The probability of epidemic burnout in the stochastic SIR model with vital dynamics.

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.

Forward-looking serial intervals correctly link epidemic growth to reproduction numbers.

The reproduction number R and the growth rate r are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of R based on r. Here we explore how these intervals vary over the course of an epidemic, and the implications for R estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link R with r. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect R estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of R for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial R by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and R estimates for COVID-19.

Patterns of smallpox mortality in London, England, over three centuries.

Smallpox is unique among infectious diseases in the degree to which it devastated human populations, its long history of control interventions, and the fact that it has been successfully eradicated. Mortality from smallpox in London, England was carefully documented, weekly, for nearly 300 years, providing a rare and valuable source for the study of ecology and evolution of infectious disease. We describe and analyze smallpox mortality in London from 1664 to 1930. We digitized the weekly records published in the London Bills of Mortality (LBoM) and the Registrar General's Weekly Returns (RGWRs). We annotated the resulting time series with a sequence of historical events that might have influenced smallpox dynamics in London. We present a spectral analysis that reveals how periodicities in reported smallpox mortality changed over decades and centuries; many of these changes in epidemic patterns are correlated with changes in control interventions and public health policies. We also examine how the seasonality of reported smallpox mortality changed from the 17th to 20th centuries in London.

Acceleration of plague outbreaks in the second pandemic.

Historical records reveal the temporal patterns of a sequence of plague epidemics in London, United Kingdom, from the 14th to 17th centuries. Analysis of these records shows that later epidemics spread significantly faster ("accelerated"). Between the Black Death of 1348 and the later epidemics that culminated with the Great Plague of 1665, we estimate that the epidemic growth rate increased fourfold. Currently available data do not provide enough information to infer the mode of plague transmission in any given epidemic; nevertheless, order-of-magnitude estimates of epidemic parameters suggest that the observed slow growth rates in the 14th century are inconsistent with direct (pneumonic) transmission. We discuss the potential roles of demographic and ecological factors, such as climate change or human or rat population density, in driving the observed acceleration.

Testing and Isolation Efficacy: Insights from a Simple Epidemic Model.

Testing individuals for pathogens can affect the spread of epidemics. Understanding how individual-level processes of sampling and reporting test results can affect community- or population-level spread is a dynamical modeling question. The effect of testing processes on epidemic dynamics depends on factors underlying implementation, particularly testing intensity and on whom testing is focused. Here, we use a simple model to explore how the individual-level effects of testing might directly impact population-level spread. Our model development was motivated by the COVID-19 epidemic, but has generic epidemiological and testing structures. To the classic SIR framework we have added a per capita testing intensity, and compartment-specific testing weights, which can be adjusted to reflect different testing emphases-surveillance, diagnosis, or control. We derive an analytic expression for the relative reduction in the basic reproductive number due to testing, test-reporting and related isolation behaviours. Intensive testing and fast test reporting are expected to be beneficial at the community level because they can provide a rapid assessment of the situation, identify hot spots, and may enable rapid contact-tracing. Direct effects of fast testing at the individual level are less clear, and may depend on how individuals' behaviour is affected by testing information. Our simple model shows that under some circumstances both increased testing intensity and faster test reporting can reduce the effectiveness of control, and allows us to explore the conditions under which this occurs. Conversely, we find that focusing testing on infected individuals always acts to increase effectiveness of control.

From science to politics: COVID-19 information fatigue on YouTube.

OBJECTIVE: The COVID-19 pandemic is the first pandemic where social media platforms relayed information on a large scale, enabling an "infodemic" of conflicting information which undermined the global response to the pandemic. Understanding how the information circulated and evolved on social media platforms is essential for planning future public health campaigns. This study investigated what types of themes about COVID-19 were most viewed on YouTube during the first 8 months of the pandemic, and how COVID-19 themes progressed over this period. METHODS: We analyzed top-viewed YouTube COVID-19-related videos in English from December 1, 2019 to August 16, 2020 with an open inductive content analysis. We coded 536 videos associated with 1.1 billion views across the study period. East Asian countries were the first to report the virus, while most of the top-viewed videos in English were from the US. Videos from straight news outlets dominated the top-viewed videos throughout the outbreak, and public health authorities contributed the fewest. Although straight news was the dominant COVID-19 video source with various types of themes, its viewership per video was similar to that for entertainment news and YouTubers after March. RESULTS: We found, first, that collective public attention to the COVID-19 pandemic on YouTube peaked around March 2020, before the outbreak peaked, and flattened afterwards despite a spike in worldwide cases. Second, more videos focused on prevention early on, but videos with political themes increased through time. Third, regarding prevention and control measures, masking received much less attention than lockdown and social distancing in the study period. CONCLUSION: Our study suggests that a transition of focus from science to politics on social media intensified the COVID-19 infodemic and may have weakened mitigation measures during the first waves of the COVID-19 pandemic. It is recommended that authorities should consider co-operating with reputable social media influencers to promote health campaigns and improve health literacy. In addition, given high levels of globalization of social platforms and polarization of users, tailoring communication towards different digital communities is likely to be essential.

Fast estimation of time-varying infectious disease transmission rates.

Compartmental epidemic models have been used extensively to study the historical spread of infectious diseases and to inform strategies for future control. A critical parameter of any such model is the transmission rate. Temporal variation in the transmission rate has a profound influence on disease spread. For this reason, estimation of time-varying transmission rates is an important step in identifying mechanisms that underlie patterns in observed disease incidence and mortality. Here, we present and test fast methods for reconstructing transmission rates from time series of reported incidence. Using simulated data, we quantify the sensitivity of these methods to parameters of the data-generating process and to mis-specification of input parameters by the user. We show that sensitivity to the user's estimate of the initial number of susceptible individuals-considered to be a major limitation of similar methods-can be eliminated by an efficient, "peak-to-peak" iterative technique, which we propose. The method of transmission rate estimation that we advocate is extremely fast, for even the longest infectious disease time series that exist. It can be used independently or as a fast way to obtain better starting conditions for computationally expensive methods, such as iterated filtering and generalized profiling.

On inferring evolutionary stability in finite populations using infinite population models.

Models of evolution by natural selection often make the simplifying assumption that populations are infinitely large. In this infinite population limit, rare mutations that are selected against always go extinct, whereas in finite populations they can persist and even reach fixation. Nevertheless, for mutations of arbitrarily small phenotypic effect, it is widely believed that in sufficiently large populations, if selection opposes the invasion of rare mutants, then it also opposes their fixation. Here, we identify circumstances under which infinite-population models do or do not accurately predict evolutionary outcomes in large, finite populations. We show that there is no population size above which considering only invasion generally suffices: for any finite population size, there are situations in which selection opposes the invasion of mutations of arbitrarily small effect, but favours their fixation. This is not an unlikely limiting case; it can occur when fitness is a smooth function of the evolving trait, and when the selection process is biologically sensible. Nevertheless, there are circumstances under which opposition of invasion does imply opposition of fixation: in fact, for the [Formula: see text]-player snowdrift game (a common model of cooperation) we identify sufficient conditions under which selection against rare mutants of small effect precludes their fixation-in sufficiently large populations-for any selection process. We also find conditions under which-no matter how large the population-the trait that fixes depends on the selection process, which is important because any particular selection process is only an approximation of reality.

Correction to: Determinants of Influenza Mortality Trends: Age-Period-Cohort Analysis of Influenza Mortality in the United States, 1959-2016.

First, we use Lexis surfaces based on Serfling models to highlight influenza mortality patterns as well as to identify lingering effects of early-life exposure to specific influenza virus subtypes (e.g., H1N1, H3N2).

Determinants of Influenza Mortality Trends: Age-Period-Cohort Analysis of Influenza Mortality in the United States, 1959-2016.

This study examines the roles of age, period, and cohort in influenza mortality trends over the years 1959-2016 in the United States. First, we use Lexis surfaces based on Serfling models to highlight influenza mortality patterns as well as to identify lingering effects of early-life exposure to specific influenza virus subtypes (e.g., H1N1, H3N2). Second, we use age-period-cohort (APC) methods to explore APC linear trends and identify changes in the slope of these trends (contrasts). Our analyses reveal a series of breakpoints where the magnitude and direction of birth cohort trends significantly change, mostly corresponding to years in which important antigenic drifts or shifts took place (i.e., 1947, 1957, 1968, and 1978). Whereas child, youth, and adult influenza mortality appear to be influenced by a combination of cohort- and period-specific factors, reflecting the interaction between the antigenic experience of the population and the evolution of the influenza virus itself, mortality patterns of the elderly appear to be molded by broader cohort factors. The latter would reflect the processes of physiological capital improvement in successive birth cohorts through secular changes in early-life conditions. Antigenic imprinting, cohort morbidity phenotype, and other mechanisms that can generate the observed cohort effects, including the baby boom, are discussed.

Patterns of seasonal and pandemic influenza-associated health care and mortality in Ontario, Canada.

BACKGROUND: Mathematical and statistical models are used to project the future time course of infectious disease epidemics and the expected future burden on health care systems and economies. Influenza is a particularly important disease in this context because it causes annual epidemics and occasional pandemics. In order to forecast health care utilization during epidemics-and the effects of hospitalizations and deaths on the contact network and, in turn, on transmission dynamics-modellers must make assumptions about the lengths of time between infection, visiting a physician, being admitted to hospital, leaving hospital, and death. More reliable forecasts could be be made if the distributions of times between these types of events ("delay distributions") were known. METHODS: We estimated delay distributions in the province of Ontario, Canada, between 2006 and 2010. To do so, we used encrypted health insurance numbers to link 1.34 billion health care billing records to 4.27 million hospital inpatient stays. Because the four year period we studied included three typical influenza seasons and the 2009 influenza pandemic, we were able to compare the delay distributions in non-pandemic and pandemic settings. We also estimated conditional probabilities such as the probability of hospitalization within the year if diagnosed with influenza. RESULTS: In non-pandemic [pandemic] years, delay distribution medians (inter-quartile ranges) were: Service to Admission 6.3 days (0.1-17.6 days) [2.4 days (-0.3-13.6 days)], Admission to Discharge 3 days (1.4-5.9 days) [2.6 days (1.2-5.1 days)], Admission to Death 5.3 days (2.1-11 days) [6 days (2.6-13.1 days)]. (Service date is defined as the date, within the year, of the first health care billing that included a diagnostic code for influenza-like-illness.) Among individuals diagnosed with either pneumonia or influenza in a given year, 19% [16%] were hospitalized within the year and 3% [2%] died in hospital. Among all individuals who were hospitalized, 10% [12%] were diagnosed with pneumonia or influenza during the year and 5% [5%] died in hospital. CONCLUSION: Our empirical delay distributions and conditional probabilities should help facilitate more accurate forecasts in the future, including improved predictions of hospital bed demands during influenza outbreaks, and the expected effects of hospitalizations on epidemic dynamics.

On selection in finite populations.

Two major forces shaping evolution are drift and selection. The standard models of neutral drift-the Wright-Fisher (WF) and Moran processes-can be extended to include selection. However, these standard models are not always applicable in practice, and-even without selection-many other drift models make very different predictions. For example, "generalised Wright-Fisher" models (so-called because their first two conditional moments agree with those of the WF process) can yield wildly different absorption times from WF. Additionally, evolutionary stability in finite populations depends only on fixation probabilities, which can be evaluated under less restrictive assumptions than those required to estimate fixation times or more complex population-genetic quantities. We therefore distill the notion of a selection process into a broad class of finite-population, mutationless models of drift and selection (including the WF and Moran processes). We characterize when selection favours fixation of one strategy over another, for any selection process, which allows us to derive finite-population conditions for evolutionary stability independent of the selection process. In applications, the precise details of the selection process are seldom known, yet by exploiting these new theoretical results it is now possible to make rigorously justifiable inferences about fixation of traits.

Second-pandemic strain of Vibrio cholerae from the Philadelphia cholera outbreak of 1849.

In the 19th century, there were several major cholera pandemics in the Indian subcontinent, Europe, and North America. The causes of these outbreaks and the genomic strain identities remain a mystery. We used targeted high-throughput sequencing to reconstruct the Vibrio cholerae genome from the preserved intestine of a victim of the 1849 cholera outbreak in Philadelphia, part of the second cholera pandemic. This O1 biotype strain has 95 to 97% similarity with the classical O395 genome, differing by 203 single-nucleotide polymorphisms (SNPs), lacking three genomic islands, and probably having one or more tandem cholera toxin prophage (CTX) arrays, which potentially affected its virulence. This result highlights archived medical remains as a potential resource for investigations into the genomic origins of past pandemics.

A draft genome of Yersinia pestis from victims of the Black Death.

Technological advances in DNA recovery and sequencing have drastically expanded the scope of genetic analyses of ancient specimens to the extent that full genomic investigations are now feasible and are quickly becoming standard. This trend has important implications for infectious disease research because genomic data from ancient microbes may help to elucidate mechanisms of pathogen evolution and adaptation for emerging and re-emerging infections. Here we report a reconstructed ancient genome of Yersinia pestis at 30-fold average coverage from Black Death victims securely dated to episodes of pestilence-associated mortality in London, England, 1348-1350. Genetic architecture and phylogenetic analysis indicate that the ancient organism is ancestral to most extant strains and sits very close to the ancestral node of all Y. pestis commonly associated with human infection. Temporal estimates suggest that the Black Death of 1347-1351 was the main historical event responsible for the introduction and widespread dissemination of the ancestor to all currently circulating Y. pestis strains pathogenic to humans, and further indicates that contemporary Y. pestis epidemics have their origins in the medieval era. Comparisons against modern genomes reveal no unique derived positions in the medieval organism, indicating that the perceived increased virulence of the disease during the Black Death may not have been due to bacterial phenotype. These findings support the notion that factors other than microbial genetics, such as environment, vector dynamics and host susceptibility, should be at the forefront of epidemiological discussions regarding emerging Y. pestis infections.

Evolutionary stability in continuous nonlinear public goods games.

We investigate a type of public goods games played in groups of individuals who choose how much to contribute towards the production of a common good, at a cost to themselves. In these games, the common good is produced based on the sum of contributions from all group members, then equally distributed among them. In applications, the dependence of the common good on the total contribution is often nonlinear (e.g., exhibiting synergy or diminishing returns). To date, most theoretical and experimental studies have addressed scenarios in which the set of possible contributions is discrete. However, in many real-world situations, contributions are continuous (e.g., individuals volunteering their time). The "n-player snowdrift games" that we analyze involve continuously varying contributions. We establish under what conditions populations of contributing (or "cooperating") individuals can evolve and persist. Previous work on snowdrift games, using adaptive dynamics, has found that what we term an "equally cooperative" strategy is locally convergently and evolutionarily stable. Using static evolutionary game theory, we find conditions under which this strategy is actually globally evolutionarily stable. All these results refer to stability to invasion by a single mutant. We broaden the scope of existing stability results by showing that the equally cooperative strategy is locally stable to potentially large population perturbations, i.e., allowing for the possibility that mutants make up a non-negligible proportion of the population (due, for example, to genetic drift, environmental variability or dispersal).

Live Attenuated Versus Inactivated Influenza Vaccine in Hutterite Children: A Cluster Randomized Blinded Trial.

BACKGROUND: Whether vaccinating children with intranasal live attenuated influenza vaccine (LAIV) is more effective than inactivated influenza vaccine (IIV) in providing both direct protection in vaccinated persons and herd protection in unvaccinated persons is uncertain. Hutterite colonies, where members live in close-knit, small rural communities in which influenza virus infection regularly occurs, offer an opportunity to address this question. OBJECTIVE: To determine whether vaccinating children and adolescents with LAIV provides better community protection than IIV. DESIGN: A cluster randomized blinded trial conducted between October 2012 and May 2015 over 3 influenza seasons. (ClinicalTrials.gov: NCT01653015). SETTING: 52 Hutterite colonies in Alberta and Saskatchewan, Canada. PARTICIPANTS: 1186 Canadian children and adolescents aged 36 months to 15 years who received the study vaccine and 3425 community members who did not. INTERVENTION: Children were randomly assigned according to community in a blinded manner to receive standard dosing of either trivalent LAIV or trivalent IIV. MEASUREMENTS: The primary outcome was reverse transcriptase polymerase chain reaction-confirmed influenza A or B virus in all participants (vaccinated children and persons who did not receive the study vaccine). RESULTS: Mean vaccine coverage among children in the LAIV group was 76.9% versus 72.3% in the IIV group. Influenza virus infection occurred at a rate of 5.3% (295 of 5560 person-years) in the LAIV group versus 5.2% (304 of 5810 person-years) in the IIV group. The hazard ratio comparing LAIV with IIV for influenza A or B virus was 1.03 (95% CI, 0.85 to 1.24). LIMITATION: The study was conducted in Hutterite communities, which may limit generalizability. CONCLUSION: Immunizing children with LAIV does not provide better community protection against influenza than IIV. PRIMARY FUNDING SOURCE: The Canadian Institutes for Health Research.

Population-level effects of suppressing fever.

Fever is commonly attenuated with antipyretic medication as a means to treat unpleasant symptoms of infectious diseases. We highlight a potentially important negative effect of fever suppression that becomes evident at the population level: reducing fever may increase transmission of associated infections. A higher transmission rate implies that a larger proportion of the population will be infected, so widespread antipyretic drug use is likely to lead to more illness and death than would be expected in a population that was not exposed to antipyretic pharmacotherapies. We assembled the published data available for estimating the magnitudes of these individual effects for seasonal influenza. While the data are incomplete and heterogeneous, they suggest that, overall, fever suppression increases the expected number of influenza cases and deaths in the US: for pandemic influenza with reproduction number , the estimated increase is 1% (95% CI: 0.0-2.7%), whereas for seasonal influenza with , the estimated increase is 5% (95% CI: 0.2-12.1%).