathy (BSE) by the oral route and the likelihood that sheep were fed BSE-infected meat and bone meal has led to extensive speculation as to whether or not sheep are naturally infected with BSE. In response, the UK government has initiated the National Scrapie Plan (NSP), an ambitious £120 million per year project to create a BSE- and scrapie-resistant national sheep flock, by selectively breeding for a genotype of sheep believed to be resistant to both diseases. This genotype has recently been shown to be susceptible to BSE by intracerebral (i.c.) inoculation. Should these sheep be sufficiently susceptible to BSE via natural transmission, the NSP might fail. Here we estimate the susceptibility of this genotype to horizontal (sheep-to-sheep) transmission of BSE by comparison with more extensive oral and i.c. exposure data for other sheep genotypes. We show that a previous estimate of the risk of BSE transmission to sheep via the feedborne route remains robust. However, using a mathematical model for the within-flock transmission of BSE, we show that, while the best estimate indicates that the NSP should be successful, current data cannot exclude the failure of the NSP.

Repeated challenge with prion disease: the risk of infection and impact on incubation period

Natural exposure to prion disease is likely to occur throughout successive challenges, yet most experiments focus on single large doses of infectious material. We analyze the results from an experiment in which rodents were exposed to multiple doses of feed contaminated with the scrapie agent. We formally define hypotheses for how the doses combine in terms of statistical models. The competing hypotheses are that only the total dose of infectivity is important (cumulative model), doses act independently, or a general alternative that interaction between successive doses occurs (to raise or lower the risk of infection). We provide sample size calculations to distinguish these hypotheses. In the experiment, a fixed total dose has a significantly reduced probability of causing infection if the material is presented as multiple challenges, and as the time between challenges lengthens. Incubation periods are shorter and less variable if all material is consumed on one occasion. We show that the probability of infection is inconsistent with the hypothesis that each dose acts as a cumulative or independent challenge. The incubation periods are inconsistent with the independence hypothesis. Thus, although a trend exists for the risk of infection with prion disease to increase with repeated doses, it does so to a lesser degree than is expected if challenges combine independently or in a cumulative manner.

BSE - a wolf in sheep's clothing?

The entire sheep flock in the UK has been threatened with slaughter if BSE is found in farmed sheep, largely on the grounds that an epidemic of BSE in sheep could be harder to contain than was the case for cattle, and that lamb could present a greater risk to consumers than beef. However, identifying BSE in a sheep is not straightforward, because of its similarities to the related disease, scrapie. Here, we review the likelihood that any UK sheep have BSE, how they might have got it, how a case could be identified and what the Government is doing in terms of surveillance and possible control methods.