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      Scientific and ethical basis for social-distancing interventions against COVID-19

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      The Lancet. Infectious Diseases
      Elsevier Ltd.

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          Abstract

          On Dec 31, 2019, the WHO China Country Office received notice of a cluster of pneumonia cases of unknown aetiology in the Chinese city of Wuhan, Hubei province. 1 The incidence of coronavirus disease 2019 (COVID-19; caused by severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) has since risen exponentially, now affecting all WHO regions. The number of cases reported to date is likely to represent an underestimation of the true burden as a result of shortcomings in surveillance and diagnostic capacity affecting case ascertainment in both high-resource and low-resource settings. 2 By all scientifically meaningful criteria, the world is undergoing a COVID-19 pandemic. In the absence of any pharmaceutical intervention, the only strategy against COVID-19 is to reduce mixing of susceptible and infectious people through early ascertainment of cases or reduction of contact. In The Lancet Infectious Diseases, Joel Koo and colleagues 3 assessed the potential effect of such social distancing interventions on SARS-CoV-2 spread and COVID-19 burden in Singapore. The context is worthy of study, since Singapore was among the first settings to report imported cases, and has so far succeeded in preventing community spread. During the 2003 severe acute respiratory syndrome coronavirus (SARS-CoV) outbreak in Singapore, numerous non-pharmaceutical interventions were implemented successfully, including effective triage and infection control measures in health-care settings, isolation and quarantine of patients with SARS and their contacts, and mass screening of school-aged children for febrile illness. 4 Each of these measures represented an escalation of typical public health action. However, the scale and disruptive impact of these interventions were small compared with the measures that have been implemented in China in response to COVID-19, including closure of schools, workplaces, roads, and transit systems; cancellation of public gatherings; mandatory quarantine of uninfected people without known exposure to SARS-CoV-2; and large-scale electronic surveillance.5, 6 Although these actions have been praised by WHO, 5 the possibility of imposing similar measures in other countries raises important questions. Populations for whom social-distancing interventions have been implemented require and deserve assurance that the decision to enact these measures is informed by the best attainable evidence. For a novel pathogen such as SARS-CoV-2, mathematical modelling of transmission under differing scenarios is the only viable and timely method to generate such evidence. Koo and colleagues 3 adapted an existing influenza epidemic simulation model 7 using granular data on the composition and behaviour of the population of Singapore to assess the potential consequences of specific social-distancing interventions on the transmission dynamics of SARS-CoV-2. The authors considered three infectivity scenarios (basic reproduction number [R 0] of 1·5, 2·0, or 2·5) and assumed between 7·5% and 50·0% of infections were asymptomatic. The interventions were quarantine with or without school closure and workplace distancing (whereby 50% of workers telecommute). Although the complexity of the model makes it difficult to understand the impact of each parameter, the primary conclusions were robust to sensitivity analyses. The combined intervention, in which quarantine, school closure, and workplace distancing were implemented, was the most effective: compared with the baseline scenario of no interventions, the combined intervention reduced the estimated median number of infections by 99·3% (IQR 92·6–99·9) when R 0 was 1·5, by 93·0% (81·5–99·7) when R 0 was 2·0, and by 78·2% (59·0–94·4) when R 0 was 2·5. The observation that the greatest reduction in COVID-19 cases was achieved under the combined intervention is not surprising. However, the assessment of the additional benefit of each intervention, when implemented in combination, offers valuable insight. Since each approach individually will result in considerable societal disruption, it is important to understand the extent of intervention needed to reduce transmission and disease burden. New findings emerge daily about transmission routes and the clinical profile of SARS-CoV-2, including the substantially underestimated rate of infection among children. 8 The implications of such findings with regard to the authors' conclusions about school closure remain unclear. Additionally, reproductive number estimates for Singapore are not yet available. The authors estimated that 7·5% of infections are clinically asymptomatic, although data on the proportion of infections that are asymptomatic are scarce; as shown by Koo and colleagues in sensitivity analyses with higher asymptomatic proportions, this value will influence the effectiveness of social-distancing interventions. Additionally, the analysis assumes high compliance of the general population, which is not guaranteed. Although the scientific basis for these interventions might be robust, ethical considerations are multifaceted. 9 Importantly, political leaders must enact quarantine and social-distancing policies that do not bias against any population group. The legacies of social and economic injustices perpetrated in the name of public health have lasting repercussions. 10 Interventions might pose risks of reduced income and even job loss, disproportionately affecting the most disadvantaged populations: policies to lessen such risks are urgently needed. Special attention should be given to protections for vulnerable populations, such as homeless, incarcerated, older, or disabled individuals, and undocumented migrants. Similarly, exceptions might be necessary for certain groups, including people who are reliant on ongoing medical treatment. The effectiveness and societal impact of quarantine and social distancing will depend on the credibility of public health authorities, political leaders, and institutions. It is important that policy makers maintain the public's trust through use of evidence-based interventions and fully transparent, fact-based communication. © 2020 Caia Image/Science Photo Library 2020 Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

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          Interventions to mitigate early spread of SARS-CoV-2 in Singapore: a modelling study

          Summary Background Since the coronavirus disease 2019 outbreak began in the Chinese city of Wuhan on Dec 31, 2019, 68 imported cases and 175 locally acquired infections have been reported in Singapore. We aimed to investigate options for early intervention in Singapore should local containment (eg, preventing disease spread through contact tracing efforts) be unsuccessful. Methods We adapted an influenza epidemic simulation model to estimate the likelihood of human-to-human transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in a simulated Singaporean population. Using this model, we estimated the cumulative number of SARS-CoV-2 infections at 80 days, after detection of 100 cases of community transmission, under three infectivity scenarios (basic reproduction number [R 0] of 1·5, 2·0, or 2·5) and assuming 7·5% of infections are asymptomatic. We first ran the model assuming no intervention was in place (baseline scenario), and then assessed the effect of four intervention scenarios compared with a baseline scenario on the size and progression of the outbreak for each R 0 value. These scenarios included isolation measures for infected individuals and quarantining of family members (hereafter referred to as quarantine); quarantine plus school closure; quarantine plus workplace distancing; and quarantine, school closure, and workplace distancing (hereafter referred to as the combined intervention). We also did sensitivity analyses by altering the asymptomatic fraction of infections (22·7%, 30·0%, 40·0%, and 50·0%) to compare outbreak sizes under the same control measures. Findings For the baseline scenario, when R 0 was 1·5, the median cumulative number of infections at day 80 was 279 000 (IQR 245 000–320 000), corresponding to 7·4% (IQR 6·5–8·5) of the resident population of Singapore. The median number of infections increased with higher infectivity: 727 000 cases (670 000–776 000) when R 0 was 2·0, corresponding to 19·3% (17·8–20·6) of the Singaporean population, and 1 207 000 cases (1 164 000–1 249 000) when R 0 was 2·5, corresponding to 32% (30·9–33·1) of the Singaporean population. Compared with the baseline scenario, the combined intervention was the most effective, reducing the estimated median number of infections by 99·3% (IQR 92·6–99·9) when R 0 was 1·5, by 93·0% (81·5–99·7) when R 0 was 2·0, and by 78·2% (59·0 −94·4) when R 0 was 2·5. Assuming increasing asymptomatic fractions up to 50·0%, up to 277 000 infections were estimated to occur at day 80 with the combined intervention relative to 1800 for the baseline at R 0 of 1·5. Interpretation Implementing the combined intervention of quarantining infected individuals and their family members, workplace distancing, and school closure once community transmission has been detected could substantially reduce the number of SARS-CoV-2 infections. We therefore recommend immediate deployment of this strategy if local secondary transmission is confirmed within Singapore. However, quarantine and workplace distancing should be prioritised over school closure because at this early stage, symptomatic children have higher withdrawal rates from school than do symptomatic adults from work. At higher asymptomatic proportions, intervention effectiveness might be substantially reduced requiring the need for effective case management and treatments, and preventive measures such as vaccines. Funding Singapore Ministry of Health, Singapore Population Health Improvement Centre.
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            An ethics framework for public health.

            Nancy Kass (2001)
            More than 100 years ago, public health began as an organized discipline, its purpose being to improve the health of populations rather than of individuals. Given its population-based focus, however, public health perennially faces dilemmas concerning the appropriate extent of its reach and whether its activities infringe on individual liberties in ethically troublesome ways. In this article a framework for ethics analysis of public health programs is proposed. To advance traditional public health goals while maximizing individual liberties and furthering social justice, public health interventions should reduce morbidity or mortality; data must substantiate that a program (or the series of programs of which a program is a part) will reduce morbidity or mortality; burdens of the program must be identified and minimized; the program must be implemented fairly and must, at times, minimize preexisting social injustices; and fair procedures must be used to determine which burdens are acceptable to a community.
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              Is Open Access

              FluTE, a Publicly Available Stochastic Influenza Epidemic Simulation Model

              Introduction Mathematical and computer models of epidemics have contributed to our understanding of the spread of infectious disease and the measures needed to contain or mitigate them [1]–[9]. Detailed computer simulations will play an important role in evaluating containment and mitigation strategies for future epidemics [8]. Although many simulation models have been described in the literature, few are publicly available. Releasing the source code of models would allow others to evaluate the quality of the simulation, replicate results, and alter and improve the model. We have released the source code for a new stochastic model of influenza epidemics, FluTE. FluTE is an individual-based model capable of simulating the spread of influenza across major metropolitan areas or the continental United States. The model's structure is based on previously published work [3],[6], but FluTE incorporates a more sophisticated natural history of influenza, more realistic intervention strategies, and can run on a personal computer. Here, we describe the new model and illustrate how it can be used to study the dynamics of an epidemic and to investigate the population-level effects of interventions. Model FluTE is an individual-based simulation model of influenza epidemics. In this section, we describe the model's community structure, natural history of influenza, and simulated interventions. Briefly, all individuals in the model are members of social mixing groups, within which influenza is transmitted by random mixing. The model can simulate several intervention strategies, and these can either change the transmission characteristics of influenza (e.g., vaccination) or change the contact probabilities between individuals (e.g., social distancing). Interventions can occur before the epidemic or in response to an ongoing epidemic. Community structure and social contacts The simulation creates synthetic populations based on typical American communities. The population is divided into census tracts, and each tract is subdivided into communities of 500–3000 individuals based on earlier models [6],[10]. Each community is populated by randomly generated households of size 1–7 using the US-wide family size distribution from the 2000 Census (Table 1). The household is the closest social mixing group, within which contacts between individuals occur most frequently and thus influenza is transmitted most often. The population is organized as a hierarchy of increasingly large but less intimate mixing groups, from the household cluster (sets of four socially close households), neighborhoods (1/4 of a community), and the community. Although the model results are not sensitive to the exact size of these groups, including such groups creates a realistic contact network for disease transmission [11]. At night, everyone can make contact with other individuals in their families, household clusters, home neighborhoods, and home communities. In the daytime, individuals might interact with additional groups. During the day, most children attend school or a playgroup, where there is a relatively high probability of transmission. Preschool-age children usually belong to either a playgroup of four children or a neighborhood preschool, which typically has 14 students. Each community has mixing groups that represent two elementary schools, one middle school, and one high school, which typically have 79, 128, and 155 students, respectively. 10.1371/journal.pcbi.1000656.t001 Table 1 Frequency of household sizes. Frequency Family size 33% single adult 34% two people (two adults or a parent and child) 13% two adults, one child 10% two adults, two children 7% two adults, three children 2% two adults, four children 1% two adults, five children Data from [6]. Most working-age adults (about 72% of 19–64 year-olds) are employed. Employment rates are determined on a tract-by-tract basis using data from the US Census 2000's Summary File 3, table PCT35. Employed individuals often work outside of their home communities. Each employed individual is assigned to work in a destination census tract based on commuting data taken from Part 3 of the Census Transportation Planning Package (http://www.fhwa.dot.gov/ctpp/dataprod.htm), which provides information on the home and destination census tracts of workers in the United States. We eliminated commutes over 100 miles from the data as in [6] because many of these trips represent sporadic long-distance travel rather than daily commutes. Working individuals are assigned to communities and neighborhoods within their destination tracts to simulate casual community contacts during the day, and a work group of about 20 people to represent their close contacts at the workplace. Unemployed individuals remain in their home communities and do not have close daytime contacts except with members of their households who are not employed or enrolled in school. Individuals can engage in short-term, long-distance domestic travel to represent vacations and other trips. Travel in our model is based on the implementation in [6], which uses data from the 1995 American Travel Survey data available from the U. S. Department of Transportation, Bureau of Transportation Statistics (http://www.bts.gov/publications/national_transportation_statistics/). Each day, an individual has a fixed probability of starting a trip based on an age-specific probability of traveling: 0.0023 for 0–4 year olds, 0.0023 for 5–18, 0.0050 for 19–29, 0.0053 for 30–64, and 0.0028 for 65 and older. The traveler will stay at the destination for 0–11 nights, with 23.9% of trips lasting for a single day (and no nights), 50.2% including 1–3 nights away, 18.5% including 4–7 nights away, and 7.4% for 8–11 nights. We do not include differences in travel frequency or duration during different times of the year (e.g., summer and holiday trips). The destination is a randomly selected census tract, in which a random community, neighborhood, and workplace (if the traveler is between 19 and 64 years old) are assigned to be the traveler's mixing groups. A random member of this community is assigned to be the traveler's contact person, and at night the traveler will behave as if he/she belongs to the contact's household, household cluster, and neighborhood. The traveler may withdraw to this household if ill. The exact implementation of short-term, long-distance travel is not important, but some long-distance travel is required in large populations for the epidemic to spread in a realistic manner. For simulations of smaller regions, such as a single county, there is no need to include long-distance travel. New infected individuals are introduced to a simulation by infecting randomly selected people. This epidemic seeding process can occur once at the beginning of a simulation or daily. In addition, one can simulate an epidemic that is seeded from international travelers. In this scenario, randomly selected individuals in the counties with one of the United States' 15 busiest international airports are infected each day, proportional to the daily traffic of these airports (see Table 2). 10.1371/journal.pcbi.1000656.t002 Table 2 International traffic to the 15 US airports built into FluTE. Airport City Passengers/year JFK New York, NY 21,842,544 LAX Los Angeles, CA 17,019,166 MIA Miami, FL 15,509,279 ORD Chicago, IL 11375367 EWR Newark, NJ 10,812,993 ATL Atlanta, GA 9,166,055 SFO San Francisco, CA 8,648,219 IAH Houston, TX 7,627,942 IAD Washington, DC 5,893,142 DFW Dallas/Ft. Worth, TX 4,872,207 DTW Detroit, MI 3,887,481 PHL Philadelphia, PA 3,734,127 BOS Boston, MA 3,673,748 FLL Fort Lauderdale, FL 3,062,384 SEA Seattle, WA 2,766,576 Data from [45]. Influenza natural history and transmission The current modeling of the natural history of influenza is as follows: An individual is infectious for six days starting the day after becoming infected. The individual's infectiousness is proportional to the log of the daily viral titers taken from a randomly chosen one of the six experimentally infected patients described in [12],[13] (Figure 1). An individual is asymptomatic during the incubation period, which lasts from one, two, or three days (with 30%, 50%, and 20% probabilities, respectively). After incubation, the individual has a 67% chance of becoming symptomatic [14],[15]. Symptomatic individuals are twice as infectious as asymptomatic people and may withdraw to the home after 0 to 2 days [16] (with probabilities summarized in Table 3). People who withdraw interact only with their households. Six days after infection, an individual recovers and is no longer susceptible. 10.1371/journal.pcbi.1000656.g001 Figure 1 The natural history of influenza of simulated individuals in FLuTE. When a susceptible individual is infected (at time ), that person will be infectious for six days with infectiousness proportional to his or her viral load. The six possible viral load trajectories are plotted. Most individuals become symptomatic, which occurs after a 1, 2, or 3 day incubation period. Symptomatic individuals are twice as infectious as asymptomatic individuals (i.e., infectiousness is proportional to twice the viral load). Individuals recover six days after infection and are immune. 10.1371/journal.pcbi.1000656.t003 Table 3 Probabilities that an individual will withdraw to the home 0, 1, or 2 days after becoming symptomatic. Age group 0 days 1 day 2 days Preschool-age children 0.304 0.575 0.324 School-age children 0.203 0.498 0.375 Adults 0.100 0.333 0.167 Data from [16]. The simulation runs in discrete time, with two time steps per simulated day to represent daytime and nighttime social interactions. The contact probability of two individuals in the same mixing group is the probability that they will have sufficient contact for transmission during a time step. Contact probabilities of individuals within families were tuned so that the simulated household secondary attack rates match estimates from [17] (Table 4). Contact probabilities within other mixing groups were tuned so that the final age-specific illness attack rates were similar to past influenza pandemics (Table 5), particularly Asian A (H2N2) and 2009 novel influenza A(H1N1) influenza, and the percentage of transmissions that can be attributed to each mixing group matched those in [6], [18]–[20], although these values depend on the transmissibility ( ) of the disease (Table 6). These contact probabilities are in general agreement with other simulation models [8] and with a recent study of physical contacts between individuals [21]. Contact probabilities for all types of mixing groups are summarized in Table 7. 10.1371/journal.pcbi.1000656.t004 Table 4 Estimates of secondary household attack rates from [17] and illness attack rates using FluTE, stratified by the ages of the index and secondary cases. Exposed Addy 1991 simulated ( ) child adult child adult Infectious child 29.0% 14.2% 28.6% 13.5% adult 10.3% 15.6% 9.3% 16.2% 10.1371/journal.pcbi.1000656.t005 Table 5 Age-specific influenza illness attack rates in past influenza epidemics (from [46]) and in a simulation of metropolitan Seattle. Age group Asian A (H2N2) Hong Kong A (H3N2) Age group simulated 1957–8 1968–9 ( ) Pre-school children 35% 34% 0–4 years 38% School-age children 55% 35% 5–18 years 53% Young adults 25% 35% 19–29 years 26% Middle adults 20% 32% 30–64 years 28% Old adults 14% 31% 65 years 23% Overall 31% 34% 33% 10.1371/journal.pcbi.1000656.t006 Table 6 Major sources of influenza transmission in simulations of metropolitan Seattle. Mixing group Fraction of transmissions household 32% 31% 29% schools/daycares 30% 24% 21% workplace 10% 13% 15% neighborhood/community 18% 21% 23% 10.1371/journal.pcbi.1000656.t007 Table 7 Person-to-person contact probabilities for all social mixing groups in FluTE. Exposed child 0–4 child 5–18 adult 19–29 adult 30–64 adult 65+ Family, infectious is child 0.8 0.8 0.35 0.35 0.35 Family, infectious is adult 0.25 0.25 0.4 0.4 0.4 Household cluster, infectious is child 0.08 0.08 0.035 0.035 0.035 Household cluster, infectious is adult 0.025 0.025 0.04 0.04 0.04 Neighborhood 0.0000435 0.0001305 0.000348 0.000348 0.000696 Community 0.0000109 0.0000326 0.000087 0.000087 0.000174 Workplace 0.05 0.05 Playgroup 0.28 Daycare 0.12 Elementary school 0.0348 Middle school 0.03 High school 0.0252 Transmission probabilities in the simulation are adjusted by multiplying all contact probabilities by a scalar, , to obtain the desired , the basic reproductive number, which is defined as the average number of secondary infections from a typical infected individual in a fully susceptible population [22]. To derive the relationship between and , we infected a single randomly selected person in an otherwise fully susceptible 2000-person community with a 74% working-age adult employment rate and counted the number of individuals that person infected, repeating this procedure 1,000 times for several values of . The relationship between the average number of secondary cases was approximately linear for a biologically plausible range of values: (Figure 2). However, the average number of secondary cases was higher when the index case was a child because children tend to infect more individuals (and become infected more often) than adults. Therefore, in a procedure borrowed from [6], we measured the age distribution of secondary cases when the index case was randomly selected and used this distribution to weight the contribution from the various age groups to the calculation to define . The definition of applies to a population with no pre-existing immunity, an assumption that may be violated for seasonal influenza. One can use the model to simulate seasonal influenza epidemics by substituting with the desired , the average number of people a typical infected case infects in a population with pre-existing immunity. 10.1371/journal.pcbi.1000656.g002 Figure 2 Influenza transmission properties in the simulation. (A) Observed secondary cases vs by the age of the index case and the weighted average. (B) Average case generation time vs . The simulated case generation time, or the time between infection of an individual and the transmission to susceptibles, was 3.4 days for a wide range of in a fully susceptible population (Figure 2B). This is consistent with other estimates for seasonal and pandemic influenza [20],[23]. Simulated interventions The primary pharmaceutical intervention is vaccination. Vaccinated individuals in the simulation have a reduced probability of becoming infected (VE S ), of becoming ill given infection (VE P ), and of transmitting infection (VE I ) [24]. In the model, these efficacy parameters are implemented by multiplying the transmission probability per time step by (1−VE S ) if the susceptible individual is vaccinated and by (1−VE I ) if the infectious individual is vaccinated. The probability of vaccinated individuals becoming symptomatic (ill) after they are infected is the baseline probability (67%) multiplied by (1−VE P ). Vaccines do not reach full efficacy immediately – their protective effects may gradually increase over several weeks. The default behavior in the model is that the vaccine takes two weeks to reach maximum efficacy, with the efficacy increasing exponentially starting the day after the vaccination. Because of the delay in reaching maximum efficacy, it may be necessary to vaccinate the population early. In the simulation, vaccines can be administered at least four weeks before the epidemic (i.e., pre-vaccination), during the epidemic (reactive), or one dose can be administered at least three weeks before the epidemic and the boost can be administered reactively (prime-boost). Antiviral agents (neuraminidase inhibitors) can be used for treatment of cases and for prophylaxis of susceptibles. A single course of antiviral agents is enough for 10 days of prophylaxis or 5 days of treatment. In the model, 5% of individuals taking antiviral agents prophylactically stop after 2 days and 5% taking them for treatment stop after 1 day [19]. As with vaccines, individuals taking antiviral agents can have reduced susceptibility (AVE S ), probability of becoming ill given infection (AVE P ), and transmitting infection (AVE I ). However, unlike vaccines, the protective effects of the antiviral agents last only as long as they are being taken (5 to 10 days). When a case is ascertained, the individual is treated with antiviral agents, and that individual's household members will also each be given a course if household targeted antiviral prophylaxis (HHTAP) is in effect. Several non-pharmaceutical interventions can be simulated in the model. School closures are simulated by eliminating school group contacts (including preschools and daycares but not playgroups) for those enrolled in school, but adding daytime contacts with other household members not in school or at work and doubling their daytime neighborhood and community contact probabilities to account for their non-school activities. Schools can be closed when cases are ascertained in communities or in the schools, and they can be closed for a fixed number of days or for the duration of the simulation. During an epidemic, individuals may be requested to stay at home if they become ill. When simulating isolation of cases, individuals withdraw to the home one day after becoming symptomatic (with a certain probability to represent the compliance probability). This will eliminate any daytime social contacts that they have other than with household members who are not working or at school. We simulate a liberal leave policy in a similar manner: employed individuals withdraw to the home with a pre-set compliance probability for one week one day after becoming symptomatic. During an epidemic, those living with symptomatic individuals may be requested to stay home [25]. In simulations of household quarantine, family members of symptomatic individuals will independently decide (based on a compliance probability) whether to obey quarantine for 7 days one day after the first individual becomes symptomatic. Individuals electing to quarantine themselves withdraw to the household and interact only with household members. If other family members become ill during quarantine, household members independently decide whether to obey quarantine for 7 days one day after each individual becomes symptomatic. Implementation of the stochastic model FluTE is written in C/C++ and is released under the GNU General Public License (GPLv3, see http://www.gnu.org/licenses/gpl.html). The source code is available at http://www.csquid.org/software, https://www.epimodels.org/midas/flute.do, and the Models of Infectious Disease Agent Study (MIDAS) repository [26]. The software includes two source code files that are also freely distributable but may come with different licenses because they were written by others: one for the pseudorandom number generator (SIMD oriented Fast Mersenne Twister (SFMT) pseudorandom number generator [27]) and one to generate binomially distributed random numbers (from Numerical Recipes in C [28]). Version 1.11 of FluTE was used to produce the results in this manuscript. A configuration file is used to specify the population to use for the simulation, the parameters for starting the epidemic, the transmissibility of the infectious agent, and the desired intervention strategies. The configuration file is text-based and can be typed in by a user or generated with a script. The simulation outputs results to text files, which can be easily parsed for plotting or statistical analysis. A parallelized version of the code supports simulations of large populations (up to the entire continental United States). This version of the program assigns the populations of different counties to different processors, and OpenMPI is used to update the status of individuals who travel between communities that are located on different processors and to update the global status of the epidemic and the interventions (e.g., the total number of vaccines used). The simulation uses approximately 80 megabytes of memory per million simulated individuals. The simulation was written with several competing goals: to explicitly represent each individual in the population, to conserve memory, to run quickly, and to be (relatively) easy to read and modify. Each simulated individual is represented by a C structure that includes unique identifiers for the person and for each of the social mixing groups to which that person belongs, the age of the individual, the person's infection and vaccination status and dates, and other attributes. For each infected individual, the simulation identifies all susceptible individuals in that person's community who share a common mixing group, the infectiousness of the infected individual, the susceptibility of the susceptible, and the probability that transmission takes place for every time step. Although comparing each individual with every other within a community results in the number of comparisons increasing with the square of the number of individuals, community sizes are always smaller than 3,000 residents. Therefore, the number of comparisons made between individuals scales approximately linearly with the number of individuals in the simulation. More sophisticated algorithms could improve the simulation's performance, but may do so at the expense of the code's flexibility and readability. The running time depends on the number of individuals infected during the course of a simulation. Simulating an epidemic in a population of 10 million people can take up to two hours (on a single processor on an Intel Core2 Duo T9400), but it may take only seconds if the virus is not highly transmissible (low ) or if there are effective interventions (e.g., high vaccination rates). On a cluster of 32 processors, simulating an epidemic covering the continental United States (population of 280 million) takes about 6 hours (192 hours of total CPU time). Results We illustrate the use of the model by simulating epidemics in metropolitan Seattle, a major metropolitan area with a population of approximately 560,000 according to the US 2000 Census. We ran simulations with different values of , starting with ten infected individuals chosen at random, and found that the epidemic could peak as early as 45 days after the start if is high ( ) (Figure 3A). Pre-vaccination (with vaccine efficacies of VE S  = 40%, VE P  = 67%, VE I  = 40%, which correspond to a well-matched seasonal influenza vaccine [29]) is likely to both lower and delay the epidemic peak (Figure 3B). Use of antivirals alone (AVE S  = 30%, AVE P  = 60%, and AVE I  = 62% [11]) did not greatly reduce the epidemic peak, but they could reduce illness and mortality in an epidemic. Non-pharmaceutical interventions could be quite effective, but the epidemic may spike immediately upon ending the intervention (compare permanent school closure with school closure for 60 days in Figure 3B). 10.1371/journal.pcbi.1000656.g003 Figure 3 Illness attack rates and daily prevalence of influenza in simulations of metropolitan Seattle. (A) Daily prevalence of symptomatic influenza in simulations of metropolitan Seattle for various and (B) for with various interventions. The interventions, which begin 30 days after the first case is detected, are: giving a course of antiviral agents to ascertained cases, closing schools either permanently or for 60 days, and pre-vaccination of 50% of the population with a well-matched seasonal influenza vaccine. (C) Final illness attack rates (180 days) vs for FluTE (simulating metropolitan Seattle) and a model with random mixing. Results for all panels are from one run of metropolitan Seattle for each or intervention strategy except for the simulation for in panel (A), which was run 5 times with different random number seeds and plotted to show stochastic variability. The illness attack rates in the simulation are lower than those in a SIR model with random mixing (where [30], where AR is the infection attack rate, and the illness attack rate is 0.67 AR) (Figure 3C). As observed in earlier studies, models with community structure have lower attack rates than those with random mixing [31]–[33]. Simulated epidemics struck school-age children earlier than adults, which had been observed in earlier studies [6],[34]. Therefore, we predict that early in an epidemic, the proportion of cases who are school-age children will be higher than later in the epidemic (Figure 4). This phenomenon might affect the accuracy of estimates in unfolding epidemics. For example, most confirmed cases in the recent novel influenza A(H1N1) outbreaks in the United States have been school-age children [35] and several early estimates of have been above 2 [36],[37]. In our model, we observed that infected children generate more secondary cases than infected adults (Figure 2A). For example, infected school-age children would transmit to an average of other individuals in a simulated epidemic with . Therefore, estimates of could be high early in an epidemic when a disproportionate number of infections are in children. 10.1371/journal.pcbi.1000656.g004 Figure 4 The ratio of cumulative illness attack rates between school-age children (ages 5–18) and adults (ages 19–64) over time in simulated epidemics. Results plotted are from one simulation of metropolitan Seattle for each value of . One can simulate the population of the entire continental US using the parallel version of FluTE (mpiflute). The continental US had 280 million people in 64735 census tracts in 2000, based on the US 2000 Census. In our simulations, we found that the final illness attack rates for the US to be nearly identical to those of metropolitan Seattle, but the epidemic peak for a given is later for the United States (e.g., 94 vs 65 days for ) (Figure 5). Therefore, simulations of a sufficiently large metropolitan area may be adequate for determining the effect of a strategy on the national level on final illness attack rates, but the nation-wide peak of the epidemic may be later than in the major metropolitan areas because of the time it takes the epidemic to reach outlying areas. 10.1371/journal.pcbi.1000656.g005 Figure 5 The prevalence of influenza in a single simulation of the United States 100 days after the start of an influenza epidemic with . The color of each dot corresponds to the illness prevalence in a census tract. Image created using ArcGIS (Environmental Systems Research Institute, Inc.) Discussion We have described a new publicly available influenza epidemic simulator, FluTE. It explicitly represents every individual in the simulation, so simulated epidemics can be studied in detail, even tracing individual transmission events. We illustrated the use of FluTE with examples in which we explored the effect of various intervention strategies on influenza epidemics in the United States and showed how transmissibility can be over-estimated early in an epidemic. The simulation was written so that one can easily set the transmissibility, vaccination policies (e.g., fraction of the population to vaccinate), and other reactive strategies (e.g., school closures). These settings can be used to investigate questions such as: 1) What fraction of the population will become infected or ill? 2) How much vaccine coverage is required to mitigate an epidemic with a given ? 3) What segment of the population should be vaccinated to reduce overall illness attack rates the most? 4) How long can one wait before reacting to an epidemic? and 5) What range of can be managed by a particular pandemic strategy? We have used FluTE to investigate some of these questions by simulating vaccinating children against seasonal and pandemic influenza [38] and pandemic mitigation [20]. The model was calibrated to simulate epidemics of a virus similar to 1957/1958 Asian A(H2N2) and 2009 pandemic A(H1N1). We attempted to model realistic pharmaceutical and non-pharmaceutical interventions, but their effects on an epidemic have not been well quantified. The model's results are plausible and likely to be qualitatively correct, but there is insufficient data to calibrate it to produce quantitatively accurate results for the various possible disease parameters and mitigation strategies. Although the model generates realistic population-level results, the spatial dynamics of the epidemics it produces should be used for illustrative purposes only. When using the model to evaluate mitigation strategies, it is important to consider one's goals. For example, using antiviral agents to treat cases does not greatly reduce the final illness attack rate in the simulation, but it could greatly reduce mortality. The model does not directly evaluate the cost of interventions, but the numbers of cases in a simulated epidemic can be linked to cost and healthcare utilization data [39]. Differential equation models are the most popular approach to disease modeling. The simplest of these (such as the SIR model [40]) can be used to study epidemics analytically, and more complex versions have been used to model the dynamics of epidemics on a global scale [41],[42]. However, if one wants to include a complicated natural history of disease or detailed intervention strategies, individual-based models, such as FluTE, may be more suitable. The current software supports a limited set of configuration options and is intended for batch runs using a scripting language. Using the model for scenarios not supported by the existing code, such as testing a novel intervention strategy or altering the contact parameters for a different attack rate pattern, would require modification of the source code, which we have released so that others can make such changes if needed. We decided to adopt the GNU General Public License (GPL), so that the source code of derivative works must be released. We believe this will facilitate the sharing of improvements. The availability of source code allows others to adapt the model to simulate outbreaks of other airborne infectious diseases such as smallpox [3],[43],[44] or to simulate other regions of the world with different social structures [3]. In the future, we would like to make our model more accessible to non-programmers. This may involve developing a user interface or adding new parameters to the configuration file. We would also like to include intervention strategies that best reflect government pandemic mitigation plans. Achieving these goals would depend upon close collaboration with public health officials to better understand their needs and to carefully simulate existing pandemic mitigation plans and capacities. Although we have calibrated our model to the best available data, more detailed and reliable information on the natural history of influenza, influenza transmission, human behavior in response to infection, and vaccine efficacy is needed. Sensitivity analyses of similar epidemic models have shown that results are robust to uncertainty in many parameters [3],[5],[6],[11]. However, more accurate model inputs would improve the quantitative predictions. Well-designed studies are needed to acquire these data.
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                Contributors
                Journal
                Lancet Infect Dis
                Lancet Infect Dis
                The Lancet. Infectious Diseases
                Elsevier Ltd.
                1473-3099
                1474-4457
                23 March 2020
                23 March 2020
                :
                Affiliations
                [a ]Division of Epidemiology, School of Public Health and Center for Computational Biology, College of Engineering, University of California, Berkeley, CA 94720, USA
                [b ]Department of Medicine, University of California, San Francisco, CA, USA
                Article
                S1473-3099(20)30190-0
                10.1016/S1473-3099(20)30190-0
                7118670
                32213329
                2aceb8d9-48b5-4b50-8411-e079a2e8589e
                © 2020 Elsevier Ltd. All rights reserved.

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                Infectious disease & Microbiology
                Infectious disease & Microbiology

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