A model of behavioural response to risk accurately predicts the statistical distribution of COVID-19 infection and reproduction numbers.

One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This homeostatic response is active until approximate herd immunity is reached: in this domain the model predicts that the reproduction rate R will be centred around a median of 1, that proportional change in infection numbers will follow the standard Cauchy distribution with location and scale parameters 0 and 1, and that high infection numbers will follow a power-law frequency distribution with exponent 2. To test these predictions we used worldwide COVID-19 data from 1st February 2020 to 30th June 2022 to calculate [Formula: see text] confidence interval estimates across countries for these R, location, scale and exponent parameters. The resulting median R estimate was [Formula: see text] (predicted value 1) the proportional change location estimate was [Formula: see text] (predicted value 0), the proportional change scale estimate was [Formula: see text] (predicted value 1), and the frequency distribution exponent estimate was [Formula: see text] (predicted value 2); in each case the observed estimate agreed with model predictions.

Individual Genetic Heterogeneity.

Genetic variation has been widely covered in literature, however, not from the perspective of an individual in any species. Here, a synthesis of genetic concepts and variations relevant for individual genetic constitution is provided. All the different levels of genetic information and variation are covered, ranging from whether an organism is unmixed or hybrid, has variations in genome, chromosomes, and more locally in DNA regions, to epigenetic variants or alterations in selfish genetic elements. Genetic constitution and heterogeneity of microbiota are highly relevant for health and wellbeing of an individual. Mutation rates vary widely for variation types, e.g., due to the sequence context. Genetic information guides numerous aspects in organisms. Types of inheritance, whether Mendelian or non-Mendelian, zygosity, sexual reproduction, and sex determination are covered. Functions of DNA and functional effects of variations are introduced, along with mechanism that reduce and modulate functional effects, including TARAR countermeasures and intraindividual genetic conflict. TARAR countermeasures for tolerance, avoidance, repair, attenuation, and resistance are essential for life, integrity of genetic information, and gene expression. The genetic composition, effects of variations, and their expression are considered also in diseases and personalized medicine. The text synthesizes knowledge and insight on individual genetic heterogeneity and organizes and systematizes the central concepts.

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

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

Accounting for the Potential of Overdispersion in Estimation of the Time-varying Reproduction Number.

BACKGROUND: The time-varying reproduction number, Rt, is commonly used to monitor the transmissibility of an infectious disease during an epidemic, but standard methods for estimating Rt seldom account for the impact of overdispersion on transmission. METHODS: We developed a negative binomial framework to estimate Rt and a time-varying dispersion parameter (kt). We applied the framework to COVID-19 incidence data in Hong Kong in 2020 and 2021. We conducted a simulation study to compare the performance of our model with the conventional Poisson-based approach. RESULTS: Our framework estimated an Rt peaking around 4 (95% credible interval = 3.13, 4.30), similar to that from the Poisson approach but with a better model fit. Our approach further estimated kt <0.5 at the start of both waves, indicating appreciable heterogeneity in transmission. We also found that kt decreased sharply to around 0.4 when a large cluster of infections occurred. CONCLUSIONS: Our proposed approach can contribute to the estimation of Rt and monitoring of the time-varying dispersion parameters to quantify the role of superspreading.

Early detection of variants of concern via funnel plots of regional reproduction numbers.

Early detection of the emergence of a new variant of concern (VoC) is essential to develop strategies that contain epidemic outbreaks. For example, knowing in which region a VoC starts spreading enables prompt actions to circumscribe the geographical area where the new variant can spread, by containing it locally. This paper presents 'funnel plots' as a statistical process control method that, unlike tools whose purpose is to identify rises of the reproduction number ([Formula: see text]), detects when a regional [Formula: see text] departs from the national average and thus represents an anomaly. The name of the method refers to the funnel-like shape of the scatter plot that the data take on. Control limits with prescribed false alarm rate are derived from the observation that regional [Formula: see text]'s are normally distributed with variance inversely proportional to the number of infectious cases. The method is validated on public COVID-19 data demonstrating its efficacy in the early detection of SARS-CoV-2 variants in India, South Africa, England, and Italy, as well as of a malfunctioning episode of the diagnostic infrastructure in England, during which the Immensa lab in Wolverhampton gave 43,000 incorrect negative tests relative to South West and West Midlands territories.

Modelling the propagation of infectious disease via transportation networks.

The dynamics of human mobility have been known to play a critical role in the spread of infectious diseases like COVID-19. In this paper, we present a simple compact way to model the transmission of infectious disease through transportation networks using widely available aggregate mobility data in the form of a zone-level origin-destination (OD) travel flow matrix. A key feature of our model is that it not only captures the propagation of infection via direct connections between zones (first-order effects) as in most existing studies but also transmission effects that are due to subsequent interactions in the remainder of the system (higher-order effects). We demonstrate the importance of capturing higher-order effects in a simulation study. We then apply our model to study the first wave of COVID-19 infections in (i) Italy, and, (ii) the New York Tri-State area. We use daily data on mobility between Italian provinces (province-level OD data) and between Tri-State Area counties (county-level OD data), and daily reported caseloads at the same geographical levels. Our empirical results indicate substantial predictive power, particularly during the early stages of the outbreak. Our model forecasts at least 85% of the spatial variation in observed weekly COVID-19 cases. Most importantly, our model delivers crucial metrics to identify target areas for intervention.

EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number.

In infectious disease epidemiology, the instantaneous reproduction number [Formula: see text] is a time-varying parameter defined as the average number of secondary infections generated by an infected individual at time t. It is therefore a crucial epidemiological statistic that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool (EpiLPS) for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible intervals of [Formula: see text] by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of [Formula: see text] in only a few seconds; and (2) an approach based on a Markov chain Monte Carlo (MCMC) scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a negative binomial distribution to account for potential overdispersion in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a "plug-in'' estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of [Formula: see text] as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and on the SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.

Review of the impact of COVID-19 on male reproduction, and its implications on assisted reproductive technology services.

The announcement in 2019 of a new coronavirus disease that quickly became a major pandemic, is an exceptional challenge to healthcare systems never seen before. Such a public health emergency can largely influence various aspects of people's health as well as reproductive outcome. IVF specialists should be vigilant, monitoring the situation whilst contributing by sharing novel evidence to counsel patients, both pregnant women and would-be mothers. Coronavirus infection might adversely affect pregnant women and their offspring. Consequently, this review paper aims to analyse its potential risks for reproductive health, as well as potential effects of the virus on gamete function and embryo development. In addition, reopening fertility clinics poses several concerns that need immediate addressing, such as the effect of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) on reproductive cells and also the potential risk of cross-contamination and viral transmission. Therefore, this manuscript summarizes what is currently known about the effect of the SARS-CoV-2 infection on medically assisted reproductive treatments and its effect on reproductive health and pregnancy.

Estimation of heterogeneous instantaneous reproduction numbers with application to characterize SARS-CoV-2 transmission in Massachusetts counties.

The reproductive number is an important metric that has been widely used to quantify the infectiousness of communicable diseases. The time-varying instantaneous reproductive number is useful for monitoring the real-time dynamics of a disease to inform policy making for disease control. Local estimation of this metric, for instance at a county or city level, allows for more targeted interventions to curb transmission. However, simultaneous estimation of local reproductive numbers must account for potential sources of heterogeneity in these time-varying quantities-a key element of which is human mobility. We develop a statistical method that incorporates human mobility between multiple regions for estimating region-specific instantaneous reproductive numbers. The model also can account for exogenous cases imported from outside of the regions of interest. We propose two approaches to estimate the reproductive numbers, with mobility data used to adjust incidence in the first approach and to inform a formal priori distribution in the second (Bayesian) approach. Through a simulation study, we show that region-specific reproductive numbers can be well estimated if human mobility is reasonably well approximated by available data. We use this approach to estimate the instantaneous reproductive numbers of COVID-19 for 14 counties in Massachusetts using CDC case report data and the human mobility data collected by SafeGraph. We found that, accounting for mobility, our method produces estimates of reproductive numbers that are distinct across counties. In contrast, independent estimation of county-level reproductive numbers tends to produce similar values, as trends in county case-counts for the state are fairly concordant. These approaches can also be used to estimate any heterogeneity in transmission, for instance, age-dependent instantaneous reproductive number estimates. As people are more mobile and interact frequently in ways that permit transmission, it is important to account for this in the estimation of the reproductive number.

Temporal evolution of the Covid19 pandemic reproduction number: Estimations from proximal optimization to Monte Carlo sampling.

Monitoring the evolution of the Covid19 pandemic constitutes a critical step in sanitary policy design. Yet, the assessment of the pandemic intensity within the pandemic period remains a challenging task because of the limited quality of data made available by public health authorities (missing data, outliers and pseudoseasonalities, notably), that calls for cumbersome and ad-hoc preprocessing (denoising) prior to estimation. Recently, the estimation of the reproduction number, a measure of the pandemic intensity, was formulated as an inverse problem, combining data-model fidelity and space-time regularity constraints, solved by nonsmooth convex proximal minimizations. Though promising, that formulation lacks robustness against the limited quality of the Covid19 data and confidence assessment. The present work aims to address both limitations: First, it discusses solutions to produce a robust assessment of the pandemic intensity by accounting for the low quality of the data directly within the inverse problem formulation. Second, exploiting a Bayesian interpretation of the inverse problem formulation, it devises a Monte Carlo sampling strategy, tailored to a nonsmooth log-concave a posteriori distribution, to produce relevant credibility interval-based estimates for the Covid19 reproduction number. Clinical relevance Applied to daily counts of new infections made publicly available by the Health Authorities for around 200 countries, the proposed procedures permit robust assessments of the time evolution of the Covid19 pandemic intensity, updated automatically and on a daily basis.

Reproduction Numbers of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Variants: A Systematic Review and Meta-analysis.

The coronavirus disease 2019 (COVID-19) pandemic continues to pose substantial risks to public health, worsened by the emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants that may have a higher transmissibility and reduce vaccine effectiveness. We conducted a systematic review and meta-analysis on reproduction numbers of SARS-CoV-2 variants and provided pooled estimates for each variant.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number.

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimation of local time-varying reproduction numbers in noisy surveillance data.

A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Fitting the reproduction number from UK coronavirus case data and why it is close to 1.

We present a method for rapid calculation of coronavirus growth rates and [Formula: see text]-numbers tailored to publicly available UK data. We assume that the case data comprise a smooth, underlying trend which is differentiable, plus systematic errors and a non-differentiable noise term, and use bespoke data processing to remove systematic errors and noise. The approach is designed to prioritize up-to-date estimates. Our method is validated against published consensus [Formula: see text]-numbers from the UK government and is shown to produce comparable results two weeks earlier. The case-driven approach is combined with weight-shift-scale methods to monitor trends in the epidemic and for medium-term predictions. Using case-fatality ratios, we create a narrative for trends in the UK epidemic: increased infectiousness of the B1.117 (Alpha) variant, and the effectiveness of vaccination in reducing severity of infection. For longer-term future scenarios, we base future [Formula: see text] on insight from localized spread models, which show [Formula: see text] going asymptotically to 1 after a transient, regardless of how large the [Formula: see text] transient is. This accords with short-lived peaks observed in case data. These cannot be explained by a well-mixed model and are suggestive of spread on a localized network. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimating relative generation times and reproduction numbers of Omicron BA.1 and BA.2 with respect to Delta variant in Denmark.

The Omicron variant spreads fastest as ever among the severe acute respiratory syndrome coronaviruses 2 (SARS-CoV-2) we had so far. The BA.1 and BA.2 sublineages of Omicron are circulating worldwide and it is urgent to evaluate the transmission advantages of these sublineages. Using a mathematical model describing trajectories of variant frequencies that assumes a constant ratio in mean generation times and a constant ratio in effective reproduction numbers among variants, trajectories of variant frequencies in Denmark from November 22, 2021 to February 26, 2022 were analyzed. We found that the mean generation time of Omicron BA.1 is 0.44-0.46 times that of Delta and the effective reproduction number of Omicron BA.1 is 1.88-2.19 times larger than Delta under the epidemiological conditions at the time. We also found that the mean generation time of Omicron BA.2 is 0.76-0.80 times that of BA.1 and the effective reproduction number of Omicron BA.2 is 1.25-1.27 times larger than Omicron BA.1. These estimates on the ratio of mean generation times and the ratio of effective reproduction numbers have epidemiologically important implications. The contact tracing for Omicron BA.2 infections must be done more quickly than that for BA.1 to stop further infections by quarantine. In the Danish population, the control measures against Omicron BA.2 need to reduce 20-21% of additional contacts compared to that against BA.1.

A new estimation method for COVID-19 time-varying reproduction number using active cases.

We propose a new method to estimate the time-varying effective (or instantaneous) reproduction number of the novel coronavirus disease (COVID-19). The method is based on a discrete-time stochastic augmented compartmental model that describes the virus transmission. A two-stage estimation method, which combines the Extended Kalman Filter (EKF) to estimate the reported state variables (active and removed cases) and a low pass filter based on a rational transfer function to remove short term fluctuations of the reported cases, is used with case uncertainties that are assumed to follow a Gaussian distribution. Our method does not require information regarding serial intervals, which makes the estimation procedure simpler without reducing the quality of the estimate. We show that the proposed method is comparable to common approaches, e.g., age-structured and new cases based sequential Bayesian models. We also apply it to COVID-19 cases in the Scandinavian countries: Denmark, Sweden, and Norway, where the positive rates were below 5% recommended by WHO.

Molecular evidence for suppression of swimming behavior and reproduction in the estuarine rotifer Brachionus koreanus in response to COVID-19 disinfectants.

The increased use of disinfectants due to the spread of the novel coronavirus infection (e.g. COVID-19) has caused burden in the environment but knowledge on its ecotoxicological impact on the estuary environment is limited. Here we report in vivo and molecular endpoints that we used to assess the effects of chloroxylenol (PCMX) and benzalkonium chloride (BAC), which are ingredients in liquid handwash, dish soap products, and sanitizers used by consumers and healthcare workers on the estuarine rotifer Brachionus koreanus. PCMX and BAC significantly affected the life table parameters of B. koreanus. These chemicals modulated the activities of antioxidant enzymes such as superoxide dismutase and catalase and increased reactive oxygen species even at low concentrations. Also, PCMX and BAC caused alterations in the swimming speed and rotation rate of B. koreanus. Furthermore, an RNA-seq-based ingenuity pathway analysis showed that PCMX affected several signaling pathways, allowing us to predict that a low concentration of PCMX will have deleterious effects on B. koreanus. The neurotoxic and mitochondrial dysfunction event scenario induced by PCMX reflects the underlying molecular mechanisms by which PCMX produces outcomes deleterious to aquatic organisms.

Reproduction Numbers of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Variants: A Systematic Review and Meta-analysis.

The coronavirus disease 2019 (COVID-19) pandemic continues to pose substantial risks to public health, worsened by the emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants that may have a higher transmissibility and reduce vaccine effectiveness. We conducted a systematic review and meta-analysis on reproduction numbers of SARS-CoV-2 variants and provided pooled estimates for each variant.

Refining Reproduction Number Estimates to Account for Unobserved Generations of Infection in Emerging Epidemics.

BACKGROUND: Estimating the transmissibility of infectious diseases is key to inform situational awareness and for response planning. Several methods tend to overestimate the basic (R0) and effective (Rt) reproduction numbers during the initial phases of an epidemic. In this work we explore the impact of incomplete observations and underreporting of the first generations of infections during the initial epidemic phase. METHODS: We propose a debiasing procedure that utilizes a linear exponential growth model to infer unobserved initial generations of infections and apply it to EpiEstim. We assess the performance of our adjustment using simulated data, considering different levels of transmissibility and reporting rates. We also apply the proposed correction to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) incidence data reported in Italy, Sweden, the United Kingdom, and the United States. RESULTS: In all simulation scenarios, our adjustment outperforms the original EpiEstim method. The proposed correction reduces the systematic bias, and the quantification of uncertainty is more precise, as better coverage of the true R0 values is achieved with tighter credible intervals. When applied to real-world data, the proposed adjustment produces basic reproduction number estimates that closely match the estimates obtained in other studies while making use of a minimal amount of data. CONCLUSIONS: The proposed adjustment refines the reproduction number estimates obtained with the current EpiEstim implementation by producing improved, more precise estimates earlier than with the original method. This has relevant public health implications.

Spatially refined time-varying reproduction numbers of SARS-CoV-2 in Arkansas and Kentucky and their relationship to population size and public health policy, March - November 2020.

PURPOSE: To examine the time-varying reproduction number, Rt, for COVID-19 in Arkansas and Kentucky and investigate the impact of policies and preventative measures on the variability in Rt. METHODS: Arkansas and Kentucky county-level COVID-19 cumulative case count data (March 6-November 7, 2020) were obtained. Rt was estimated using the R package 'EpiEstim', by county, region (Delta, non-Delta, Appalachian, non-Appalachian), and policy measures. RESULTS: The Rt was initially high, falling below 1 in May or June depending on the region, before stabilizing around 1 in the later months. The median Rt for Arkansas and Kentucky at the end of the study were 1.15 (95% credible interval [CrI], 1.13, 1.18) and 1.10 (95% CrI, 1.08, 1.12), respectively, and remained above 1 for the non-Appalachian region. Rt decreased when facial coverings were mandated, changing by -10.64% (95% CrI, -10.60%, -10.70%) in Arkansas and -5.93% (95% CrI, -4.31%, -7.65%) in Kentucky. The trends in Rt estimates were mostly associated with the implementation and relaxation of social distancing measures. CONCLUSIONS: Arkansas and Kentucky maintained a median Rt above 1 during the entire study period. Changes in Rt estimates allow quantitative estimates of potential impact of policies such as facemask mandate.