Time-variant reproductive number of COVID-19 in Seoul, Korea.

OBJECTIVES: To estimate time-variant reproductive number (Rt) of coronavirus disease 19 based on either number of daily confirmed cases or their onset date to monitor effectiveness of quarantine policies. METHODS: Using number of daily confirmed cases from January 23, 2020 to March 22, 2020 and their symptom onset date from the official website of the Seoul Metropolitan Government and the district office, we calculated Rt using program R's package "EpiEstim". For asymptomatic cases, their symptom onset date was considered as -2, -1, 0, +1, and +2 days of confirmed date. RESULTS: Based on the information of 313 confirmed cases, the epidemic curve was shaped like 'propagated epidemic curve'. The daily Rt based on Rt_c peaked to 2.6 on February 20, 2020, then showed decreased trend and became <1.0 from March 3, 2020. Comparing both Rt from Rt_c and from the number of daily onset cases, we found that the pattern of changes was similar, although the variation of Rt was greater when using Rt_c. When we changed assumed onset date for asymptotic cases (-2 days to +2 days of the confirmed date), the results were comparable. CONCLUSIONS: Rt can be estimated based on Rt_c which is available from daily report of the Korea Centers for Disease Control and Prevention. Estimation of Rt would be useful to continuously monitor the effectiveness of the quarantine policy at the city and province levels.

Incorporating temporal distribution of population-level viral load enables real-time estimation of COVID-19 transmission.

Many locations around the world have used real-time estimates of the time-varying effective reproductive number ([Formula: see text]) of COVID-19 to provide evidence of transmission intensity to inform control strategies. Estimates of [Formula: see text] are typically based on statistical models applied to case counts and typically suffer lags of more than a week because of the latent period and reporting delays. Noting that viral loads tend to decline over time since illness onset, analysis of the distribution of viral loads among confirmed cases can provide insights into epidemic trajectory. Here, we analyzed viral load data on confirmed cases during two local epidemics in Hong Kong, identifying a strong correlation between temporal changes in the distribution of viral loads (measured by RT-qPCR cycle threshold values) and estimates of [Formula: see text] based on case counts. We demonstrate that cycle threshold values could be used to improve real-time [Formula: see text] estimation, enabling more timely tracking of epidemic dynamics.

Mathematical Approach to Investigate Stress due to Control Measures to Curb COVID-19.

COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number (R 0) was derived by using the next-generation matrix method, which shows that, when R 0 < 1, the disease-free equilibrium is globally asymptotically stable whereas when R 0 > 1 the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and R 0. Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.

Effect of non-pharmacological interventions on the COVID-19 epidemic in Saudi Arabia.

We quantified the potential impact of different social distancing and self-isolation scenarios on the coronavirus disease 2019 (COVID-19) pandemic trajectory in Saudi Arabia and compared the modelling results to the confirmed epidemic trajectory. Using the susceptible, exposed, infected, quarantined and self-isolated, requiring hospitalisation, recovered/immune individuals, fatalities model, we assessed the impact of a non-pharmacological interventions' subset. An unmitigated scenario (baseline), mitigation scenarios (25% reduction in social contact/twofold increase in self-isolation) and enhanced mitigation scenarios (50% reduction in social contact/twofold increase in self-isolation) were assessed and compared to the actual epidemic trajectory. For the unmitigated scenario, mitigation scenarios, enhanced mitigation scenarios and actual observed epidemic, the peak daily incidence rates (per 10 000 population) were 77.00, 16.00, 9.00 and 1.14 on days 71, 54, 35 and 136, respectively. The peak fatality rates were 35.00, 13.00, 5.00 and 0.016 on days 150, 125, 60 and 155, respectively. The R0 was 1.15, 1.14, 1.22 and 2.50, respectively. Aggressive implementation of social distancing and self-isolation contributed to the downward trend of the disease. We recommend using extensive models that comprehensively consider the natural history of COVID-19, social and behavioural patterns, age-specific data, actual network topology and population to elucidate the epidemic's magnitude and trajectory.

Evaluating the impacts of non-pharmaceutical interventions on the transmission dynamics of COVID-19 in Canada based on mobile network.

The COVID-19 outbreak has caused two waves and spread to more than 90% of Canada's provinces since it was first reported more than a year ago. During the COVID-19 epidemic, Canadian provinces have implemented many Non-Pharmaceutical Interventions (NPIs). However, the spread of the COVID-19 epidemic continues due to the complex dynamics of human mobility. We develop a meta-population network model to study the transmission dynamics of COVID-19. The model takes into account the heterogeneity of mitigation strategies in different provinces of Canada, such as the timing of implementing NPIs, the human mobility in retail and recreation, grocery and pharmacy, parks, transit stations, workplaces, and residences due to work and recreation. To determine which activity is most closely related to the dynamics of COVID-19, we use the cross-correlation analysis to find that the positive correlation is the highest between the mobility data of parks and the weekly number of confirmed COVID-19 from February 15 to December 13, 2020. The average effective reproduction numbers in nine Canadian provinces are all greater than one during the time period, and NPIs have little impact on the dynamics of COVID-19 epidemics in Ontario and Saskatchewan. After November 20, 2020, the average infection probability in Alberta became the highest since the start of the COVID-19 epidemic in Canada. We also observe that human activities around residences do not contribute much to the spread of the COVID-19 epidemic. The simulation results indicate that social distancing and constricting human mobility is effective in mitigating COVID-19 transmission in Canada. Our findings can provide guidance for public health authorities in projecting the effectiveness of future NPIs.

Superspreading quantified from bursty epidemic trajectories.

The quantification of spreading heterogeneity in the COVID-19 epidemic is crucial as it affects the choice of efficient mitigating strategies irrespective of whether its origin is biological or social. We present a method to deduce temporal and individual variations in the basic reproduction number directly from epidemic trajectories at a community level. Using epidemic data from the 98 districts in Denmark we estimate an overdispersion factor k for COVID-19 to be about 0.11 (95% confidence interval 0.08-0.18), implying that 10 % of the infected cause between 70 % and 87 % of all infections.

On the use of aggregated human mobility data to estimate the reproduction number.

The reproduction number of an infectious disease, such as CoViD-19, can be described through a modified version of the susceptible-infected-recovered (SIR) model with time-dependent contact rate, where mobility data are used as proxy of average movement trends and interpersonal distances. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 in terms of aggregated individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.

The Evolutionary Landscape of SARS-CoV-2 Variant B.1.1.519 and Its Clinical Impact in Mexico City.

The SARS-CoV-2 pandemic is one of the most concerning health problems around the globe. We reported the emergence of SARS-CoV-2 variant B.1.1.519 in Mexico City. We reported the effective reproduction number (Rt) of B.1.1.519 and presented evidence of its geographical origin based on phylogenetic analysis. We also studied its evolution via haplotype analysis and identified the most recurrent haplotypes. Finally, we studied the clinical impact of B.1.1.519. The B.1.1.519 variant was predominant between November 2020 and May 2021, reaching 90% of all cases sequenced in February 2021. It is characterized by three amino acid changes in the spike protein: T478K, P681H, and T732A. Its Rt varies between 0.5 and 2.9. Its geographical origin remain to be investigated. Patients infected with variant B.1.1.519 showed a highly significant adjusted odds ratio (aOR) increase of 1.85 over non-B.1.1.519 patients for developing a severe/critical outcome (p = 0.000296, 1.33-2.6 95% CI) and a 2.35-fold increase for hospitalization (p = 0.005, 1.32-4.34 95% CI). The continuous monitoring of this and other variants will be required to control the ongoing pandemic as it evolves.

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves.

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

A Mathematical Model of COVID-19 with Vaccination and Treatment.

We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures-vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number R 0(v) is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever R 0(v) > 1, even if vaccine coverage is high. Pontryagin's maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number R 0 = 1.31 at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when R 0(v) > 1, additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate b, the vaccine efficacy ε, the vaccination rate v, the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes σ and ϕ are the most impactful parameters.

Mitigating COVID-19 outbreaks in workplaces and schools by hybrid telecommuting.

The COVID-19 epidemic has forced most countries to impose contact-limiting restrictions at workplaces, universities, schools, and more broadly in our societies. Yet, the effectiveness of these unprecedented interventions in containing the virus spread remain largely unquantified. Here, we develop a simulation study to analyze COVID-19 outbreaks on three real-life contact networks stemming from a workplace, a primary school and a high school in France. Our study provides a fine-grained analysis of the impact of contact-limiting strategies at workplaces, schools and high schools, including: (1) Rotating strategies, in which workers are evenly split into two shifts that alternate on a daily or weekly basis; and (2) On-Off strategies, where the whole group alternates periods of normal work interactions with complete telecommuting. We model epidemics spread in these different setups using a stochastic discrete-time agent-based transmission model that includes the coronavirus most salient features: super-spreaders, infectious asymptomatic individuals, and pre-symptomatic infectious periods. Our study yields clear results: the ranking of the strategies, based on their ability to mitigate epidemic propagation in the network from a first index case, is the same for all network topologies (workplace, primary school and high school). Namely, from best to worst: Rotating week-by-week, Rotating day-by-day, On-Off week-by-week, and On-Off day-by-day. Moreover, our results show that below a certain threshold for the original local reproduction number [Formula: see text] within the network (< 1.52 for primary schools, < 1.30 for the workplace, < 1.38 for the high school, and < 1.55 for the random graph), all four strategies efficiently control outbreak by decreasing effective local reproduction number to [Formula: see text] < 1. These results can provide guidance for public health decisions related to telecommuting.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic.

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

The effect of human mobility restrictions on the COVID-19 transmission network in China.

BACKGROUND: COVID-19 poses a severe threat worldwide. This study analyzes its propagation and evaluates statistically the effect of mobility restriction policies on the spread of the disease. METHODS: We apply a variation of the stochastic Susceptible-Infectious-Recovered model to describe the temporal-spatial evolution of the disease across 33 provincial regions in China, where the disease was first identified. We employ Bayesian Markov Chain Monte-Carlo methods to estimate the model and to characterize a dynamic transmission network, which enables us to evaluate the effectiveness of various local and national policies. RESULTS: The spread of the disease in China was predominantly driven by community transmission within regions, which dropped substantially after local governments imposed various lockdown policies. Further, Hubei was only the epicenter of the early epidemic stage. Secondary epicenters, such as Beijing and Guangdong, had already become established by late January 2020. The transmission from these epicenters substantially declined following the introduction of mobility restrictions across regions. CONCLUSIONS: The spatial transmission network is able to differentiate the effect of the local lockdown policies and the cross-region mobility restrictions. We conclude that both are important policy tools for curbing the disease transmission. The coordination between central and local governments is important in suppressing the spread of infectious diseases.

Cure and death play a role in understanding dynamics for COVID-19: Data-driven competing risk compartmental models, with and without vaccination.

Several factors have played a strong role in influencing the dynamics of COVID-19 in the U.S. One being the economy, where a tug of war has existed between lockdown measures to control disease versus loosening of restrictions to address economic hardship. A more recent effect has been availability of vaccines and the mass vaccination efforts of 2021. In order to address the challenges in analyzing this complex process, we developed a competing risk compartmental model framework with and without vaccination compartment. This framework separates instantaneous risk of removal for an infectious case into competing risks of cure and death, and when vaccinations are present, the vaccinated individual can also achieve immunity before infection. Computations are performed using a simple discrete time algorithm that utilizes a data driven contact rate. Using population level pre-vaccination data, we are able to identify and characterize three wave patterns in the U.S. Estimated mortality rates for second and third waves are 1.7%, which is a notable decrease from 8.5% of a first wave observed at onset of disease. This analysis reveals the importance cure time has on infectious duration and disease transmission. Using vaccination data from 2021, we find a fourth wave, however the effect of this wave is suppressed due to vaccine effectiveness. Parameters playing a crucial role in this modeling were a lower cure time and a signficantly lower mortality rate for the vaccinated.

Predicting COVID-19 cases with unknown homogeneous or heterogeneous resistance to infectivity.

We present a restricted infection rate inverse binomial-based approach to better predict COVID-19 cases after a family gathering. The traditional inverse binomial (IB) model is inappropriate to match the reality of COVID-19, because the collected data contradicts the model's requirement that variance should be larger than the expected value. Our version of an IB model is more appropriate, as it can accommodate all potential data scenarios in which the variance is smaller, equal, or larger than the mean. This is unlike the usual IB, which accommodates only the scenario in which the variance is more than the mean. Therefore, we propose a refined version of an IB model to be able to accommodate all potential data scenarios. The application of the approach is based on a restricted infectivity rate and methodology on COVID-19 data, which exhibit two clusters of infectivity. Cluster 1 has a smaller number of primary cases and exhibits larger variance than the expected cases with a negative correlation of 28%, implying that the number of secondary cases is lesser when the number of primary cases increases and vice versa. The traditional IB model is appropriate for Cluster 1. The probability of contracting COVID-19 is estimated to be 0.13 among the primary, but is 0.75 among the secondary in Cluster 1, with a wider gap. Cluster 2, with a larger number of primary cases, exhibits smaller variance than the expected cases with a correlation of 79%, implying that the number of primary and secondary cases do increase or decrease together. Cluster 2 disqualifies the traditional IB model and requires its refined version. The probability of contracting COVID-19 is estimated to be 0.74 among the primary, but is 0.72 among the secondary in Cluster 2, with a narrower gap. The advantages of the proposed approach include the model's ability to estimate the community's health system memory, as future policies might reduce COVID's spread. In our approach, the current hazard level to be infected with COVID-19 and the odds of not contracting COVID-19 among the primary in comparison to the secondary groups are estimable and interpretable.

Estimates of regional infectivity of COVID-19 in the United Kingdom following imposition of social distancing measures.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reproduction number has become an essential parameter for monitoring disease transmission across settings and guiding interventions. The UK published weekly estimates of the reproduction number in the UK starting in May 2020 which are formed from multiple independent estimates. In this paper, we describe methods used to estimate the time-varying SARS-CoV-2 reproduction number for the UK. We used multiple data sources and estimated a serial interval distribution from published studies. We describe regional variability and how estimates evolved during the early phases of the outbreak, until the relaxing of social distancing measures began to be introduced in early July. Our analysis is able to guide localized control and provides a longitudinal example of applying these methods over long timescales. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Real-time nowcasting and forecasting of COVID-19 dynamics in England: the first wave.

England has been heavily affected by the SARS-CoV-2 pandemic, with severe 'lockdown' mitigation measures now gradually being lifted. The real-time pandemic monitoring presented here has contributed to the evidence informing this pandemic management throughout the first wave. Estimates on the 10 May showed lockdown had reduced transmission by 75%, the reproduction number falling from 2.6 to 0.61. This regionally varying impact was largest in London with a reduction of 81% (95% credible interval: 77-84%). Reproduction numbers have since then slowly increased, and on 19 June the probability of the epidemic growing was greater than 5% in two regions, South West and London. By this date, an estimated 8% of the population had been infected, with a higher proportion in London (17%). The infection-to-fatality ratio is 1.1% (0.9-1.4%) overall but 17% (14-22%) among the over-75s. This ongoing work continues to be key to quantifying any widespread resurgence, should accrued immunity and effective contact tracing be insufficient to preclude a second wave. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Dynamics of SARS-CoV-2 with waning immunity in the UK population.

The dynamics of immunity are crucial to understanding the long-term patterns of the SARS-CoV-2 pandemic. Several cases of reinfection with SARS-CoV-2 have been documented 48-142 days after the initial infection and immunity to seasonal circulating coronaviruses is estimated to be shorter than 1 year. Using an age-structured, deterministic model, we explore potential immunity dynamics using contact data from the UK population. In the scenario where immunity to SARS-CoV-2 lasts an average of three months for non-hospitalized individuals, a year for hospitalized individuals, and the effective reproduction number after lockdown ends is 1.2 (our worst-case scenario), we find that the secondary peak occurs in winter 2020 with a daily maximum of 387 000 infectious individuals and 125 000 daily new cases; threefold greater than in a scenario with permanent immunity. Our models suggest that longitudinal serological surveys to determine if immunity in the population is waning will be most informative when sampling takes place from the end of the lockdown in June until autumn 2020. After this period, the proportion of the population with antibodies to SARS-CoV-2 is expected to increase due to the secondary wave. Overall, our analysis presents considerations for policy makers on the longer-term dynamics of SARS-CoV-2 in the UK and suggests that strategies designed to achieve herd immunity may lead to repeated waves of infection as immunity to reinfection is not permanent. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

The population attributable fraction of cases due to gatherings and groups with relevance to COVID-19 mitigation strategies.

Many countries have banned groups and gatherings as part of their response to the pandemic caused by the coronavirus, SARS-CoV-2. Although there are outbreak reports involving mass gatherings, the contribution to overall transmission is unknown. We used data from a survey of social contact behaviour that specifically asked about contact with groups to estimate the population attributable fraction (PAF) due to groups as the relative change in the basic reproduction number when groups are prevented. Groups of 50+ individuals accounted for 0.5% of reported contact events, and we estimate that the PAF due to groups of 50+ people is 5.4% (95% confidence interval 1.4%, 11.5%). The PAF due to groups of 20+ people is 18.9% (12.7%, 25.7%) and the PAF due to groups of 10+ is 25.2% (19.4%, 31.4%). Under normal circumstances with pre-COVID-19 contact patterns, large groups of individuals have a relatively small epidemiological impact; small- and medium-sized groups between 10 and 50 people have a larger impact on an epidemic. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.