Erratum to "Learnings from the Australian first few X household transmission project for COVID-19" [The Lancet Regional Health - Western Pacific 28 (2022) 100573].

[This corrects the article DOI: 10.1016/j.lanwpc.2022.100573.].

A synthetic dataset of Danish residential electricity prosumers.

Conventional residential electricity consumers are becoming prosumers who not only consume electricity but also produce it. This shift is expected to occur over the next few decades at a large scale, and it presents numerous uncertainties and risks for the operation, planning, investment, and viable business models of the electricity grid. To prepare for this shift, researchers, utilities, policymakers, and emerging businesses require a comprehensive understanding of future prosumers' electricity consumption. Unfortunately, there is a limited amount of data available due to privacy concerns and the slow adoption of new technologies such as battery electric vehicles and home automation. To address this issue, this paper introduces a synthetic dataset containing five types of residential prosumers' imported and exported electricity data. The dataset was developed using real traditional consumers' data from Denmark, PV generation data from the global solar energy estimator (GSEE) model, electric vehicle (EV) charging data generated using emobpy package, a residential energy storage system (ESS) operator and a generative adversarial network (GAN) based model to produce synthetic data. The quality of the dataset was assessed and validated through qualitative inspection and three methods: empirical statistics, metrics based on information theory, and evaluation metrics based on machine learning techniques.

The effect of bottleneck size on evolution in nested Darwinian populations.

Previous work has shown how a minimal ecological structure consisting of patchily distributed resources and recurrent dispersal between patches can scaffold Darwinian properties onto collections of cells. When the timescale of dispersal is long compared with the time to consume resources, patch fitness increases but comes at a cost to cell growth rates. This creates conditions that initiate evolutionary transitions in individuality. A key feature of the scaffold is a bottleneck created during dispersal, causing patches to be founded by single cells. The bottleneck decreases competition within patches and, hence, creates a strong hereditary link at the level of patches. Here, we construct a fully stochastic model to investigate the effect of bottleneck size on the evolutionary dynamics of both cells and collectives. We show that larger bottlenecks simply slow the dynamics, but, at some point, which depends on the parameters of the within-patch model, the direction of evolution towards the equilibrium reverses. Introduction of random fluctuations in bottleneck sizes with some positive probability of smaller sizes counteracts this, even when the probability of smaller bottlenecks is minimal.

Learnings from the Australian first few X household transmission project for COVID-19.

Background: First Few "X" (FFX) studies provide a platform to collect the required epidemiological, clinical and virological data to help address emerging information needs about the COVID-19 pandemic. Methods: We adapted the WHO FFX protocol for COVID-19 to understand severity and household transmission dynamics in the early stages of the pandemic in Australia. Implementation strategies were developed for participating sites; all household members were followed for 14 days from case identification. Household contacts completed symptom diaries and had multiple respiratory swabs taken irrespective of symptoms. We modelled the spread of COVID-19 within households using a susceptible-exposed-infectious-recovered-type model, and calculated the household secondary attack rate and key epidemiological parameters. Findings: 96 households with 101 cases and 286 household contacts were recruited into the study between April-October 2020. Forty household contacts tested positive for SARS-CoV-2 in the study follow-up period. Our model estimated the household secondary attack rate to be 15% (95% CI 8-25%), which scaled up with increasing household size. Our findings suggest children were less infectious than their adult counterparts but were also more susceptible to infection. Interpretation: Our study provides important baseline data characterising the transmission of early SARS-CoV-2 strains from children and adults in Australia, against which properties of variants of concern can be benchmarked. We encountered many challenges with respect to logistics, ethics, governance and data management. Continued efforts to invest in preparedness research will help to test, refine and further develop Australian FFX study protocols in advance of future outbreaks. Funding: Australian Government Department of Health.

The pesticide health risk index - An application to the world's countries.

While the use of pesticides continues to rise worldwide, our understanding of the pervasiveness of associated contamination and the health risks humans may be exposed to remain limited to small samples size, and based on small geographic scales, the exposed population, or the pesticide types. Using our recent mapping of global pesticide use, we quantify three complementary health risk metrics for 92 active ingredients: (i) the pesticide hazard load (PHL); (ii) the population exposure (PE); and (iii) the human intake relative to the acceptable dose (INTR). We integrated these metrics into the pesticide health risk index (PHRI) to assess the standing of 133 nations against the global averages of PHL and PE and the acceptable levels of INTR using data of 2015 (PHRI > 1 indicates a concern). We found that some low-toxicity ingredients have PHL values equivalent to high-toxicity ones, and hence neglecting low-toxicity ingredients may cause biases in risk assessments. The geography of PHL, PE, and INTR show hotspots across the Americas, East and South Asia, and Europe, but with the EU27 countries generally showing lower PHL than other countries possibly due to strict governance on pesticide use. By our measure, about 1.7 billion people (24% of the world population) reside in close proximity to where pesticide applications are greater than 100 kg-a.i. km-2 year-1; about 2.3 billion people (32% of the world population) may exceed the acceptable pesticide intake and about 1.1 billion (15% of the world population) may exceed this by 10 fold. We identified 36 countries with PHRI > 1 and 6 countries with PHRI > 5; of these countries, 10 belong to lower-middle and low income economies. Our analyses show that proximity exposure to pesticides may be more widespread than revealed in occupational studies, and therefore assessments of potential health effects over wider scales may be needed.

Coronavirus Disease Model to Inform Transmission-Reducing Measures and Health System Preparedness, Australia.

The ability of health systems to cope with coronavirus disease (COVID-19) cases is of major concern. In preparation, we used clinical pathway models to estimate healthcare requirements for COVID-19 patients in the context of broader public health measures in Australia. An age- and risk-stratified transmission model of COVID-19 demonstrated that an unmitigated epidemic would dramatically exceed the capacity of the health system of Australia over a prolonged period. Case isolation and contact quarantine alone are insufficient to constrain healthcare needs within feasible levels of expansion of health sector capacity. Overlaid social restrictions must be applied over the course of the epidemic to ensure systems do not become overwhelmed and essential health sector functions, including care of COVID-19 patients, can be maintained. Attention to the full pathway of clinical care is needed, along with ongoing strengthening of capacity.

Ecological scaffolding and the evolution of individuality.

Evolutionary transitions in individuality are central to the emergence of biological complexity. Recent experiments provide glimpses of processes underpinning the transition from single cells to multicellular life and draw attention to the critical role of ecology. Here, we emphasize this ecological dimension and argue that its current absence from theoretical frameworks hampers development of general explanatory solutions. Using mechanistic mathematical models, we show how a minimal ecological structure comprising patchily distributed resources and between-patch dispersal can scaffold Darwinian-like properties on collectives of cells. This scaffolding causes cells to participate directly in the process of evolution by natural selection as if they were members of multicellular collectives, with collectives participating in a death-birth process arising from the interplay between the timing of dispersal events and the rate of resource use by cells. When this timescale is sufficiently long and new collectives are founded by single cells, collectives experience conditions that favour evolution of a reproductive division of labour. Together our simple model makes explicit key events in the major evolutionary transition to multicellularity. It also makes predictions concerning the life history of certain pathogens and serves as an ecological recipe for experimental realization of evolutionary transitions.

Bayesian model discrimination for partially-observed epidemic models.

An efficient method for Bayesian model selection is presented for a broad class of continuous-time Markov chain models and is subsequently applied to two important problems in epidemiology. The first problem is to identify the shape of the infectious period distribution; the second problem is to determine whether individuals display symptoms before, at the same time, or after they become infectious. In both cases we show that the correct model can be identified, in the majority of cases, from symptom onset data generated from multiple outbreaks in small populations. The method works by evaluating the likelihood using a particle filter that incorporates a novel importance sampling algorithm designed for partially-observed continuous-time Markov chains. This is combined with another importance sampling method to unbiasedly estimate the model evidence. These come with estimates of precision, which allow for stopping criterion to be employed. Our method is general and can be applied to a wide range of model selection problems in biological and epidemiological systems with intractable likelihood functions.

The distribution of the time taken for an epidemic to spread between two communities.

Assessing the risk of disease spread between communities is important in our highly connected modern world. However, the impact of disease- and population-specific factors on the time taken for an epidemic to spread between communities, as well as the impact of stochastic disease dynamics on this spreading time, are not well understood. In this study, we model the spread of an acute infection between two communities ('patches') using a susceptible-infectious-removed (SIR) metapopulation model. We develop approximations to efficiently evaluate the probability of a major outbreak in a second patch given disease introduction in a source patch, and the distribution of the time taken for this to occur. We use these approximations to assess how interventions, which either control disease spread within a patch or decrease the travel rate between patches, change the spreading probability and median spreading time. We find that decreasing the basic reproduction number in the source patch is the most effective way of both decreasing the spreading probability, and delaying epidemic spread to the second patch should this occur. Moreover, we show that the qualitative effects of interventions are the same regardless of the approximations used to evaluate the spreading time distribution, but for some regions in parameter space, quantitative findings depend upon the approximations used. Importantly, if we neglect the possibility that an intervention prevents a large outbreak in the source patch altogether, then intervention effectiveness is not estimated accurately.

Inference of epidemiological parameters from household stratified data.

We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters-governing within-household transmission, recovery, and between-household transmission-from data of the day upon which each individual became infectious and the household in which each infection occurred, as might be available from First Few Hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be a good approximation and remains computationally efficient as the amount of data is increased.

Characterising pandemic severity and transmissibility from data collected during first few hundred studies.

Early estimation of the probable impact of a pandemic influenza outbreak can assist public health authorities to ensure that response measures are proportionate to the scale of the threat. Recently, frameworks based on transmissibility and severity have been proposed for initial characterization of pandemic impact. Data requirements to inform this assessment may be provided by "First Few Hundred" (FF100) studies, which involve surveillance-possibly in person, or via telephone-of household members of confirmed cases. This process of enhanced case finding enables detection of cases across the full spectrum of clinical severity, including the date of symptom onset. Such surveillance is continued until data for a few hundred cases, or satisfactory characterization of the pandemic strain, has been achieved. We present a method for analysing these data, at the household level, to provide a posterior distribution for the parameters of a model that can be interpreted in terms of severity and transmissibility of a pandemic strain. We account for imperfect case detection, where individuals are only observed with some probability that can increase after a first case is detected. Furthermore, we test this methodology using simulated data generated by an independent model, developed for a different purpose and incorporating more complex disease and social dynamics. Our method recovers transmissibility and severity parameters to a high degree of accuracy and provides a computationally efficient approach to estimating the impact of an outbreak in its early stages.

Choice of Antiviral Allocation Scheme for Pandemic Influenza Depends on Strain Transmissibility, Delivery Delay and Stockpile Size.

Recently, pandemic response has involved the use of antivirals. These antivirals are often allocated to households dynamically throughout the pandemic with the aim being to retard the spread of infection. A drawback of this is that there is a delay until infection is confirmed and antivirals are delivered. Here an alternative allocation scheme is considered, where antivirals are instead preallocated to households at the start of a pandemic, thus reducing this delay. To compare these two schemes, a deterministic approximation to a novel stochastic household model is derived, which allows efficient computation of key quantities such as the expected epidemic final size, expected early growth rate, expected peak size and expected peak time of the epidemic. It is found that the theoretical best choice of allocation scheme depends on strain transmissibility, the delay in delivering antivirals under a dynamic allocation scheme and the stockpile size. A broad summary is that for realistic stockpile sizes, a dynamic allocation scheme is superior with the important exception of the epidemic final size under a severe pandemic scenario. Our results, viewed in conjunction with the practical considerations of implementing a preallocation scheme, support a focus on attempting to reduce the delay in delivering antivirals under a dynamic allocation scheme during a future pandemic.

Contact tracing and antiviral prophylaxis in the early stages of a pandemic: the probability of a major outbreak.

Antiviral prophylaxis forms a significant component of health management plans for many countries around the world. A number of studies have shown that the delays typically encountered in distributing these antivirals to households, following the first infectious case, can result in their efficacy being severely reduced. Here, we investigate the use of contact tracing as a method to reduce the delays and hence mitigate the reduction in efficacy of antivirals. We assess the usefulness of contact tracing in terms of the probability of a major outbreak. It is found, with parameter distributions appropriate to the 2009 H1N1 pandemic and distributions reflecting commonly experienced delays, that standard contact tracing renders an outbreak impossible approximately one in five times compared with approximately one in ten times in its absence. A contact-tracing efficiency of 50% would see further improvements with an outbreak being impossible approximately one in four times, and a reduction of the median probability of a major outbreak from 0.41 to below 0.27.

Computation of epidemic final size distributions.

We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is both computationally efficient and numerically stable. The algorithms we present are also physically transparent and so allow us to extend this method from the basic SIR model to a model with a phase-type infectious period and another with waning immunity. The underlying theory is applicable to many Markovian models where we wish to efficiently calculate hitting probabilities.

The effect of clumped population structure on the variability of spreading dynamics.

Processes that spread through local contact, including outbreaks of infectious diseases, are inherently noisy, and are frequently observed to be far noisier than predicted by standard stochastic models that assume homogeneous mixing. One way to reproduce the observed levels of noise is to introduce significant individual-level heterogeneity with respect to infection processes, such that some individuals are expected to generate more secondary cases than others. Here we consider a population where individuals can be naturally aggregated into clumps (subpopulations) with stronger interaction within clumps than between them. This clumped structure induces significant increases in the noisiness of a spreading process, such as the transmission of infection, despite complete homogeneity at the individual level. Given the ubiquity of such clumped aggregations (such as homes, schools and workplaces for humans or farms for livestock) we suggest this as a plausible explanation for noisiness of many epidemic time series.

Estimating a Markovian epidemic model using household serial interval data from the early phase of an epidemic.

The clinical serial interval of an infectious disease is the time between date of symptom onset in an index case and the date of symptom onset in one of its secondary cases. It is a quantity which is commonly collected during a pandemic and is of fundamental importance to public health policy and mathematical modelling. In this paper we present a novel method for calculating the serial interval distribution for a Markovian model of household transmission dynamics. This allows the use of Bayesian MCMC methods, with explicit evaluation of the likelihood, to fit to serial interval data and infer parameters of the underlying model. We use simulated and real data to verify the accuracy of our methodology and illustrate the importance of accounting for household size. The output of our approach can be used to produce posterior distributions of population level epidemic characteristics.

Epidemiological consequences of household-based antiviral prophylaxis for pandemic influenza.

Antiviral treatment offers a fast acting alternative to vaccination; as such it is viewed as a first-line of defence against pandemic influenza in protecting families and households once infection has been detected. In clinical trials, antiviral treatments have been shown to be efficacious in preventing infection, limiting disease and reducing transmission, yet their impact at containing the 2009 influenza A(H1N1)pdm outbreak was limited. To understand this seeming discrepancy, we develop a general and computationally efficient model for studying household-based interventions. This allows us to account for uncertainty in quantities relevant to the 2009 pandemic in a principled way, accounting for the heterogeneity and variability in each epidemiological process modelled. We find that the population-level effects of delayed antiviral treatment and prophylaxis mean that their limited overall impact is quantitatively consistent (at current levels of precision) with their reported clinical efficacy under ideal conditions. Hence, effective control of pandemic influenza with antivirals is critically dependent on early detection and delivery ideally within 24 h.

Mixing times in evolutionary game dynamics.

Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics. However, many biological arguments focus on stationary distributions in a mutation-selection equilibrium. Here, we address the mixing time required to reach stationarity in the presence of mutation. We show that mixing times in evolutionary games have the opposite behavior from fixation times when the intensity of selection increases: in coordination games with bistabilities, the fixation time decreases, but the mixing time increases. In coexistence games with metastable states, the fixation time increases, but the mixing time decreases. Our results are based on simulations and the Wentzel-Kramers-Brillouin approximation of the master equation.

Stochastic formulation of ecological models and their applications.

The increasing use of computer simulation by theoretical ecologists started a move away from models formulated at the population level towards individual-based models. However, many of the models studied at the individual level are not analysed mathematically and remain defined in terms of a computer algorithm. This is not surprising, given that they are intrinsically stochastic and require tools and techniques for their study that may be unfamiliar to ecologists. Here, we argue that the construction of ecological models at the individual level and their subsequent analysis is, in many cases, straightforward and leads to important insights. We discuss recent work that highlights the importance of stochastic effects for parameter ranges and systems where it was previously thought that such effects would be negligible.