The impact of long-term non-pharmaceutical interventions on COVID-19 epidemic dynamics and control: the value and limitations of early models.

Mathematical models of epidemics are important tools for predicting epidemic dynamics and evaluating interventions. Yet, because early models are built on limited information, it is unclear how long they will accurately capture epidemic dynamics. Using a stochastic SEIR model of COVID-19 fitted to reported deaths, we estimated transmission parameters at different time points during the first wave of the epidemic (March-June, 2020) in Santa Clara County, California. Although our estimated basic reproduction number ([Formula: see text]) remained stable from early April to late June (with an overall median of 3.76), our estimated effective reproduction number ([Formula: see text]) varied from 0.18 to 1.02 in April before stabilizing at 0.64 on 27 May. Between 22 April and 27 May, our model accurately predicted dynamics through June; however, the model did not predict rising summer cases after shelter-in-place orders were relaxed in June, which, in early July, was reflected in cases but not yet in deaths. While models are critical for informing intervention policy early in an epidemic, their performance will be limited as epidemic dynamics evolve. This paper is one of the first to evaluate the accuracy of an early epidemiological compartment model over time to understand the value and limitations of models during unfolding epidemics.

Public parks and the pandemic: How park usage has been affected by COVID-19 policies.

Public parks serve an important societal function as recreational spaces for diverse communities of people, with well documented physical and mental health benefits. As such, parks may be crucial for how people have handled effects of the COVID-19 pandemic, particularly the increasingly limited recreational opportunities, widespread financial uncertainty, and consequent heightened anxiety. Despite the documented benefits of parks, however, many states have instituted park shutdown orders due to fears that public parks could facilitate SARS-CoV-2 transmission. Here we use geotagged social media data from state, county, and local parks throughout New Jersey to examine whether park visitation increased when the COVID-19 pandemic began and whether park shutdown orders were effective at deterring park usage. We compare park usage during four discrete stages of spring 2020: (1) before the pandemic began, (2) during the beginning of the pandemic, (3) during the New Jersey governor's state-wide park shutdown order, and (4) following the lifting of the shutdown. We find that park visitation increased by 63.4% with the onset of the pandemic. The subsequent park shutdown order caused visitation in closed parks to decline by 76.1% while parks that remained open continued to experience elevated visitation levels. Visitation then returned to elevated pre-shutdown levels when closed parks were allowed to reopen. Altogether, our results indicate that parks continue to provide crucial services to society, particularly in stressful times when opportunities for recreation are limited. Furthermore, our results suggest that policies targeting human behavior can be effective and are largely reversible. As such, we should continue to invest in public parks and to explore the role of parks in managing public health and psychological well-being.

Development and dissemination of infectious disease dynamic transmission models during the COVID-19 pandemic: what can we learn from other pathogens and how can we move forward?

The current COVID-19 pandemic has resulted in the unprecedented development and integration of infectious disease dynamic transmission models into policy making and public health practice. Models offer a systematic way to investigate transmission dynamics and produce short-term and long-term predictions that explicitly integrate assumptions about biological, behavioural, and epidemiological processes that affect disease transmission, burden, and surveillance. Models have been valuable tools during the COVID-19 pandemic and other infectious disease outbreaks, able to generate possible trajectories of disease burden, evaluate the effectiveness of intervention strategies, and estimate key transmission variables. Particularly given the rapid pace of model development, evaluation, and integration with decision making in emergency situations, it is necessary to understand the benefits and pitfalls of transmission models. We review and highlight key aspects of the history of infectious disease dynamic models, the role of rigorous testing and evaluation, the integration with data, and the successful application of models to guide public health. Rather than being an expansive history of infectious disease models, this Review focuses on how the integration of modelling can continue to be advanced through policy and practice in appropriate and conscientious ways to support the current pandemic response.

Chopping the tail: How preventing superspreading can help to maintain COVID-19 control.

Disease transmission is notoriously heterogeneous, and SARS-CoV-2 is no exception. A skewed distribution where few individuals or events are responsible for the majority of transmission can result in explosive, superspreading events, which produce rapid and volatile epidemic dynamics, especially early or late in epidemics. Anticipating and preventing superspreading events can produce large reductions in overall transmission rates. Here, we present a stochastic compartmental (SEIR) epidemiological model framework for estimating transmission parameters from multiple imperfectly observed data streams, including reported cases, deaths, and mobile phone-based mobility that incorporates individual-level heterogeneity in transmission using previous estimates for SARS-CoV-1 and SARS-CoV-2. We parameterize the model for COVID-19 epidemic dynamics by estimating a time-varying transmission rate that incorporates the impact of non-pharmaceutical intervention strategies that change over time, in five epidemiologically distinct settings-Los Angeles and Santa Clara Counties, California; Seattle (King County), Washington; Atlanta (Dekalb and Fulton Counties), Georgia; and Miami (Miami-Dade County), Florida. We find that the effective reproduction number (RE) dropped below 1 rapidly in all five locations following social distancing orders in mid-March, 2020, but that gradually increasing mobility starting around mid-April led to an RE once again above 1 in late May (Los Angeles, Miami, and Atlanta) or early June (Santa Clara County and Seattle). However, we find that increased social distancing starting in mid-July in response to epidemic resurgence once again dropped RE below 1 in all locations by August 14. We next used the fitted model to ask: how does truncating the individual-level transmission rate distribution (which removes periods of time with especially high individual transmission rates and thus models superspreading events) affect epidemic dynamics and control? We find that interventions that truncate the transmission rate distribution while partially relaxing social distancing are broadly effective, with impacts on epidemic growth on par with the strongest population-wide social distancing observed in April, 2020. Given that social distancing interventions will be needed to maintain epidemic control until a vaccine becomes widely available, "chopping off the tail" to reduce the probability of superspreading events presents a promising option to alleviate the need for extreme general social distancing.

Chopping the tail: how preventing superspreading can help to maintain COVID-19 control.

Disease transmission is notoriously heterogeneous, and SARS-CoV-2 is no exception. A skewed distribution where few individuals or events are responsible for the majority of transmission can result in explosive, superspreading events, which produce rapid and volatile epidemic dynamics, especially early or late in epidemics. Anticipating and preventing superspreading events can produce large reductions in overall transmission rates. Here, we present a compartmental (SEIR) epidemiological model framework for estimating transmission parameters from multiple imperfectly observed data streams, including reported cases, deaths, and mobile phone-based mobility that incorporates individual-level heterogeneity in transmission using previous estimates for SARS-CoV-1 and SARS-CoV-2. We parameterize the model for COVID-19 epidemic dynamics by estimating a time-varying transmission rate that incorporates the impact of non-pharmaceutical intervention strategies that change over time, in five epidemiologically distinct settings---Los Angeles and Santa Clara Counties, California; Seattle (King County), Washington; Atlanta (Dekalb and Fulton Counties), Georgia; and Miami (Miami-Dade County), Florida. We find the effective reproduction number R E dropped below 1 rapidly following social distancing orders in mid-March, 2020 and remained there into June in Santa Clara County and Seattle, but climbed above 1 in late May in Los Angeles, Miami, and Atlanta, and has trended upward in all locations since April. With the fitted model, we ask: how does truncating the tail of the individual-level transmission rate distribution affect epidemic dynamics and control? We find interventions that truncate the transmission rate distribution while partially relaxing social distancing are broadly effective, with impacts on epidemic growth on par with the strongest population-wide social distancing observed in April, 2020. Given that social distancing interventions will be needed to maintain epidemic control until a vaccine becomes widely available, "chopping off the tail" to reduce the probability of superspreading events presents a promising option to alleviate the need for extreme general social distancing.

Disease and healthcare burden of COVID-19 in the United States.

As of 24 April 2020, the SARS-CoV-2 epidemic has resulted in over 830,000 confirmed infections in the United States1. The incidence of COVID-19, the disease associated with this new coronavirus, continues to rise. The epidemic threatens to overwhelm healthcare systems, and identifying those regions where the disease burden is likely to be high relative to the rest of the country is critical for enabling prudent and effective distribution of emergency medical care and public health resources. Globally, the risk of severe outcomes associated with COVID-19 has consistently been observed to increase with age2,3. We used age-specific mortality patterns in tandem with demographic data to map projections of the cumulative case burden of COVID-19 and the subsequent burden on healthcare resources. The analysis was performed at the county level across the United States, assuming a scenario in which 20% of the population of each county acquires infection. We identified counties that will probably be consistently, heavily affected relative to the rest of the country across a range of assumptions about transmission patterns, such as the basic reproductive rate, contact patterns and the efficacy of quarantine. We observed a general pattern that per capita disease burden and relative healthcare system demand may be highest away from major population centers. These findings highlight the importance of ensuring equitable and adequate allocation of medical care and public health resources to communities outside of major urban areas.

Coexisting attractors in the context of cross-scale population dynamics: measles in London as a case study.

Patterns of measles infection in large urban populations have long been considered the paradigm of synchronized nonlinear dynamics. Indeed, recurrent epidemics appear approximately mass-action despite underlying heterogeneity. However, using a subset of rich, newly digitized mortality data (1897-1906), we challenge that proposition. We find that sub-regions of London exhibited a mixture of simultaneous annual and biennial dynamics, while the aggregate city-level dynamics appears firmly annual. Using a simple stochastic epidemic model and maximum-likelihood inference methods, we show that we can capture this observed variation in periodicity. We identify agreement between theory and data, indicating that both changes in periodicity and epidemic coupling between regions can follow relatively simple rules; in particular we find local variation in seasonality drives periodicity. Our analysis underlines that multiple attractors can coexist in a strongly mixed population and follow theoretical predictions.

A competing-risks model explains hierarchical spatial coupling of measles epidemics en route to national elimination.

Apart from its global health importance, measles is a paradigm for the low-dimensional mechanistic understanding of local nonlinear population interactions. A central question for spatio-temporal dynamics is the relative roles of hierarchical spread from large cities to small towns and metapopulation transmission among local small population clusters in measles persistence. Quantifying this balance is critical to planning the regional elimination and global eradication of measles. Yet, current gravity models do not allow a formal comparison of hierarchical versus metapopulation spread. We address this gap with a competing-risks framework, capturing the relative importance of competing sources of reintroductions of infection. We apply the method to the uniquely spatio-temporally detailed urban incidence dataset for measles in England and Wales, from 1944 to the infection's vaccine-induced nadir in the 1990s. We find that despite the regional influence of a few large cities (for example, London and Liverpool), metapopulation aggregation in neighbouring towns and cities played an important role in driving national dynamics in the prevaccination era. As vaccination levels increased in the 1970s and 1980s, the signature of spatially predictable spread diminished: increasingly, infection was introduced from unidentifiable random sources possibly outside regional metapopulations. The resulting erratic dynamics highlight the challenges of identifying shifting sources of infection and characterizing patterns of incidence in times of high vaccination coverage. More broadly, the underlying incidence and demographic data, accompanying this paper, will also provide an important resource for exploring nonlinear spatiotemporal population dynamics.

Long-term dynamics of measles in London: Titrating the impact of wars, the 1918 pandemic, and vaccination.

A key question in ecology is the relative impact of internal nonlinear dynamics and external perturbations on the long-term trajectories of natural systems. Measles has been analyzed extensively as a paradigm for consumer-resource dynamics due to the oscillatory nature of the host-pathogen life cycle, the abundance of rich data to test theory, and public health relevance. The dynamics of measles in London, in particular, has acted as a prototypical test bed for such analysis using incidence data from the pre-vaccination era (1944-1967). However, during this timeframe there were few external large-scale perturbations, limiting an assessment of the relative impact of internal and extra demographic perturbations to the host population. Here, we extended the previous London analyses to include nearly a century of data that also contains four major demographic changes: the First and Second World Wars, the 1918 influenza pandemic, and the start of a measles mass vaccination program. By combining mortality and incidence data using particle filtering methods, we show that a simple stochastic epidemic model, with minimal historical specifications, can capture the nearly 100 years of dynamics including changes caused by each of the major perturbations. We show that the majority of dynamic changes are explainable by the internal nonlinear dynamics of the system, tuned by demographic changes. In addition, the 1918 influenza pandemic and World War II acted as extra perturbations to this basic epidemic oscillator. Our analysis underlines that long-term ecological and epidemiological dynamics can follow very simple rules, even in a non-stationary population subject to significant perturbations and major secular changes.

tsiR: An R package for time-series Susceptible-Infected-Recovered models of epidemics.

tsiR is an open source software package implemented in the R programming language designed to analyze infectious disease time-series data. The software extends a well-studied and widely-applied algorithm, the time-series Susceptible-Infected-Recovered (TSIR) model, to infer parameters from incidence data, such as contact seasonality, and to forward simulate the underlying mechanistic model. The tsiR package aggregates a number of different fitting features previously described in the literature in a user-friendly way, providing support for their broader adoption in infectious disease research. Also included in tsiR are a number of diagnostic tools to assess the fit of the TSIR model. This package should be useful for researchers analyzing incidence data for fully-immunizing infectious diseases.

Estimating enhanced prevaccination measles transmission hotspots in the context of cross-scale dynamics.

A key question in clarifying human-environment interactions is how dynamic complexity develops across integrative scales from molecular to population and global levels. Apart from its public health importance, measles is an excellent test bed for such an analysis. Simple mechanistic models have successfully illuminated measles dynamics at the city and country levels, revealing seasonal forcing of transmission as a major driver of long-term epidemic behavior. Seasonal forcing ties closely to patterns of school aggregation at the individual and community levels, but there are few explicit estimates of school transmission due to the relative lack of epidemic data at this scale. Here, we use data from a 1904 measles outbreak in schools in Woolwich, London, coupled with a stochastic Susceptible-Infected-Recovered model to analyze measles incidence data. Our results indicate that transmission within schools and age classes is higher than previous population-level serological data would suggest. This analysis sheds quantitative light on the role of school-aged children in measles cross-scale dynamics, as we illustrate with references to the contemporary vaccination landscape.

Hydrodynamic schooling of flapping swimmers.

Fish schools and bird flocks are fascinating examples of collective behaviours in which many individuals generate and interact with complex flows. Motivated by animal groups on the move, here we explore how the locomotion of many bodies emerges from their flow-mediated interactions. Through experiments and simulations of arrays of flapping wings that propel within a collective wake, we discover distinct modes characterized by the group swimming speed and the spatial phase shift between trajectories of neighbouring wings. For identical flapping motions, slow and fast modes coexist and correspond to constructive and destructive wing-wake interactions. Simulations show that swimming in a group can enhance speed and save power, and we capture the key phenomena in a mathematical model based on memory or the storage and recollection of information in the flow field. These results also show that fluid dynamic interactions alone are sufficient to generate coherent collective locomotion, and thus might suggest new ways to characterize the role of flows in animal groups.