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.

Multimodel Approaches Are Not the Best Way to Understand Multifactorial Systems.

Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified models. (2) MMA improves on IT model selection by implementing a simple form of shrinkage estimation (a way to make accurate predictions from a model with many parameters relative to the amount of data, by "shrinking" parameter estimates toward zero). However, other shrinkage estimators such as penalized regression or Bayesian hierarchical models with regularizing priors are more computationally efficient and better supported theoretically. (3) In general, the procedures for extracting confidence intervals from MMA are overconfident, providing overly narrow intervals. If researchers want to use limited data sets to accurately estimate the strength of multiple competing ecological processes along with reliable confidence intervals, the current best approach is to use full (maximal) statistical models (possibly with Bayesian priors) after making principled, a priori decisions about model complexity.

The role of fire in terrestrial vertebrate richness patterns.

Productivity is strongly associated with terrestrial species richness patterns, although the mechanisms underpinning such patterns have long been debated. Despite considerable consumption of primary productivity by fire, its influence on global diversity has received relatively little study. Here we examine the sensitivity of terrestrial vertebrate biodiversity (amphibians, birds and mammals) to fire, while accounting for other drivers. We analyse global data on terrestrial vertebrate richness, net primary productivity, fire occurrence (fraction of productivity consumed) and additional influences unrelated to productivity (i.e., historical phylogenetic and area effects) on species richness. For birds, fire is associated with higher diversity, rivalling the effects of productivity on richness, and for mammals, fire's positive association with diversity is even stronger than productivity; for amphibians, in contrast, there are few clear associations. Our findings suggest an underappreciated role for fire in the generation of animal species richness and the conservation of global biodiversity.

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.

Consequences of nest site selection vary along a tidal gradient.

Parents providing care must sometimes choose between rearing locations that are most favourable for offspring versus those that are most favourable for themselves. Here, we measured how both parental and offspring performance varied in nest sites distributed along an environmental gradient. The plainfin midshipman fish Porichthys notatus nests along a tidal gradient. When ascending from the subtidal to the high intertidal at low tide, both nest temperature and frequency of air exposure increase. We used one lab and two field experiments to investigate how parental nest site choices across tidal elevations are linked to the physiological costs incurred by parents and the developmental benefits accrued by offspring. Under warmer incubation conditions, simulating high intertidal nests, offspring developed faster but had higher mortality rates compared to those incubated in cooler conditions that mimicked subtidal nests. In the field, males in higher intertidal nests were more active caregivers, but their young still died at the fastest rates. Larger males claimed and retained low intertidal nests, where offspring survival and development rates were also highest. Our results suggest that males compete more intensively for nest sites in the low intertidal, where they can raise their young quickly and with lower per-offspring investments. Smaller, less-competitive males forced into higher intertidal sites nest earlier in the season and provide more active parental care, possibly to bolster brood survival under harsh environmental conditions.

Age-dependence of healthcare interventions for COVID-19 in Ontario, Canada.

BACKGROUND: Patient age is one of the most salient clinical indicators of risk from COVID-19. Age-specific distributions of known SARS-CoV-2 infections and COVID-19-related deaths are available for many regions. Less attention has been given to the age distributions of serious medical interventions administered to COVID-19 patients, which could reveal sources of potential pressure on the healthcare system should SARS-CoV-2 prevalence increase, and could inform mass vaccination strategies. The aim of this study is to quantify the relationship between COVID-19 patient age and serious outcomes of the disease, beyond fatalities alone. METHODS: We analysed 277,555 known SARS-CoV-2 infection records for Ontario, Canada, from 23 January 2020 to 16 February 2021 and estimated the age distributions of hospitalizations, Intensive Care Unit admissions, intubations, and ventilations. We quantified the probability of hospitalization given known SARS-CoV-2 infection, and of survival given COVID-19-related hospitalization. RESULTS: The distribution of hospitalizations peaks with a wide plateau covering ages 60-90, whereas deaths are concentrated in ages 80+. The estimated probability of hospitalization given known infection reaches a maximum of 27.8% at age 80 (95% CI 26.0%-29.7%). The probability of survival given hospitalization is nearly 100% for adults younger than 40, but declines substantially after this age; for example, a hospitalized 54-year-old patient has a 91.7% chance of surviving COVID-19 (95% CI 88.3%-94.4%). CONCLUSIONS: Our study demonstrates a significant need for hospitalization in middle-aged individuals and young seniors. This need is not captured by the distribution of deaths, which is heavily concentrated in very old ages. The probability of survival given hospitalization for COVID-19 is lower than is generally perceived for patients over 40. If acute care capacity is exceeded due to an increase in COVID-19 prevalence, the distribution of deaths could expand toward younger ages. These results suggest that vaccine programs should aim to prevent infection not only in old seniors, but also in young seniors and middle-aged individuals, to protect them from serious illness and to limit stress on the healthcare system.

A Note on Observation Processes in Epidemic Models.

Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR) model to compare two common assumptions about disease incidence reports: Individuals can report their infection as soon as they become infected or as soon as they recover. We show that incorrect assumptions about the underlying observation processes can bias estimates of the basic reproduction number and lead to overly narrow confidence intervals.

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.

Effects of contact structure on the transient evolution of HIV virulence.

Early in an epidemic, high densities of susceptible hosts select for relatively high parasite virulence; later in the epidemic, lower susceptible densities select for lower virulence. Thus over the course of a typical epidemic the average virulence of parasite strains increases initially, peaks partway through the epidemic, then declines again. However, precise quantitative outcomes, such as the peak virulence reached and its timing, may depend sensitively on epidemiological details. Fraser et al. proposed a model for the eco-evolutionary dynamics of HIV that incorporates the tradeoffs between transmission and virulence (mediated by set-point viral load, SPVL) and their heritability between hosts. Their model used implicit equations to capture the effects of partnership dynamics that are at the core of epidemics of sexually transmitted diseases. Our models combine HIV virulence tradeoffs with a range of contact models, explicitly modeling partnership formation and dissolution and allowing for individuals to transmit disease outside of partnerships. We assess summary statistics such as the peak virulence (corresponding to the maximum value of population mean log10 SPVL achieved throughout the epidemic) across models for a range of parameters applicable to the HIV epidemic in sub-Saharan Africa. Although virulence trajectories are broadly similar across models, the timing and magnitude of the virulence peak vary considerably. Previously developed implicit models predicted lower virulence and slower progression at the peak (a maximum of 3.5 log10 SPVL) compared both to more realistic models and to simple random-mixing models with no partnership structure at all (both with a maximum of ≈ 4.7 log10 SPVL). In this range of models, the simplest random-mixing structure best approximates the most realistic model; this surprising outcome occurs because the dominance of extra-pair contact in the realistic model swamps the effects of partnership structure.

The Mortality and Myocardial Effects of Antidepressants Are Moderated by Preexisting Cardiovascular Disease: A Meta-Analysis.

BACKGROUND: Antidepressants (ADs) are commonly prescribed medications, but their long-term health effects are debated. ADs disrupt multiple adaptive processes regulated by evolutionarily ancient biochemicals, potentially increasing mortality. However, many ADs also have anticlotting properties that can be efficacious in treating cardiovascular disease. We conducted a meta-analysis assessing the effects of ADs on all-cause mortality and cardiovascular events in general-population and cardiovascular-patient samples. METHODS: Two reviewers independently assessed articles from PubMed, EMBASE, and Google Scholar for AD-related mortality controlling for depression and other comorbidities. From these articles, we extracted information about cardiovascular events, cardiovascular risk status, and AD class. We conducted mixed-effect meta-analyses testing sample type and AD class as moderators of all-cause mortality and new cardiovascular events. RESULTS: Seventeen studies met our search criteria. Sample type consistently moderated health risks. In general-population samples, AD use increased the risks of mortality (HR = 1.33, 95% CI: 1.14-1.55) and new cardiovascular events (HR = 1.14, 95% CI: 1.08-1.21). In cardiovascular patients, AD use did not significantly affect risks. AD class also moderated mortality, but the serotonin reuptake inhibitors were not significantly different from tricyclic ADs (TCAs) (HR = 1.10, 95% CI: 0.93-1.31, p = 0.27). Only "other ADs" were differentiable from TCAs (HR = 1.35, 95% CI: 1.08-1.69). Mortality risk estimates increased when we analyzed the subset of studies controlling for premedication depression, suggesting the absence of confounding by indication. CONCLUSIONS: The results support the hypothesis that ADs are harmful in the general population but less harmful in cardiovascular patients.

Multicopy gene family evolution on primate Y chromosomes.

BACKGROUND: The primate Y chromosome is distinguished by a lack of inter-chromosomal recombination along most of its length, extensive gene loss, and a prevalence of repetitive elements. A group of genes on the male-specific portion of the Y chromosome known as the "ampliconic genes" are present in multiple copies that are sometimes part of palindromes, and that undergo a form of intra-chromosomal recombination called gene conversion, wherein the nucleotides of one copy are homogenized by those of another. With the aim of further understanding gene family evolution of these genes, we collected nucleotide sequence and gene copy number information for several species of papionin monkey. We then tested for evidence of gene conversion, and developed a novel statistical framework to evaluate alternative models of gene family evolution using our data combined with other information from a human, a chimpanzee, and a rhesus macaque. RESULTS: Our results (i) recovered evidence for several novel examples of gene conversion in papionin monkeys and indicate that (ii) ampliconic gene families evolve faster than autosomal gene families and than single-copy genes on the Y chromosome and that (iii) Y-linked singleton and autosomal gene families evolved faster in humans and chimps than they do in the other Old World Monkey lineages we studied. CONCLUSIONS: Rapid evolution of ampliconic genes cannot be attributed solely to residence on the Y chromosome, nor to variation between primate lineages in the rate of gene family evolution. Instead other factors, such as natural selection and gene conversion, appear to play a role in driving temporal and genomic evolutionary heterogeneity in primate gene families.

Hidden semi-Markov models reveal multiphasic movement of the endangered Florida panther.

Animals must move to find food and mates, and to avoid predators; movement thus influences survival and reproduction, and ultimately determines fitness. Precise description of movement and understanding of spatial and temporal patterns as well as relationships with intrinsic and extrinsic factors is important both for theoretical and applied reasons. We applied hidden semi-Markov models (HSMM) to hourly geographic positioning system (GPS) location data to understand movement patterns of the endangered Florida panther (Puma concolor coryi) and to discern factors influencing these patterns. Three distinct movement modes were identified: (1) Resting mode, characterized by short step lengths and turning angles around 180(o); (2) Moderately active (or intermediate) mode characterized by intermediate step lengths and variable turning angles, and (3) Traveling mode, characterized by long step lengths and turning angles around 0(o). Males and females, and females with and without kittens, exhibited distinctly different movement patterns. Using the Viterbi algorithm, we show that differences in movement patterns of male and female Florida panthers were a consequence of sex-specific differences in diurnal patterns of state occupancy and sex-specific differences in state-specific movement parameters, whereas the differences between females with and without dependent kittens were caused solely by variation in state occupancy. Our study demonstrates the use of HSMM methodology to precisely describe movement and to dissect differences in movement patterns according to sex, and reproductive status.

Evolutionary Stability of Minimal Mutation Rates in an Evo-epidemiological Model.

We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. We model virulence as a quantitative genetic trait in a haploid population and mutation as continuous diffusion in the trait space. There is a mutation rate threshold above which the pathogen cannot invade a wholly susceptible population. The evolutionarily stable (ESS) mutation rate is the one which drives the lowest average density, over the course of one forcing period, of susceptible individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen strain with zero mutation. We discuss how this result arises within our model and how the model might be modified to obtain a nonzero optimum.

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%).

Estimating initial epidemic growth rates.

The initial exponential growth rate of an epidemic is an important measure of disease spread, and is commonly used to infer the basic reproduction number [Formula: see text]. While modern techniques (e.g., MCMC and particle filtering) for parameter estimation of mechanistic models have gained popularity, maximum likelihood fitting of phenomenological models remains important due to its simplicity, to the difficulty of using modern methods in the context of limited data, and to the fact that there is not always enough information available to choose an appropriate mechanistic model. However, it is often not clear which phenomenological model is appropriate for a given dataset. We compare the performance of four commonly used phenomenological models (exponential, Richards, logistic, and delayed logistic) in estimating initial epidemic growth rates by maximum likelihood, by fitting them to simulated epidemics with known parameters. For incidence data, both the logistic model and the Richards model yield accurate point estimates for fitting windows up to the epidemic peak. When observation errors are small, the Richards model yields confidence intervals with better coverage. For mortality data, the Richards model and the delayed logistic model yield the best growth rate estimates. We also investigate the width and coverage of the confidence intervals corresponding to these fits.