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.

Spreading processes with mutations over multilayer networks.

A key scientific challenge during the outbreak of novel infectious diseases is to predict how the course of the epidemic changes under countermeasures that limit interaction in the population. Most epidemiological models do not consider the role of mutations and heterogeneity in the type of contact events. However, pathogens have the capacity to mutate in response to changing environments, especially caused by the increase in population immunity to existing strains, and the emergence of new pathogen strains poses a continued threat to public health. Further, in the light of differing transmission risks in different congregate settings (e.g., schools and offices), different mitigation strategies may need to be adopted to control the spread of infection. We analyze a multilayer multistrain model by simultaneously accounting for i) pathways for mutations in the pathogen leading to the emergence of new pathogen strains, and ii) differing transmission risks in different settings, modeled as network layers. Assuming complete cross-immunity among strains, namely, recovery from any infection prevents infection with any other (an assumption that will need to be relaxed to deal with COVID-19 or influenza), we derive the key epidemiological parameters for the multilayer multistrain framework. We demonstrate that reductions to existing models that discount heterogeneity in either the strain or the network layers may lead to incorrect predictions. Our results highlight that the impact of imposing/lifting mitigation measures concerning different contact network layers (e.g., school closures or work-from-home policies) should be evaluated in connection with their effect on the likelihood of the emergence of new strains.

Some properties of branching processes with random control functions and affected by viral infectivity in random environments.

In this paper, a model of branching processes with random control functions and affected by viral infectivity in independent and identically distributed random environments is established, and the Markov property of the model and a sufficient condition for the model to be certainly extinct under some conditions are discussed. Then, the limit properties of the model are studied. Under the normalization factor {Sn:n∈N}, the normalization processes {Wˆn:n∈N} are studied, and the sufficient conditions of {Wˆn:n∈N} a.s., L1 and L2 convergence are given; A sufficient condition and a necessary condition for convergence to a nondegenerate at zero random variable are obtained. Under the normalization factor {In:n∈N}, the normalization processes {W¯n:n∈N} are studied, and the sufficient conditions of {W¯n:n∈N} a.s., and L1 convergence are obtained.

Assessing epidemic curves for evidence of superspreading.

The expected number of secondary infections arising from each index case, referred to as the reproduction or R number, is a vital summary statistic for understanding and managing epidemic diseases. There are many methods for estimating R ; however, few explicitly model heterogeneous disease reproduction, which gives rise to superspreading within the population. We propose a parsimonious discrete-time branching process model for epidemic curves that incorporates heterogeneous individual reproduction numbers. Our Bayesian approach to inference illustrates that this heterogeneity results in less certainty on estimates of the time-varying cohort reproduction number R t . We apply these methods to a COVID-19 epidemic curve for the Republic of Ireland and find support for heterogeneous disease reproduction. Our analysis allows us to estimate the expected proportion of secondary infections attributable to the most infectious proportion of the population. For example, we estimate that the 20% most infectious index cases account for approximately 75%-98% of the expected secondary infections with 95% posterior probability. In addition, we highlight that heterogeneity is a vital consideration when estimating R t .

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.

Summarizing Global SARS-CoV-2 Geographical Spread by Phylogenetic Multitype Branching Models

Using available phylogeographical data of 3585 SARS–CoV–2 genomes we attempt at providing a global picture of the virus's dynamics in terms of directly interpretable parameters. To this end we fit a hidden state multistate speciation and extinction model to a pre-estimated phylogenetic tree with information on the place of sampling of each strain. We find that even with such coarse–grained data the dominating transition rates exhibit weak similarities with the most popular, continent–level aggregated, airline passenger flight routes. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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.

Generation Of Macro-scale And Mature Lung Organoids Through Engineering Cell Microenvironment

Purpose/Objectives: <Most used lower respiratory tract models consist of cell monolayers which lack of tissue and organ level response and of in-vivo phenotype. Ex-vivo lung tissues have short viability and limited availability. Lung organoids, which recapitulates better the 3D cellular complex structures, architecture, and in-vivo function, fail to reach maturity even after 85 -185 days of culture. Therefore, these models have a limited use to study fetal lung diseases. Other lung models, consist of only one structure of the lower track, such as bronchial tubes or alveoli, but fail to recapitulate the whole organ structure. In this work, cell microenvironment was used to promote the self-organization of epithelial and mesenchymal cells into macro-structures, aiming to mimic the whole and adult lower respiratory tract model> Methodology: <Different parts of the microenvironment were considered to create a compliant matrix. Alginate-Gelatin hydrogels were used for 3D encapsulation of mesenchymal origin cells. This hydrogel provided a stiffness like the one on the lung. Base membrane zone proteins were used to induce the attachment and guidance of epithelial cells into 3D structures. The interactions between both cell types, further guided them into lung fate. The morphology of resulting organoids was analyzed using immunostaining and confocal microscopy, LSM710, with the purpose of evaluate polarization, protein markers, and different cell populations. Quantitative PCR was performed to evaluate and compare the expression of lung fate genes with traditional cell monocultures.> Results: <The engineered microenvironment and protocol development done in this work resulted in macro-scale structures, in which branching morphogenesis occurred at day 21. Different structures were identified in the organoid including bronchial tube, bronchioles, and alveoli. Polarization of the organoids was confirmed by visualization of E-cadherin, and ZO-1. Expression of Surfactant Protein B and C into the organoids confirmed the presence of alveolar type II cells, which are only present in the later development stage. Surfactant Protein B, Transmembrane protease, serine 2, TMPRSS-2, and Angiotensin-converting enzyme 2, ACE2 were found to be significantly higher expressed into the organoids in comparison with traditional epithelial cells monolayers.> Conclusion/Significance: <Growth factors are normally used to induce the fate of stem cells into lung organoids;however, these fail to reach maturity. Here, we developed a new methodology to induce the formation of the organoids based on the cell microenvironment. The resulting organoids require less time for development. The initial stage of adult cells can be modulated through culture conditions induce a 3D structure like the adult lung. As such, these organoids have the potential to be used for modeling adult diseases and to develop specific models from patient cells, which is one step forward to personalized medicine. SFTPB is one of the main proteins which facilitates the breathing process. Its high expression into our model may indicate that breathing occurs into our lung organoids. The higher expression of TMPRSS-2 and ACE2 into the organoids has a major significance in the field of virology since both proteins are the mainly entrance of SARS-CoV-2, and influenza H1N1.>.

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.

What is the future of the bank branch in the midst of the 4.0 industrial revolution? Answers from Vietnam

Digital channels (websites, bank apps, mobile banking) are incrementally improving as a result of technology innovation and changing customer behavior. The unprecedented Covid-19 pandemic has just added to this trend by urging people to work and make all financial transaction through the Internet. In this context, the question arises of whether banks should revive their physical branches or take the opportunity to shift to mainly digital platform? This research focuses on the branch network trend of Vietnamese commercial banks during the period 2012–2019 to answer the question, what is the contribution of bank branch networks to the banks’ profits. Panel data from 22 largest Vietnamese commercial banks in terms of owners’ capital has been analyzed, using Random Effect Model (REM) regression models. The results show that Vietnamese banks are still expanding their branch networks, despite the fact that bank customers are increasingly engaging in digital bank services. The number of branches has a positive correlation with the banks’ profits, although there is a disparity between large network banks and the rest. The research suggests some implications that can help optimize the branch network in the context of digitalization in an emerging market. © Thuy Thu Pham, Hien Thi Thu Hoang, Ha Thi Thu Do, 2022.

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.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number.

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

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.