Quantifying the impact of COVID-19 control measures using a Bayesian model of physical distancing

On the Asymptotic Capacity of Information-Theoretic Privacy-Preserving Epidemiological Data Collection

The paradigm-shifting developments of cryptography and information theory have focused on the privacy of data-sharing systems, such as epidemiological studies, where agencies are collecting far more personal data than they need, causing intrusions on patients' privacy. To study the capability of the data collection while protecting privacy from an information theory perspective, we formulate a new distributed multiparty computation problem called privacy-preserving epidemiological data collection. In our setting, a data collector requires a linear combination of K users' data through a storage system consisting of N servers. Privacy needs to be protected when the users, servers, and data collector do not trust each other. For the users, any data are required to be protected from up to E colluding servers; for the servers, any more information than the desired linear combination cannot be leaked to the data collector; and for the data collector, any single server can not know anything about the coefficients of the linear combination. Our goal is to find the optimal collection rate, which is defined as the ratio of the size of the user's message to the total size of downloads from N servers to the data collector. For achievability, we propose an asymptotic capacity-achieving scheme when E<N-1, by applying the cross-subspace alignment method to our construction; for the converse, we proved an upper bound of the asymptotic rate for all achievable schemes when E<N-1. Additionally, we show that a positive asymptotic capacity is not possible when E≥N-1. The results of the achievability and converse meet when the number of users goes to infinity, yielding the asymptotic capacity. Our work broadens current researches on data privacy in information theory and gives the best achievable asymptotic performance that any epidemiological data collector can obtain.

The Role of Sports in the Subjective Psychological Well-Being of Hungarian Adult Population in Three Waves of the COVID-19 Pandemic

(1) Background: In this study, sport and subjective psychological well-being is investigated in three waves of the COVID-19 pandemic. (2) Methods: We have conducted three different representative sample surveys (n = 3600 altogether) on the Hungarian adult population and investigated the sample's subjective psychological well-being with the WHO-5 Well-Being Index, as well as changes in their subjective well-being through the different waves of the pandemic. Sporting habits and socio-economic variables were also surveyed, and OLS regression models were created focused on the WHO-5 measures. (3) Results: The subjective psychological well-being of the Hungarian adult population decreased significantly, but in the second and third wave of pandemic restrictions, an increase in subjective psychological well-being has been measured. The relationships between the time spent on doing sports and subjective psychological well-being were significant in each pandemic waves. The highest subjective psychological well-being and its highest increase were reported by those who could increase their time spent on doing sports as well. (4) Conclusions: The relationships between the sports activities, physical health, size of settlement, changes in income and subjective psychological well-being of the Hungarian adult population were significant in all three waves of the COVID-19 pandemic.

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013-2015 West Africa Ebola outbreak.

Estimation of SARS‐CoV‐2 antibody prevalence through serological uncertainty and daily incidence

Serology tests for SARS‐CoV‐2 provide a paradigm for estimating the number of individuals who have had an infection in the past (including cases that are not detected by routine testing, which has varied over the course of the pandemic and between jurisdictions). Such estimation is challenging in cases for which we only have limited serological data and do not take into account the uncertainty of the serology test. In this work, we provide a joint Bayesian model to improve the estimation of the sero‐prevalence (the proportion of the population with SARS‐CoV‐2 antibodies) through integrating multiple sources of data, priors on the sensitivity and specificity of the serological test, and an effective epidemiological dynamics model. We apply our model to the Greater Vancouver area, British Columbia, Canada, with data acquired during the pandemic from the end of January to May 2020. Our estimated sero‐prevalence is consistent with previous literature but with a tighter credible interval.

Optimal shutdown strategies for COVID-19 with economic and mortality costs: British Columbia as a case study

Decision makers with the responsibility of managing policy for the COVID-19 epidemic have faced difficult choices in balancing the competing claims of saving lives and the high economic cost of shutdowns. In this paper, we formulate a model with both epidemiological and economic content to assist this decision-making process. We consider two ways to handle the balance between economic costs and deaths. First, we use the statistical value of life, which in Canada is about C$7 million, to optimize over a single variable, which is the sum of the economic cost and the value of lives lost. Our second method is to calculate the Pareto optimal front when we look at the two variables-deaths and economic costs. In both cases we find that, for most parameter values, the optimal policy is to adopt an initial shutdown level which reduces the reproduction number of the epidemic to close to 1. This level is then reduced once a vaccination programme is underway. Our model also indicates that an oscillating policy of strict and mild shutdowns is less effective than a policy which maintains a moderate shutdown level.

Prioritising COVID-19 vaccination in changing social and epidemiological landscapes: a mathematical modelling study

BACKGROUND

During the COVID-19 pandemic, authorities must decide which groups to prioritise for vaccination in a shifting social-epidemiological landscape in which the success of large-scale non-pharmaceutical interventions requires broad social acceptance. We aimed to compare projected COVID-19 mortality under four different strategies for the prioritisation of SARS-CoV-2 vaccines.

METHODS

We developed a coupled social-epidemiological model of SARS-CoV-2 transmission in which social and epidemiological dynamics interact with one another. We modelled how population adherence to non-pharmaceutical interventions responds to case incidence. In the model, schools and workplaces are also closed and reopened on the basis of reported cases. The model was parameterised with data on COVID-19 cases and mortality, SARS-CoV-2 seroprevalence, population mobility, and demography from Ontario, Canada (population 14·5 million). Disease progression parameters came from the SARS-CoV-2 epidemiological literature. We assumed a vaccine with 75% efficacy against disease and transmissibility. We compared vaccinating those aged 60 years and older first (oldest-first strategy), vaccinating those younger than 20 years first (youngest-first strategy), vaccinating uniformly by age (uniform strategy), and a novel contact-based strategy. The latter three strategies interrupt transmission, whereas the first targets a vulnerable group to reduce disease. Vaccination rates ranged from 0·5% to 5% of the population per week, beginning on either Jan 1 or Sept 1, 2021.

FINDINGS

Case notifications, non-pharmaceutical intervention adherence, and lockdown undergo successive waves that interact with the timing of the vaccine programme to determine the relative effectiveness of the four strategies. Transmission-interrupting strategies become relatively more effective with time as herd immunity builds. The model predicts that, in the absence of vaccination, 72 000 deaths (95% credible interval 40 000-122 000) would occur in Ontario from Jan 1, 2021, to March 14, 2025, and at a vaccination rate of 1·5% of the population per week, the oldest-first strategy would reduce COVID-19 mortality by 90·8% on average (followed by 89·5% in the uniform, 88·9% in the contact-based, and 88·2% in the youngest-first strategies). 60 000 deaths (31 000-108 000) would occur from Sept 1, 2021, to March 14, 2025, in the absence of vaccination, and the contact-based strategy would reduce COVID-19 mortality by 92·6% on average (followed by 92·1% in the uniform, 91·0% in the oldest-first, and 88·3% in the youngest-first strategies) at a vaccination rate of 1·5% of the population per week.

INTERPRETATION

The most effective vaccination strategy for reducing mortality due to COVID-19 depends on the time course of the pandemic in the population. For later vaccination start dates, use of SARS-CoV-2 vaccines to interrupt transmission might prevent more deaths than prioritising vulnerable age groups.

FUNDING

Ontario Ministry of Colleges and Universities.

Data-driven optimized control of the COVID-19 epidemics

Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different Metropolitan Statistical Areas (MSAs) within the US to parametrize a model that well describes the propagation of the disease in each area. We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time. We find that with the exception of the initial time and of the final time, the optimal control input is well approximated by a constant, specific to each area, which contrasts with the implemented system of reopening 'in phases'. For all the areas considered, this optimal level corresponds to stricter social distancing than the level estimated from data. Proper selection of the time period for application of the control action optimally is important: depending on the particular MSA this period should be either short or long or intermediate. We also consider the case that the transmissibility increases in time (due e.g. to increasingly colder weather), for which we find that the optimal control solution yields progressively stricter measures of social distancing. We finally compute the optimal control solution for a model modified to incorporate the effects of vaccinations on the population and we see that depending on a number of factors, social distancing measures could be optimally reduced during the period over which vaccines are administered to the population.

Daily Forecasting of New Cases for Regional Epidemics of Coronavirus Disease 2019 with Bayesian Uncertainty Quantification

To increase situational awareness and support evidence-based policy-making, we formulated a mathematical model for COVID-19 transmission within a regional population. This compartmental model accounts for quarantine, self-isolation, social distancing, a non-exponentially distributed incubation period, asymptomatic individuals, and mild and severe forms of symptomatic disease. Using Bayesian inference, we have been calibrating region-specific models daily for consistency with new reports of confirmed cases from the 15 most populous metropolitan statistical areas in the United States and quantifying uncertainty in parameter estimates and predictions of future case reports. This online learning approach allows for early identification of new trends despite considerable variability in case reporting.

ARTICLE SUMMARY LINE

We report models for regional COVID-19 epidemics and use of Bayesian inference to quantify uncertainty in daily predictions of expected reporting of new cases, enabling identification of new trends in surveillance data.

Analysis of COVID-19 Prevention and Control Effects Based on the SEITRD Dynamic Model and Wuhan Epidemic Statistics

Since December 2019, millions of people worldwide have been diagnosed with COVID-19, which has caused enormous losses. Given that there are currently no effective treatment or prevention drugs, most countries and regions mainly rely on quarantine and travel restrictions to prevent the spread of the epidemic. How to find proper prevention and treatment methods has been a hot topic of discussion. The key to the problem is to understand when these intervention measures are the best strategies for disease control and how they might affect disease dynamics. In this paper, we build a transmission dynamic model in combination with the transmission characteristics of COVID-19. We thoroughly study the dynamical behavior of the model and analyze how to determine the relevant parameters, and how the parameters influence the transmission process. Furthermore, we subsequently compare the impact of different control strategies on the epidemic, the variables include intervention time, control duration, control intensity, and other model parameters. Finally, we can find a better control method by comparing the results under different schemes and choose the proper preventive control strategy according to the actual epidemic stage and control objectives.

A social network model of COVID-19

I construct a dynamic social-network model of the COVID-19 epidemic which embeds the SIR epidemiological model onto a graph of person-to-person interactions. The standard SIR framework assumes uniform mixing of infectious persons in the population. This abstracts from important elements of realism and locality: (i) people are more likely to interact with members of their social networks and (ii) health and economic policies can affect differentially the rate of viral transmission via a person's social network vs. the population as a whole. The proposed network-augmented (NSIR) model allows the evaluation, via simulations, of (i) health and economic policies and outcomes for all or subset of the population: lockdown/distancing, herd immunity, testing, contact tracing; (ii) behavioral responses and/or imposing or lifting policies at specific times or conditional on observed states. I find that viral transmission over a network-connected population can proceed slower and reach lower peak than transmission via uniform mixing. Network connections introduce uncertainty and path dependence in the epidemic dynamics, with a significant role for bridge links and superspreaders. Testing and contact tracing are more effective in the network model. If lifted early, distancing policies mostly shift the infection peak into the future, with associated economic costs. Delayed or intermittent interventions or endogenous behavioral responses generate a multi-peaked infection curve, a form of 'curve flattening', but may have costlier economic consequences by prolonging the epidemic duration.

Safety-Critical Control of Active Interventions for COVID-19 Mitigation

The world has recently undergone the most ambitious mitigation effort in a century, consisting of wide-spread quarantines aimed at preventing the spread of COVID-19. The use of influential epidemiological models of COVID-19 helped to encourage decision makers to take drastic non-pharmaceutical interventions. Yet, inherent in these models are often assumptions that the active interventions are static, e.g., that social distancing is enforced until infections are minimized, which can lead to inaccurate predictions that are ever evolving as new data is assimilated. We present a methodology to dynamically guide the active intervention by shifting the focus from viewing epidemiological models as systems that evolve in autonomous fashion to control systems with an "input" that can be varied in time in order to change the evolution of the system. We show that a safety-critical control approach to COVID-19 mitigation gives active intervention policies that formally guarantee the safe evolution of compartmental epidemiological models. This perspective is applied to current US data on cases while taking into account reduction of mobility, and we find that it accurately describes the current trends when time delays associated with incubation and testing are incorporated. Optimal active intervention policies are synthesized to determine future mitigations necessary to bound infections, hospitalizations, and death, both at national and state levels. We therefore provide means in which to model and modulate active interventions with a view toward the phased reopenings that are currently beginning across the US and the world in a decentralized fashion. This framework can be converted into public policies, accounting for the fractured landscape of COVID-19 mitigation in a safety-critical fashion.

Local lockdowns outperform global lockdown on the far side of the COVID-19 epidemic curve

In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission among an interconnected group of population centers representing counties, municipalities, and districts (collectively, "counties"). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of reopening (and reclosing, as needed) schools and workplaces county by county, according to triggers for county-specific infection prevalence, to a global strategy of province-wide reopening and reclosing, according to triggers for province-wide infection prevalence. For trigger levels that result in the same number of COVID-19 cases between the two strategies, the local strategy causes significantly fewer person-days of closure, even under high intercounty travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage, but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for reopening and reclosing.