To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic

Abstract
 
 Face mask use by the general public for limiting the spread of the COVID-19 pandemic is controversial, though increasingly recommended, and the potential of this intervention is not well understood. We develop a compartmental model for assessing the community-wide impact of mask use by the general, asymptomatic public, a portion of which may be asymptomatically infectious. Model simulations, using data relevant to COVID-19 dynamics in the US states of New York and Washington, suggest that broad adoption of even relatively ineffective face masks may meaningfully reduce community transmission of COVID-19 and decrease peak hospitalizations and deaths. Moreover, mask use decreases the effective transmission rate in nearly linear proportion to the product of mask effectiveness (as a fraction of potentially infectious contacts blocked) and coverage rate (as a fraction of the general population), while the impact on epidemiologic outcomes (death, hospitalizations) is highly nonlinear, indicating masks could synergize with other non-pharmaceutical measures. Notably, masks are found to be useful with respect to both preventing illness in healthy persons and preventing asymptomatic transmission. Hypothetical mask adoption scenarios, for Washington and New York state, suggest that immediate near universal (80%) adoption of moderately (50%) effective masks could prevent on the order of 17–45% of projected deaths over two months in New York, while decreasing the peak daily death rate by 34–58%, absent other changes in epidemic dynamics. Even very weak masks (20% effective) can still be useful if the underlying transmission rate is relatively low or decreasing: In Washington, where baseline transmission is much less intense, 80% adoption of such masks could reduce mortality by 24–65% (and peak deaths 15–69%), compared to 2–9% mortality reduction in New York (peak death reduction 9–18%). Our results suggest use of face masks by the general public is potentially of high value in curtailing community transmission and the burden of the pandemic. The community-wide benefits are likely to be greatest when face masks are used in conjunction with other non-pharmaceutical practices (such as social-distancing), and when adoption is nearly universal (nation-wide) and compliance is high.

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title: The Effect of Mask Use on the Spread of Influenza During a Pandemic
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title: A cluster randomised trial of cloth masks compared with medical masks in healthcare workers
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title: Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study
abstract: Summary
 
 Background
 Since Dec 31, 2019, the Chinese city of Wuhan has reported an outbreak of atypical pneumonia caused by the 2019 novel coronavirus (2019-nCoV). Cases have been exported to other Chinese cities, as well as internationally, threatening to trigger a global outbreak. Here, we provide an estimate of the size of the epidemic in Wuhan on the basis of the number of cases exported from Wuhan to cities outside mainland China and forecast the extent of the domestic and global public health risks of epidemics, accounting for social and non-pharmaceutical prevention interventions.
 
 
 Methods
 We used data from Dec 31, 2019,  2020, on the number of cases exported from Wuhan internationally (known days of symptom onset from Dec 25, 2019, to Jan 19, 2020) to infer the number of infections in Wuhan from Dec 1, 2019, to Jan 25, 2020. Cases exported domestically were then estimated. We forecasted the national and global spread of 2019-nCoV, accounting for the effect of the metropolitan-wide quarantine of Wuhan and surrounding cities, which began Jan 23–24, 2020. We used data on monthly flight bookings from the Official Aviation Guide and data on human mobility across more than 300 prefecture-level cities in mainland China from the Tencent database. Data on confirmed cases were obtained from the reports published by the Chinese Center for Disease Control and Prevention. Serial interval estimates were based on previous studies of severe acute respiratory syndrome coronavirus (SARS-CoV). A susceptible-exposed-infectious-recovered metapopulation model was used to simulate the epidemics across all major cities in China. The basic reproductive number was estimated using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credibile interval (CrI).
 
 
 Findings
 In our baseline scenario, we estimated that the basic reproductive number for 2019-nCoV was 2·68 (95% CrI 2·47–2·86) and that 75 815 individuals (95% CrI 37 304–130 330) have been infected in Wuhan as of Jan 25, 2020. The epidemic doubling time was 6·4 days (95% CrI 5·8–7·1). We estimated that in the baseline scenario, Chongqing, Beijing, Shanghai, Guangzhou, and Shenzhen had imported 461 (95% CrI 227–805), 113 (57–193), 98 (49–168), 111 (56–191), and 80 (40–139) infections from Wuhan, respectively. If the transmissibility of 2019-nCoV were similar everywhere domestically and over time, we inferred that epidemics are already growing exponentially in multiple major cities of China with a lag time behind the Wuhan outbreak of about 1–2 weeks.
 
 
 Interpretation
 Given that 2019-nCoV is no longer contained within Wuhan, other major Chinese cities are probably sustaining localised outbreaks. Large cities overseas with close transport links to China could also become outbreak epicentres, unless substantial public health interventions at both the population and personal levels are implemented immediately. Independent self-sustaining outbreaks in major cities globally could become inevitable because of substantial exportation of presymptomatic cases and in the absence of large-scale public health interventions. Preparedness plans and mitigation interventions should be readied for quick deployment globally.
 
 
 Funding
 Health and Medical Research Fund (Hong Kong, China).

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title: A simple Stochastic SIR model for COVID 19 Infection Dynamics for Karnataka: Learning from Europe
abstract: In this short note we model the region-wise trends of the evolution to COVID-19 infections using a stochastic SIR model. The SIR dynamics are expressed using \textit{Ito-stochastic differential equations}. We first derive the parameters of the model from the available daily data from European regions based on a 24-day history of infections, recoveries and deaths. The derived parameters have been aggregated to project future trends for the Indian subcontinent, which is currently at an early stage in the infection cycle. The projections are meant to serve as a guideline for strategizing the socio-political counter measures to mitigate COVID-19.

title: Inferring COVID-19 spreading rates and potential change points for case number forecasts
abstract: As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A main challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change as first governmental intervention measures are showing an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. For the case of COVID-19 spreading in Germany, we detect change points in the effective growth rate which correlate well with the times of publicly announced interventions.Thereby, we can (a) quantify the effects of recent governmental measures to mitigating the disease spread, and (b) incorporate analogue change points to forecast future scenarios and case numbers.Our code is freely available and can be readily adapted to any country or region.

title: Statistics based predictions of coronavirus 2019-nCoV spreading in mainland China
abstract: The epidemic outbreak cased by coronavirus 2019-nCoV is of great interest to researches because of the high rate of spread of the infection and the significant number of fatalities. A detailed scientific analysis of the phenomenon is yet to come, but the public is already interested in the questions of the duration of the epidemic, the expected number of patients and deaths. For long time predictions, the complicated mathematical models are necessary which need many efforts for unknown parameters identification and calculations. In this article, some preliminary estimates will be presented.  Since the reliable long time data are available only for mainland China, we will try to predict the epidemic characteristics only in this area. We will estimate some of the epidemic characteristics and present the most reliable dependences for victim numbers, infected and removed persons versus time.  In this study we use the known SIR model for the dynamics of an epidemic, the known exact solution of the linear equations and statistical approach developed before for investigation of the children disease, which occurred in Chernivtsi (Ukraine) in 1988-1989.  The optimal values of the SIR model parameters were identified with the use of statistical approach. The numbers of infected, susceptible and removed persons versus time were predicted.  Simple mathematical model was used to predict the characteristics of the epidemic caused by coronavirus 2019-nCoV in mainland China. The further research should focus on updating the predictions with the use of fresh data and using more complicated mathematical models.

title: COVID-19 infection and recovery in various countries: Modeling the dynamics and evaluating the non-pharmaceutical mitigation scenarios.
abstract: The coronavirus disease 2019 (COVID-19) pandemic radically impacts our lives, while the transmission/infection and recovery dynamics of COVID-19 remain obscure. A time-dependent Susceptible, Exposed, Infectious, and Recovered (SEIR) model was proposed and applied to fit and then predict the time series of COVID-19 evolution observed in the last three months (till 3/22/2020) in various provinces and metropolises in China. The model results revealed the space dependent transmission/infection rate and the significant spatiotemporal variation in the recovery rate, likely due to the continuous improvement of screening techniques and public hospital systems, as well as full city lockdowns in China. The validated SEIR model was then applied to predict COVID-19 evolution in United States, Italy, Japan, and South Korea which have responded differently to monitoring and mitigating COVID-19 so far, although these predictions contain high uncertainty due to the intrinsic change of the maximum infected population and the infection/recovery rates within the different countries. In addition, a stochastic model based on the random walk particle tracking scheme, analogous to a mixing-limited bimolecular reaction model, was developed to evaluate non-pharmaceutical strategies to mitigate COVID-19 spread. Preliminary tests using the stochastic model showed that self-quarantine may not be as efficient as strict social distancing in slowing COVID-19 spread, if not all of the infected people can be promptly diagnosed and quarantined.

title: Controlling the Transmission Dynamics of COVID-19
abstract: The outbreak of COVID-19 caused by SARS-CoV-2 in Wuhan and other cities in China in 2019 has become a global pandemic as declared by World Health Organization (WHO) in the first quarter of 2020 . The delay in diagnosis, limited hospital resources and other treatment resources leads to rapid spread of COVID-19. In this article, we consider an optimal control COVID-19 transmission model and assess the impact of some control measures that can lead to the reduction of exposed and infectious individuals in the population. We investigate three control strategies for this deadly infectious disease using personal protection, treatment with early diagnosis, treatment with delay diagnosis and spraying of virus in the environment as time-dependent control functions in our dynamical model to curb the disease spread.

title: Covid-19 spread: Reproduction of data and prediction using a SIR model on Euclidean network.
abstract: We study the datafor the cumulative as well as daily number of cases in the Covid-19 outbreak in China. The cumulative data can be fit to an empirical form obtained from a Susceptible-Infected-Removed (SIR) model studied on an Euclidean network previously. Plotting the number of cases against the distance from the epicenter for both China and Italy, we find an approximate power law variation with an exponent $\sim 1.85$ showing strongly that the spatial dependence plays a key role, a factor included in the model. We report here that the SIR model on the Eucledean network can reproduce with a high accuracy the data for China for given parameter values, and can also predict when the epidemic, at least locally, can be expected to be over.

title: Modelling transmission and control of the COVID-19 pandemic in Australia
abstract: There is a continuing debate on relative benefits of various mitigation and suppression strategies aimed to control the spread of COVID-19. Here we report the results of agent-based modelling using a fine-grained computational simulation of the ongoing COVID-19 pandemic in Australia. This model is calibrated to match key characteristics of COVID-19 transmission. An important calibration outcome is the age-dependent fraction of symptomatic cases, with this fraction for children found to be one-fifth of such fraction for adults. We apply the model to compare several intervention strategies, including restrictions on international air travel, case isolation, home quarantine, social distancing with varying levels of compliance, and school closures. School closures are not found to bring decisive benefits unless coupled with high level of social distancing compliance. We report several trade-offs, and an important transition across the levels of social distancing compliance, in the range between 70% and 80% levels, with compliance at the 90% level found to control the disease within 13–14 weeks, when coupled with effective case isolation and international travel restrictions.

title: Why is it difficult to accurately predict the COVID-19 epidemic?
abstract: Abstract
 
 Since the COVID-19 outbreak in Wuhan City in December of 2019, numerous model predictions on the COVID-19 epidemics in Wuhan and other parts of China have been reported. These model predictions have shown a wide range of variations. In our study, we demonstrate that nonidentifiability in model calibrations using the confirmed-case data is the main reason for such wide variations. Using the Akaike Information Criterion (AIC) for model selection, we show that an SIR model performs much better than an SEIR model in representing the information contained in the confirmed-case data. This indicates that predictions using more complex models may not be more reliable compared to using a simpler model. We present our model predictions for the COVID-19 epidemic in Wuhan after the lockdown and quarantine of the city on January 23, 2020. We also report our results of modeling the impacts of the strict quarantine measures undertaken in the city after February 7 on the time course of the epidemic, and modeling the potential of a second outbreak after the return-to-work in the city.

title: Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study
abstract: Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described.
               
               
                  Methods
                  In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death.
               
               
                  Findings
                  191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p<0·0001), and d-dimer greater than 1 μg/mL (18·42, 2·64–128·55; p=0·0033) on admission. Median duration of viral shedding was 20·0 days (IQR 17·0–24·0) in survivors, but SARS-CoV-2 was detectable until death in non-survivors. The longest observed duration of viral shedding in survivors was 37 days.
               
               
                  Interpretation
                  The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future.
               
               
                  Funding
                  Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.

title: Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions
abstract: Since first identified, the epidemic scale of the recently emerged novel coronavirus (2019-nCoV) in Wuhan, China, has increased rapidly, with cases arising across China and other countries and regions. using a transmission model, we estimate a basic reproductive number of 3.11 (95%CI, 2.39-4.13); 58-76% of transmissions must be prevented to stop increasing; Wuhan case ascertainment of 5.0% (3.6-7.4); 21022 (11090-33490) total infections in Wuhan 1 to 22 January.