Use of Bluetooth contact tracing technology to model COVID-19 quarantine policies in high-risk closed populations.

Containment measures in high-risk closed settings, like migrant worker (MW) dormitories, are critical for mitigating emerging infectious disease outbreaks and protecting potentially vulnerable populations in outbreaks such as coronavirus disease 2019 (COVID-19). The direct impact of social distancing measures can be assessed through wearable contact tracing devices. Here, we developed an individual-based model using data collected through a Bluetooth wearable device that collected 33.6M and 52.8M contact events in two dormitories in Singapore, one apartment style and the other a barrack style, to assess the impact of measures to reduce the social contact of cases and their contacts. The simulation of highly detailed contact networks accounts for different infrastructural levels, including room, floor, block, and dormitory, and intensity in terms of being regular or transient. Via a branching process model, we then simulated outbreaks that matched the prevalence during the COVID-19 outbreak in the two dormitories and explored alternative scenarios for control. We found that strict isolation of all cases and quarantine of all contacts would lead to very low prevalence but that quarantining only regular contacts would lead to only marginally higher prevalence but substantially fewer total man-hours lost in quarantine. Reducing the density of contacts by 30% through the construction of additional dormitories was modelled to reduce the prevalence by 14 and 9% under smaller and larger outbreaks, respectively. Wearable contact tracing devices may be used not just for contact tracing efforts but also to inform alternative containment measures in high-risk closed settings.

A practical guide to mathematical methods for estimating infectious disease outbreak risks.

Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Effects of contact tracing and nucleic acid testing on the COVID-19 outbreak in Zunyi, China: data-driven study using a branching process model.

BACKGROUND: During October 2021, China experienced localized outbreaks of COVID-19 in many cities. We analyzed the small local outbreak in Zunyi (Guizhou Province), a major city in southwestern China, and modeled the effects of different interventions on this outbreak. METHODS: Data on infections and contacts, provided by the Health Commission of Guizhou Province, were used to analyze the epidemiological characteristics of the outbreak and calculate the effectiveness of vaccination. A branching process model was used to simulate the outbreak. This model considered the time interval from exposure of the initial case to confirmation, the number of potential infections caused by the initial case, and the effects of the different interventions. RESULTS: From 18 to 25 October 2021, there were 12 patients with COVID-19 in Zunyi. Overall, the average age was 67.17 years-old, 8 patients were females, and 1 patient had an asymptomatic infection. The effectiveness of two-dose inactivated vaccine against SARS-CoV-2 infection was 16.7% (95% CI: 2.8% to 99.7%). The initial case was infected on 11 or 12 October 2021, 6.40 (95% CI: 6.37, 6.42; IQR: 4.92, 7.63) days before confirmation while the travelling in Lanzhou (Gansu Province). There were 10.07 (95% CI: 10.04, 10.09; IQR: 7.86, 11.93) potential secondary cases. When the effective vaccine coverage reached 60%, the probability of cumulative cases exceeding 20 was less than 8.77%, even if contact tracing was relaxed or eliminated. However, if the probability of tracing contacts decreased, earlier initiation of nucleic acid testing was necessary to control the outbreak. CONCLUSIONS: The COVID-19 outbreak in Zunyi was controlled quickly due to moderately effective vaccine coverage and rapid contact tracing. For controlling localized outbreaks, vaccination and contact tracing seemed to be more effective than massive nucleic acid testing in the initial phase of transmission. However, if there is low effective vaccine coverage or insufficient contact tracing, nucleic acid testing should start earlier.

Contact tracing & super-spreaders in the branching-process model.

In recent years, it became clear that super-spreader events play an important role, particularly in the spread of airborne infections. We investigate a novel model for super-spreader events, not based on a heterogeneous contact graph but on a random contact rate: Many individuals become infected synchronously in single contact events. We use the branching-process approach for contact tracing to analyze the impact of super-spreader events on the effect of contact tracing. Here we neglect a tracing delay. Roughly speaking, we find that contact tracing is more efficient in the presence of super-spreaders if the fraction of symptomatics is small, the tracing probability is high, or the latency period is distinctively larger than the incubation period. In other cases, the effect of contact tracing can be decreased by super-spreaders. Numerical analysis with parameters suited for SARS-CoV-2 indicates that super-spreaders do not decrease the effect of contact tracing crucially in case of that infection.

Quantitative assessment of the effects of massive nucleic acid testing in controlling a COVID-19 outbreak.

BACKGROUND: From 20 July to 26 August 2021, local outbreaks of COVID-19 occurred in Nanjing City and Yangzhou City (Jiangsu Province, China). We analyzed the characteristics of these outbreaks in an effort to develop specific and effective intervention strategies. METHODS: Publicly available data on the characteristics of the COVID-19 outbreaks in Jiangsu Province were collected. Logistic regression was used to assess the association of age and sex with clinical severity. Analysis of onset dates, generation time distributions, and locations were used to estimate the mean transmission distance. A branching process model was used to evaluate different management strategies. RESULTS: From 20 July to 26 August 2021, 820 patients were diagnosed with COVID-19 in Jiangsu Province, with 235 patients (28.7%) from Nanjing, 570 (69.5%) from Yangzhou, and 15 (1.8%) from other cities. Overall, 57.9% of the patients were female, 13.7% were under 20 years-old, and 58.3% had moderate disease status. The mean transmission distance was 4.12 km, and closed-loop management of the area within 2.23 km of cases seemed sufficient to control an outbreak. The model predicted that the cumulative cases in Yangzhou would increase from 311 to 642 if the interval between rounds of nucleic acid amplification testing (NAAT) increased from 1 to 6 days. It also predicted there would be 44.7% more patients if the NAAT started 10 days (rather than 0 days) after diagnosis of the first case. The proportion of cases detected by NAAT would increase from 11.16 to 44.12% when the rounds of NAAT increased from 1 to 7 within 17 days. When the effective vaccine coverage was 50%, the outbreak would be controlled even when using the most relaxed non-pharmaceutical interventions. CONCLUSIONS: The model predicted that a timely closed-loop management of a 2.23 km area around positive COVID-19 cases was sufficient to control the outbreak. Prompt serial NAAT is likely to contain an outbreak quickly, and our model results indicated that three rounds of NAAT sufficiently controlled local transmission. Trial registration We did not involve clinical trial.

Basic reproduction number of the COVID-19 Delta variant: Estimation from multiple transmission datasets.

The basic reproduction number, $ R_0 $, plays a central role in measuring the transmissibility of an infectious disease, and it thus acts as the fundamental index for planning control strategies. In the present study, we apply a branching process model to meticulously observed contact tracing data from Wakayama Prefecture, Japan, obtained in early 2020 and mid-2021. This allows us to efficiently estimate $ R_0 $ and the dispersion parameter $ k $ of the wild-type COVID-19, as well as the relative transmissibility of the Delta variant and relative transmissibility among fully vaccinated individuals, from a very limited data. $ R_0 $ for the wild type of COVID-19 is estimated to be 3.78 (95% confidence interval [CI]: 3.72-3.83), with $ k = 0.236 $ (95% CI: 0.233-0.240). For the Delta variant, the relative transmissibility to the wild type is estimated to be 1.42 (95% CI: 0.94-1.90), which gives $ R_0 = 5.37 $ (95% CI: 3.55-7.21). Vaccine effectiveness, determined by the reduction in the number of secondary transmissions among fully vaccinated individuals, is estimated to be 91% (95% CI: 85%-97%). The present study highlights that basic reproduction numbers can be accurately estimated from the distribution of minor outbreak data, and these data can provide further insightful epidemiological estimates including the dispersion parameter and vaccine effectiveness regarding the prevention of transmission.

Stochastic Modelling for Coronavirus (COVID’19) Pandemic in Bulgaria

The aim of this paper is to present the development and improvements done in the specific stochastic branching model during the progress of the COVID’19 pandemic caused by SARS-CoV-2 coronavirus up to spring of the year 2022. Our approach is data-driven and uses the parsimonious continuous time Crump-Mode-Jagers branching processes (CMJBP) model. The model provides a basis for decision makers to understand the likely trade-offs as an outbreak begins. © 2022 Copyright for this paper by its authors.

Predicting elimination of evolving virus variants.

As the SARS-CoV-2 virus spreads around the world new variants are appearing regularly. Although some countries have achieved very swift and successful vaccination campaigns, on a global scale the vast majority of the population is unvaccinated and new variants are proving more resistant to the current set of vaccines. We present a simple model of disease spread, which includes the evolution of new variants of a novel virus and varying vaccine effectiveness to these new strains. We show that rapid vaccine updates to target new strains are more effective than slow updates and containing spread through non-pharmaceutical interventions is vital while these vaccines are delivered. Finally, when measuring the key model inputs, e.g. the rate at which new mutations and variants of concern emerge, is difficult we show how an observable model output, the number of new variants that have been seen, is strongly correlated with the probability the virus is eliminated.

Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model.

Countries such as New Zealand, Australia and Taiwan responded to the Covid-19 pandemic with an elimination strategy. This involves a combination of strict border controls with a rapid and effective response to eliminate border-related re-introductions. An important question for decision makers is, when there is a new re-introduction, what is the right threshold at which to implement strict control measures designed to reduce the effective reproduction number below 1. Since it is likely that there will be multiple re-introductions, responding at too low a threshold may mean repeatedly implementing controls unnecessarily for outbreaks that would self-eliminate even without control measures. On the other hand, waiting for too high a threshold to be reached creates a risk that controls will be needed for a longer period of time, or may completely fail to contain the outbreak. Here, we use a highly idealised branching process model of small border-related outbreaks to address this question. We identify important factors that affect the choice of threshold in order to minimise the expect time period for which control measures are in force. We find that the optimal threshold for introducing controls decreases with the effective reproduction number, and increases with overdispersion of the offspring distribution and with the effectiveness of control measures. Our results are not intended as a quantitative decision-making algorithm. However, they may help decision makers understand when a wait-and-see approach is likely to be preferable over an immediate response.

A Special Type of Markov Branching Process Model for the Novel Coronavirus (Covid-19) Outbreak

Mathematical modeling has been an important tool to estimate key factors of the transmission and investigate the dynamical system of evolutionary nature in epidemics. More precisely, the outbreaks of the virus or epidemiology is generally considered as an application of branching process. Therefore, in this paper, we propose a special type of Markov branching process model to examine and explore some problems of the novel Coronavirus (COVID-19) infectious disease with the aims of reducing the effective reproduction number of an infection below unity. Since the COVID-19 has been recognized as a global pandemic, we have assessed a big amount of data such as hourly contagious, hospitalized patients, recovered and deaths. However, these data are necessary to be further processed to produce useful information for people and authorities when they make an efficient and optimal decisions. In such a decision-making process, we establish a special type of Gama Markov branching process model which has been successfully applied in other research areas such as queueing and waiting lines problems, stochastic reservoir problems, inventory controls and operation research. Specifically, we develop a three parameter Gama Markov branching process model that is structured in two parts, initial and latter transmission stages, so as to provide a comprehensive view of the virus spread through basic and effective reproduction numbers respectively, along with the probability of an outbreak sizes and duration. As an illustration, we have performed some simulations based on the daily data appearing on WHO dashboard in order to analyze the first semiannual spread of the ongoing Coronavirus pandemic in the region of Myanmar. The results show that the proposed model can be utilized for the real-life applications. © 2022, ICIC International. All rights reserved.

Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection.

Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals and considering disease-induced death, imperfect and waning vaccination protection as well as waning infections-acquired immunity. When analyzed as systems of ordinary differential equations, the model is proven to admit a backward bifurcation. A continuous time Markov chain (CTMC) version of the model is simulated numerically and compared to the results of branching process approximations. While the CTMC model detects the presence of the backward bifurcation, the branching process approximation does not. The special case of an SVIRS model is shown to have the same properties.

Critical time-dependent branching process modelling epidemic spreading with containment measures*

During the COVID pandemic, periods of exponential growth of the disease have been mitigated by containment measures that in different occasions have resulted in a power-law growth of the number of cases. The first observation of such behaviour has been obtained from 2020 late spring data coming from China by Ziff and Ziff in reference Ziff and Ziff (2020 Fractal kinetics of COVID-19 pandemic MedRxiv). After this important observation the power-law scaling (albeit with different exponents) has also been observed in other countries during periods of containment of the spread. Early interpretations of these results suggest that this phenomenon might be due to spatial effects of the spread. Here we show that temporal modulations of infectivity of individuals due to containment measures can also cause power-law growth of the number of cases over time. To this end we propose a stochastic well-mixed susceptible-infected-removed model of epidemic spreading in presence of containment measures resulting in a time dependent infectivity and we explore the statistical properties of the resulting branching process at criticality. We show that at criticality it is possible to observe power-law growth of the number of cases with exponents ranging between one and two. Our asymptotic analytical results are confirmed by extensive Monte Carlo simulations. Although these results do not exclude that spatial effects might be important in modulating the power-law growth of the number of cases at criticality, this work shows that even well-mixed populations may already feature non trivial power-law exponents at criticality.

Critical time-dependent branching process modelling epidemic spreading with containment measures This work celebrates the 70th birthday of our dear friend and colleague Bob Ziff

During the COVID pandemic, periods of exponential growth of the disease have been mitigated by containment measures that in different occasions have resulted in a power-law growth of the number of cases. The first observation of such behaviour has been obtained from 2020 late spring data coming from China by Ziff and Ziff in reference Ziff and Ziff (2020 Fractal kinetics of COVID-19 pandemic MedRxiv). After this important observation the power-law scaling (albeit with different exponents) has also been observed in other countries during periods of containment of the spread. Early interpretations of these results suggest that this phenomenon might be due to spatial effects of the spread. Here we show that temporal modulations of infectivity of individuals due to containment measures can also cause power-law growth of the number of cases over time. To this end we propose a stochastic well-mixed susceptible-infected-removed model of epidemic spreading in presence of containment measures resulting in a time dependent infectivity and we explore the statistical properties of the resulting branching process at criticality. We show that at criticality it is possible to observe power-law growth of the number of cases with exponents ranging between one and two. Our asymptotic analytical results are confirmed by extensive Monte Carlo simulations. Although these results do not exclude that spatial effects might be important in modulating the power-law growth of the number of cases at criticality, this work shows that even well-mixed populations may already feature non trivial power-law exponents at criticality. [ FROM AUTHOR] Copyright of Journal of Physics: A Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Optimizing COVID-19 control with asymptomatic surveillance testing in a university environment.

The high proportion of transmission events derived from asymptomatic or presymptomatic infections make SARS-CoV-2, the causative agent in COVID-19, difficult to control through the traditional non-pharmaceutical interventions (NPIs) of symptom-based isolation and contact tracing. As a consequence, many US universities developed asymptomatic surveillance testing labs, to augment NPIs and control outbreaks on campus throughout the 2020-2021 academic year (AY); several of those labs continue to support asymptomatic surveillance efforts on campus in AY2021-2022. At the height of the pandemic, we built a stochastic branching process model of COVID-19 dynamics at UC Berkeley to advise optimal control strategies in a university environment. Our model combines behavioral interventions in the form of group size limits to deter superspreading, symptom-based isolation, and contact tracing, with asymptomatic surveillance testing. We found that behavioral interventions offer a cost-effective means of epidemic control: group size limits of six or fewer greatly reduce superspreading, and rapid isolation of symptomatic infections can halt rising epidemics, depending on the frequency of asymptomatic transmission in the population. Surveillance testing can overcome uncertainty surrounding asymptomatic infections, with the most effective approaches prioritizing frequent testing with rapid turnaround time to isolation over test sensitivity. Importantly, contact tracing amplifies population-level impacts of all infection isolations, making even delayed interventions effective. Combination of behavior-based NPIs and asymptomatic surveillance also reduces variation in daily case counts to produce more predictable epidemics. Furthermore, targeted, intensive testing of a minority of high transmission risk individuals can effectively control the COVID-19 epidemic for the surrounding population. Even in some highly vaccinated university settings in AY2021-2022, asymptomatic surveillance testing offers an effective means of identifying breakthrough infections, halting onward transmission, and reducing total caseload. We offer this blueprint and easy-to-implement modeling tool to other academic or professional communities navigating optimal return-to-work strategies.

Not all fun and games: Potential incidence of SARS-CoV-2 infections during the Tokyo 2020 Olympic Games.

The Tokyo 2020 Olympic and Paralympic Games represent the most diverse international mass gathering event held since the start of the coronavirus disease 2019 (COVID-19) pandemic. Postponed to summer 2021, the rescheduled Games were set to be held amidst what would become the highest-ever levels of COVID-19 transmission in the host city of Tokyo. At the same time, the Delta variant of concern was gaining traction as the dominant viral strain and Japan had yet to exceed fifteen percent of its population fully vaccinated against COVID-19. To quantify the potential number of secondary cases that might arise during the Olympic Games, we performed a scenario analysis using a multitype branching process model. We considered the different contributions to transmission of Games accredited individuals, the general Tokyo population, and domestic spectators. In doing so, we demonstrate how transmission might evolve in these different groups over time, cautioning against any loosening of infection prevention protocols and supporting the decision to ban all spectators. If prevention measures were well observed, we estimated that the number of new cases among Games accredited individuals would approach zero by the end of the Games. However, if transmission was not controlled our model indicated hundreds of Games accredited individuals would become infected and daily incidence in Tokyo would reach upwards of 4,000 cases. Had domestic spectators been allowed (at 50% venue capacity), we estimated that over 250 spectators might have arrived infected to Tokyo venues, potentially generating more than 300 additional secondary infections while in Tokyo/at the Games. We also found the number of cases with infection directly attributable to hypothetical exposure during the Games was highly sensitive to the local epidemic dynamics. Therefore, reducing and maintaining transmission levels below epidemic levels using public health measures would be necessary to prevent cross-group transmission.

Modelling the impact of travel restrictions on COVID-19 cases in Newfoundland and Labrador.

In many jurisdictions, public health authorities have implemented travel restrictions to reduce coronavirus disease 2019 (COVID-19) spread. Policies that restrict travel within countries have been implemented, but the impact of these restrictions is not well known. On 4 May 2020, Newfoundland and Labrador (NL) implemented travel restrictions such that non-residents required exemptions to enter the province. We fit a stochastic epidemic model to data describing the number of active COVID-19 cases in NL from 14 March to 26 June. We predicted possible outbreaks over nine weeks, with and without the travel restrictions, and for contact rates 40-70% of pre-pandemic levels. Our results suggest that the travel restrictions reduced the mean number of clinical COVID-19 cases in NL by 92%. Furthermore, without the travel restrictions there is a substantial risk of very large outbreaks. Using epidemic modelling, we show how the NL COVID-19 outbreak could have unfolded had the travel restrictions not been implemented. Both physical distancing and travel restrictions affect the local dynamics of the epidemic. Our modelling shows that the travel restrictions are a plausible reason for the few reported COVID-19 cases in NL after 4 May.

A structured model for COVID-19 spread: modelling age and healthcare inequities.

We use a stochastic branching process model, structured by age and level of healthcare access, to look at the heterogeneous spread of COVID-19 within a population. We examine the effect of control scenarios targeted at particular groups, such as school closures or social distancing by older people. Although we currently lack detailed empirical data about contact and infection rates between age groups and groups with different levels of healthcare access within New Zealand, these scenarios illustrate how such evidence could be used to inform specific interventions. We find that an increase in the transmission rates among children from reopening schools is unlikely to significantly increase the number of cases, unless this is accompanied by a change in adult behaviour. We also find that there is a risk of undetected outbreaks occurring in communities that have low access to healthcare and that are socially isolated from more privileged communities. The greater the degree of inequity and extent of social segregation, the longer it will take before any outbreaks are detected. A well-established evidence for health inequities, particularly in accessing primary healthcare and testing, indicates that Maori and Pacific peoples are at a higher risk of undetected outbreaks in Aotearoa New Zealand. This highlights the importance of ensuring that community needs for access to healthcare, including early proactive testing, rapid contact tracing and the ability to isolate, are being met equitably. Finally, these scenarios illustrate how information concerning contact and infection rates across different demographic groups may be useful in informing specific policy interventions.

A time-modulated Hawkes process to model the spread of COVID-19 and the impact of countermeasures.

Motivated by the recent outbreak of coronavirus (COVID-19), we propose a stochastic model of epidemic temporal growth and mitigation based on a time-modulated Hawkes process. The model is sufficiently rich to incorporate specific characteristics of the novel coronavirus, to capture the impact of undetected, asymptomatic and super-diffusive individuals, and especially to take into account time-varying counter-measures and detection efforts. Yet, it is simple enough to allow scalable and efficient computation of the temporal evolution of the epidemic, and exploration of what-if scenarios. Compared to traditional compartmental models, our approach allows a more faithful description of virus specific features, such as distributions for the time spent in stages, which is crucial when the time-scale of control (e.g., mobility restrictions) is comparable to the lifetime of a single infection. We apply the model to the first and second wave of COVID-19 in Italy, shedding light onto several effects related to mobility restrictions introduced by the government, and to the effectiveness of contact tracing and mass testing performed by the national health service.

Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China.

Background: A novel coronavirus disease (COVID-19) outbreak has now spread to a number of countries worldwide. While sustained transmission chains of human-to-human transmission suggest high basic reproduction number R 0, variation in the number of secondary transmissions (often characterised by so-called superspreading events) may be large as some countries have observed fewer local transmissions than others. Methods: We quantified individual-level variation in COVID-19 transmission by applying a mathematical model to observed outbreak sizes in affected countries. We extracted the number of imported and local cases in the affected countries from the World Health Organization situation report and applied a branching process model where the number of secondary transmissions was assumed to follow a negative-binomial distribution. Results: Our model suggested a high degree of individual-level variation in the transmission of COVID-19. Within the current consensus range of R 0 (2-3), the overdispersion parameter k of a negative-binomial distribution was estimated to be around 0.1 (median estimate 0.1; 95% CrI: 0.05-0.2 for R0 = 2.5), suggesting that 80% of secondary transmissions may have been caused by a small fraction of infectious individuals (~10%). A joint estimation yielded likely ranges for R 0 and k (95% CrIs: R 0 1.4-12; k 0.04-0.2); however, the upper bound of R 0 was not well informed by the model and data, which did not notably differ from that of the prior distribution. Conclusions: Our finding of a highly-overdispersed offspring distribution highlights a potential benefit to focusing intervention efforts on superspreading. As most infected individuals do not contribute to the expansion of an epidemic, the effective reproduction number could be drastically reduced by preventing relatively rare superspreading events.

The challenges of modeling and forecasting the spread of COVID-19.

The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remains a challenge. Here, we detail three regional-scale models for forecasting and assessing the course of the pandemic. This work demonstrates the utility of parsimonious models for early-time data and provides an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies.