Origins of the problematic E in SEIR epidemic models

During the COVID-19 pandemic, over one thousand papers were published on "Susceptible-Exposed-Infectious-Removed" (SEIR) epidemic computational models. The English word "exposed" in its vernacular and public health usage means a state of having been in contact with an infectious individual, but not necessarily infected. In contrast, the term "exposed" in SEIR modeling usage typically stands for a state of already being infected but not yet being infectious to others, a state more properly termed "latently infected." In public health language, "exposed" means possibly infected, yet in SEIR modeling language, "exposed" means already infected. This paper retraces the conceptual and mathematical origins of this terminological disconnect and concludes that epidemic modelers should consider using the "SLIR" notational short-hand (L for Latent) instead of SEIR.

Protective Efficacy of Gastrointestinal SARS-CoV-2 Delivery against Intranasal and Intratracheal SARS-CoV-2 Challenge in Rhesus Macaques

Live oral vaccines have been explored for their protective efficacy against respiratory viruses, particularly for adenovirus serotypes 4 and 7. The potential of a live oral vaccine against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), however, remains unclear. In this study, we assessed the immunogenicity of live SARS-CoV-2 delivered to the gastrointestinal tract in rhesus macaques and its protective efficacy against intranasal and intratracheal SARS-CoV-2 challenge. Postpyloric administration of SARS-CoV-2 by esophagogastroduodenoscopy resulted in limited virus replication in the gastrointestinal tract and minimal to no induction of mucosal antibody titers in rectal swabs, nasal swabs, and bronchoalveolar lavage fluid. Low levels of serum neutralizing antibodies were induced and correlated with modestly diminished viral loads in nasal swabs and bronchoalveolar lavage fluid following intranasal and intratracheal SARS-CoV-2 challenge. Overall, our data show that postpyloric inoculation of live SARS-CoV-2 is weakly immunogenic and confers partial protection against respiratory SARS-CoV-2 challenge in rhesus macaques. IMPORTANCE SARS-CoV-2 remains a global threat, despite the rapid deployment but limited coverage of multiple vaccines. Alternative vaccine strategies that have favorable manufacturing timelines, greater ease of distribution, and improved coverage may offer significant public health benefits, especially in resource-limited settings. Live oral vaccines have the potential to address some of these limitations; however, no studies have yet been conducted to assess the immunogenicity and protective efficacy of a live oral vaccine against SARS-CoV-2. Here, we report that oral administration of live SARS-CoV-2 in nonhuman primates may offer prophylactic benefits, but the formulation and route of administration will require further optimization.

Estimating the Impact of Low Influenza Activity in 2020 on Population Immunity and Future Influenza Seasons in the United States

BACKGROUND

Influenza activity in the 2020-2021 season was remarkably low, likely due to implementation of public health preventive measures such as social distancing, mask wearing, and school closure. With waning immunity, the impact of low influenza activity in the 2020-2021 season on the following season is unknown.

METHODS

We built a multistrain compartmental model that captures immunity over multiple influenza seasons in the United States. Compared with the counterfactual case, where influenza activity remained at the normal level in 2020-2021, we estimated the change in the number of hospitalizations when the transmission rate was decreased by 20% in 2020-2021. We varied the level of vaccine uptake and effectiveness in 2021-2022. We measured the change in population immunity over time by varying the number of seasons with lowered influenza activity.

RESULTS

With the lowered influenza activity in 2020-2021, the model estimated 102 000 (95% CI, 57 000-152 000) additional hospitalizations in 2021-2022, without changes in vaccine uptake and effectiveness. The estimated changes in hospitalizations varied depending on the level of vaccine uptake and effectiveness in the following year. Achieving a 50% increase in vaccine coverage was necessary to avert the expected increase in hospitalization in the next influenza season. If the low influenza activity were to continue over several seasons, population immunity would remain low during those seasons, with 48% of the population susceptible to influenza infection.

CONCLUSIONS

Our study projected a large compensatory influenza season in 2021-2022 due to a light season in 2020-2021. However, higher influenza vaccine uptake would reduce this projected increase in influenza.

Carfentanil and the rise and fall of overdose deaths in the United States

BACKGROUND AND AIMS

It is widely believed that the 2018 decline in overdose deaths in the United States was attributable to a range of public health interventions, however, this decline also coincided with the regulation and decline in use of potent fentanyl analogs, especially carfentanil. The aim of this study was to investigate the association between overdose deaths and carfentanil availability in the United States.

DESIGN

Secondary analysis of drug overdose deaths from the Center for Disease Control and Prevention (CDC) and carfentanil exhibit data from drug seizures submitted to drug crime labs and published by the Drug Enforcement Administration (DEA). Trends in overdose deaths were compared in states with high carfentanil exhibits with states with low or no carfentanil exhibits.

SETTING

United States.

PARTICIPANTS

A total of 1 035 923 drug overdose death records in the United States from 1979 through 2019 were studied.

MEASUREMENTS

The outcomes studied were number of overdose deaths and mortality rates by state.

FINDINGS

Drug overdose deaths have been closely tracked along an exponential curve. The years 2016 and 2017 witnessed a hyper-exponential surge with increases in overdose deaths of 11 228 (+21.4%) and 6605 (+10.4%), respectively. Subsequently in 2018, drug overdose deaths declined by -2870 (-4.1%). This rise and then fall coincided with a surge and then decline in carfentanil drug seizure exhibits during these same years: 0 (2015), 1292 (2016), 5857 (2017) and 804 (2018). The majority of carfentanil exhibits were localized to a few states. The 2018 decline in overdose deaths in the top five states with the greatest spike in carfentanil exhibits in 2017 (Ohio, Florida, Pennsylvania, Kentucky and Michigan) was 2848, which accounted for nearly all of the total US decline.

CONCLUSIONS

The 2016-2017 acceleration and then 2018 decline in drug overdose deaths in the United States was associated with the sudden rise and then fall of carfentanil availability. Given the regional variation, carfentanil's decreased availability may have contributed to the reduction in overdose deaths in 2018.

A systematic review of antibody mediated immunity to coronaviruses: kinetics, correlates of protection, and association with severity

Many public health responses and modeled scenarios for COVID-19 outbreaks caused by SARS-CoV-2 assume that infection results in an immune response that protects individuals from future infections or illness for some amount of time. The presence or absence of protective immunity due to infection or vaccination (when available) will affect future transmission and illness severity. Here, we review the scientific literature on antibody immunity to coronaviruses, including SARS-CoV-2 as well as the related SARS-CoV, MERS-CoV and endemic human coronaviruses (HCoVs). We reviewed 2,452 abstracts and identified 491 manuscripts relevant to 5 areas of focus: 1) antibody kinetics, 2) correlates of protection, 3) immunopathogenesis, 4) antigenic diversity and cross-reactivity, and 5) population seroprevalence. While further studies of SARS-CoV-2 are necessary to determine immune responses, evidence from other coronaviruses can provide clues and guide future research.

Forecasted Size of Measles Outbreaks Associated With Vaccination Exemptions for Schoolchildren

IMPORTANCE

Vaccine exemptions, which allow unvaccinated children to attend school, have increased by a factor of 28 since 2003 in Texas. Geographic clustering of unvaccinated children facilitates the spread of measles introductions, but the potential size of outbreaks is unclear.

OBJECTIVE

To forecast the range of measles outbreak sizes in each metropolitan area of Texas at 2018 and future reduced school vaccination rates.

DESIGN, SETTING, AND PARTICIPANTS

An agent-based decision analytical model using a synthetic population of Texas, derived from the 2010 US Census, was used to simulate measles transmission in the Texas population. Real schools were represented in the simulations, and the 2018 vaccination rate of each real school was applied to a simulated hypothetical equivalent. Single cases of measles were introduced, daily activities and interactions were modeled for each population member, and the number of infections over the course of 9 months was counted for 1000 simulated runs in each Texas metropolitan area.

INTERVENTIONS

To determine the outcomes of further decreases in vaccination coverage, additional simulations were performed with vaccination rates reduced by 1% to 10% in schools with populations that are currently undervaccinated.

MAIN OUTCOMES AND MEASURES

Expected distributions of outbreak sizes in each metropolitan area of Texas at 2018 and reduced vaccination rates.

RESULTS

At 2018 vaccination rates, the median number of cases in large metropolitan areas was typically small, ranging from 1 to 3 cases, which is consistent with outbreaks in Texas 2006 to 2017. However, the upper limit of the distribution of plausible outbreaks (the 95th percentile, associated with 1 in 20 measles introductions) exceeded 400 cases in both the Austin and Dallas metropolitan areas, similar to the largest US outbreaks since measles was eliminated in 2000. Decreases in vaccination rates in schools with undervaccinated populations in 2018 were associated with exponential increases in the potential size of outbreaks: a 5% decrease in vaccination rate was associated with a 40% to 4000% increase in potential outbreak size, depending on the metropolitan area. A mean (SD) of 64% (11%) of cases occurred in students for whom a vaccine had been refused, but a mean (SD) of 36% (11%) occurred in others (ie, bystanders).

CONCLUSIONS AND RELEVANCE

This study suggests that vaccination rates in some Texas schools are currently low enough to allow large measles outbreaks. Further decreases are associated with dramatic increases in the probability of large outbreaks. Limiting vaccine exemptions could be associated with a decrease in the risk of large measles outbreaks.

Project Tycho 2.0: a repository to improve the integration and reuse of data for global population health

Objective

In 2013, we released Project Tycho, an open-access database comprising 3.6 million counts of infectious disease cases and deaths reported for over a century by public health surveillance in the United States. Our objective is to describe how Project Tycho version 1 (v1) data has been used to create new knowledge and technology and to present improvements made in the newly released version 2.0 (v2).

Materials and Methods

We analyzed our user database and conducted online searches to analyze the use of Project Tycho v1 data. For v2, we added new US data and dengue data for other countries, and grouped data into 360 datasets, each with a digital object identifier and rich metadata. In addition, we used standard vocabularies to encode data where possible, improving compliance with FAIR (findable, accessible, interoperable, reusable) guiding principles for data management.

Results

Since release, 3174 people have registered to use Project Tycho data, leading to 18 new peer-reviewed papers and 27 other creative works, such as conference papers, student theses, and software applications. Project Tycho v2 comprises 5.7 million counts of infectious diseases in the United States and of dengue-related conditions in 98 additional countries.

Discussion

Project Tycho v2 contributes to improving FAIR compliance of global health data, but more work is needed to develop community-accepted standard representations for global health data.

Conclusion

FAIR principles are a valuable guide for improving the integration and reuse of data in global health to improve disease control and save lives.

Changing dynamics of the drug overdose epidemic in the United States from 1979 through 2016

Better understanding of the dynamics of the current U.S. overdose epidemic may aid in the development of more effective prevention and control strategies. We analyzed records of 599,255 deaths from 1979 through 2016 from the National Vital Statistics System in which accidental drug poisoning was identified as the main cause of death. By examining all available data on accidental poisoning deaths back to 1979 and showing that the overall 38-year curve is exponential, we provide evidence that the current wave of opioid overdose deaths (due to prescription opioids, heroin, and fentanyl) may just be the latest manifestation of a more fundamental longer-term process. The 38+ year smooth exponential curve of total U.S. annual accidental drug poisoning deaths is a composite of multiple distinctive subepidemics of different drugs (primarily prescription opioids, heroin, methadone, synthetic opioids, cocaine, and methamphetamine), each with its own specific demographic and geographic characteristics.

Changing dynamics of the drug overdose epidemic in the United States from 1979 through 2016

Better understanding of the dynamics of the current U.S. overdose epidemic may aid in the development of more effective prevention and control strategies. We analyzed records of 599,255 deaths from 1979 through 2016 from the National Vital Statistics System in which accidental drug poisoning was identified as the main cause of death. By examining all available data on accidental poisoning deaths back to 1979 and showing that the overall 38-year curve is exponential, we provide evidence that the current wave of opioid overdose deaths (due to prescription opioids, heroin, and fentanyl) may just be the latest manifestation of a more fundamental longer-term process. The 38+ year smooth exponential curve of total U.S. annual accidental drug poisoning deaths is a composite of multiple distinctive subepidemics of different drugs (primarily prescription opioids, heroin, methadone, synthetic opioids, cocaine, and methamphetamine), each with its own specific demographic and geographic characteristics.

Exploring scenarios of chikungunya mitigation with a data-driven agent-based model of the 2014-2016 outbreak in Colombia

New epidemics of infectious diseases can emerge any time, as illustrated by the emergence of chikungunya virus (CHIKV) and Zika virus (ZIKV) in Latin America. During new epidemics, public health officials face difficult decisions regarding spatial targeting of interventions to optimally allocate limited resources. We used a large-scale, data-driven, agent-based simulation model (ABM) to explore CHIKV mitigation strategies, including strategies based on previous DENV outbreaks. Our model represents CHIKV transmission in a realistic population of Colombia with 45 million individuals in 10.6 million households, schools, and workplaces. Our model uses high-resolution probability maps for the occurrence of the Ae. aegypti mosquito vector to estimate mosquito density in Colombia. We found that vector control in all 521 municipalities with mosquito populations led to 402,940 fewer clinical cases of CHIKV compared to a baseline scenario without intervention. We also explored using data about previous dengue virus (DENV) epidemics to inform CHIKV mitigation strategies. Compared to the baseline scenario, 314,437 fewer cases occurred when we simulated vector control only in 301 municipalities that had previously reported DENV, illustrating the value of available data from previous outbreaks. When varying the implementation parameters for vector control, we found that faster implementation and scale-up of vector control led to the greatest proportionate reduction in cases. Using available data for epidemic simulations can strengthen decision making against new epidemic threats.

The Effect of Incomplete Death Certificates on Estimates of Unintentional Opioid-Related Overdose Deaths in the United States, 1999-2015

OBJECTIVES

A complete and accurate count of the number of opioid-related overdose deaths is essential to properly allocate resources. We determined the rate of unintentional overdose deaths (non-opioid-related, opioid-related, or unspecified) in the United States and by state from 1999 to 2015 and the possible effects of underreporting on national estimates of opioid abuse.

METHODS

We abstracted unintentional drug overdose deaths ( International Classification of Diseases, 10th Revision, codes X40-X44) with contributory drug-specific T codes (T36.0-T50.9) from the Mortality Multiple Cause Micro-Data Files. We assumed that the proportion of unspecified overdose deaths that might be attributed to opioids would be the same as the proportion of opioid-related overdose deaths among all overdose deaths and calculated the number of deaths that could be reallocated as opioid-related for each state and year. We then added these reallocated deaths to the reported deaths to determine their potential effect on total opioid-related deaths.

RESULTS

From 1999 to 2015, a total of 438 607 people died from unintentional drug overdoses. Opioid-related overdose deaths rose 401% (from 5868 to 29 383), non-opioid-related overdose deaths rose 150% (from 3005 to 7505), and unspecified overdose deaths rose 220% (from 2255 to 29 383). In 5 states (Alabama, Indiana, Louisiana, Mississippi, and Pennsylvania), more than 35% of unintentional overdose deaths were coded as unspecified. Our reallocation resulted in classifying more than 70 000 unspecified overdose deaths as potential additional opioid-related overdose deaths.

CONCLUSIONS

States may be greatly underestimating the effect of opioid-related overdose deaths because of incomplete cause-of-death reporting, indicating that the current opioid overdose epidemic may be worse than it appears.

Improvement in racial disparities in years of life lost in the USA since 1990

Objective

To examine changes in cause-specific Years of Life Lost (YLL) by age, race, and sex group in the USA from 1990 to 2014.

Methods

60 million death reports from the National Center for Health Statistics (NCHS) were categorized by age group, sex, race, and cause of death. YLL were calculated using age-specific life expectancies. Age groups were: infants <1, children 1–19, adults 20–64, and older adults 65+.

Results

Blacks have historically experienced more years of life lost than whites or other racial groups in the USA. In the year 1990 the YLL per 100,000 population was 21,103 for blacks, 14,160 for whites, and 7,417 for others. Between 1990 and 2014 overall YLL in the USA improved by 10%, but with marked variations in the rate of change across age, race, and sex groups. Blacks (all ages, both sexes) showed substantial improvement with a 28% reduction in YLL, compared to whites (all ages, both sexes) who showed a 4% reduction. Among blacks, improvements were seen in all age groups: reductions of 43%, 48%, 28%, and 25% among infants, children, adults, and older adults, respectively. Among whites, reductions of 33%, 44%, and 18% were seen in infants, children, and older adults, but there was a 6% increase in YLL among white adults. YLL increased by 18% in white adult females and declined 1% in white adult males. American Indian/Alaska Native women also had worsening in YLL, with an 8% increase. Asian Pacific Islanders consistently had the lowest YLL across all ages. Whites had a higher proportion of YLL due to overdose; blacks had a higher proportion due to homicide at younger ages and to heart disease at older ages.

Conclusions

Race-based disparities in YLL in the USA since 1990 have narrowed considerably, largely as a result of improvements among blacks compared to whites. Adult white and American Indian / Alaskan Native females have experienced worsening YLL, while white males have experienced essentially no change. If recent trajectories continue, adult black/white disparities in YLL will continue to narrow.

Development of antibody biomarkers of long term and recent dengue virus infections

Dengue virus (DENV) infections elicit antibody responses to the non-structural protein 1 (NS1) that are associated with protection against disease. However, the antibody isotypes and subclasses involved, and their kinetics have not been extensively studied. We characterized the antibody responses to DENV NS1 by enzyme-linked immunosorbent assay (ELISA) in a longitudinal cohort of 266 confirmed dengue cases in Recife, Northeast Brazil. Samples were collected during the febrile phase and up to over 3 years after onset of symptoms. The antibodies investigated [IgA, IgM, total IgG (all subclasses measured together) and each subclass (IgG2, IgG3 and IgG4) measured separately] had distinct kinetic profiles following primary or secondary DENV infections. Of interest, most of these antibodies were consistently detected greater than 6 months after onset of symptoms, except for IgG3. Anti-dengue NS1-specific IgG was consistently detected from the acute phase to beyond 3 years after symptom onset. In contrast, anti-dengue NS1-specific IgG3 was detected within the first week, peaked at week 2-3, and disappeared within 4-6 months after onset of symptoms. The mean duration of the IgG3 positive signal was 149 days (ranging from 126 to 172 days). In conclusion, anti-dengue NS1-specific IgG and IgG3 are potential biomarkers of long-term and recent (less than 6 months) DENV infections, respectively.

Patterns and trends in accidental poisoning death rates in the US, 1979-2014

OBJECTIVES

The purpose of this study was to examine US accidental poisoning death rates by demographic and geographic factors from 1979 to 2014, including High Intensity Drug Trafficking Areas.

METHODS

Crude and age-adjusted death rates were formed for age group, race, sex, and county for accidental poisonings (ICD 9th revision: E850-E869; ICD 10th revision: X40-X49) from 1979 to 2014 using the Mortality and Population Data System housed at the University of Pittsburgh. Rate ratios were calculated comparing rates from 2014 to 1979, overall, by sex, age group, race, and county. Joinpoint regression detected changes in trends and calculated the average annual percentage change (AAPC) as a summary measure of trend.

RESULTS

Drug poisoning mortality rates have risen an average of 6% per year since 1979. Increases are occurring in all ages 15+, and in all race-sex groups. HIDTA counties with the highest mortality rates were in Appalachia and New Mexico. Many of the HIDTA border counties had lower rates of mortality.

CONCLUSIONS

The drug poisoning mortality epidemic is continuing to grow. While HIDTA resources are appropriately targeted at many areas in the US most affected, rates are also rapidly rising in some non-HIDTA areas.

Selection of a potential diagnostic biomarker for HIV infection from a random library of non-biological synthetic peptoid oligomers

Non-biological synthetic oligomers can serve as ligands for antibodies. We hypothesized that a random combinatorial library of synthetic poly-N-substituted glycine oligomers, or peptoids, could represent a random “shape library” in antigen space, and that some of these peptoids would be recognized by the antigen-binding pocket of disease-specific antibodies. We synthesized and screened a one bead one compound combinatorial library of peptoids, in which each bead displayed an 8-mer peptoid with ten possible different amines at each position (10⁸ theoretical variants). By screening one million peptoid/beads we found 112 (approximately 1 in 10,000) that preferentially bound immunoglobulins from human sera known to be positive for anti-HIV antibodies. Reactive peptoids were then re-synthesized and rigorously evaluated in plate-based ELISAs. Four peptoids showed very good, and one showed excellent, properties for establishing a sero-diagnosis of HIV. These results demonstrate the feasibility of constructing sero-diagnostic assays for infectious diseases from libraries of random molecular shapes. In this study we sought a proof-of-principle that we could identify a potential diagnostic antibody ligand biomarker for an infectious disease in a random combinatorial library of 100 million peptoids. We believe that this is the first evidence that it is possible to develop sero-diagnostic assays – for any infectious disease – based on screening random libraries of non-biological molecular shapes.

Direct Measurement of the Astrophysical ^{38}K(p,γ)^{39}Ca Reaction and Its Influence on the Production of Nuclides toward the End Point of Nova Nucleosynthesis

We have performed the first direct measurement of the ^{38}K(p,γ)^{39}Ca reaction using a beam of radioactive ^{38}K. A proposed ℓ=0 resonance in the ^{38}K+p system has been identified at 679(2) keV with an associated strength of 120_{-30}^{+50}  meV. Upper limits of 1.16 (3.5) and 8.6 (26) meV at the 68% (95%) confidence level were also established for two further expected ℓ=0 resonances at 386 and 515 keV, respectively. The present results have reduced uncertainties in the ^{38}K(p,γ)^{39}Ca reaction rate at temperatures of 0.4 GK by more than 2 orders of magnitude and indicate that Ar and Ca may be ejected in observable quantities by oxygen-neon novae. However, based on the newly evaluated rate, the ^{38}K(p,γ)^{39}Ca path is unlikely to be responsible for the production of Ar and Ca in significantly enhanced quantities relative to solar abundances.

Patterns and Trends in Accidental Poisoning Deaths: Pennsylvania's Experience 1979-2014

Introduction

The purpose of this study was to examine county and state-level accidental poisoning mortality trends in Pennsylvania from 1979 to 2014.

Methods

Crude and age-adjusted death rates were formed for age group, race, sex, and county for accidental poisonings (ICD 10 codes X40-X49) from 1979 to 2014 for ages 15+ using the Mortality and Population Data System housed at the University of Pittsburgh. Rate ratios were calculated comparing rates from 1979 to 2014, overall and by sex, age group, and race. Joinpoint regression was used to detect statistically significant changes in trends of age-adjusted mortality rates.

Results

Rate ratios for accidental poisoning mortality in Pennsylvania increased more than 14-fold from 1979 to 2014. The largest rate ratios were among 35–44 year olds, females, and White adults. The highest accidental poisoning mortality rates were found in the counties of Southwestern Pennsylvania, those surrounding Philadelphia, and those in Northeast Pennsylvania near Scranton.

Conclusions

The patterns and locations of accidental poisoning mortality by race, sex, and age group provide direction for interventions and policy makers. In particular, this study found the highest rate ratios in PA among females, whites, and the age group 35–44.

Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns

Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics.

Computational Characterization of Transient Strain-Transcending Immunity against Influenza A

The enigmatic observation that the rapidly evolving influenza A (H3N2) virus exhibits, at any given time, a limited standing genetic diversity has been an impetus for much research. One of the first generative computational models to successfully recapitulate this pattern of consistently constrained diversity posits the existence of a strong and short-lived strain-transcending immunity. Building on that model, we explored a much broader set of scenarios (parameterizations) of a transient strain-transcending immunity, ran long-term simulations of each such scenario, and assessed its plausibility with respect to a set of known or estimated influenza empirical measures. We evaluated simulated outcomes using a variety of measures, both epidemiological (annual attack rate, epidemic duration, reproductive number, and peak weekly incidence), and evolutionary (pairwise antigenic diversity, fixation rate, most recent common ancestor, and kappa, which quantifies the potential for antigenic evolution). Taking cumulative support from all these measures, we show which parameterizations of strain-transcending immunity are plausible with respect to the set of empirically derived target values. We conclude that strain-transcending immunity which is milder and longer lasting than previously suggested is more congruent with the observed short- and long-term behavior of influenza.

A systematic review of barriers to data sharing in public health

Background

In the current information age, the use of data has become essential for decision making in public health at the local, national, and global level. Despite a global commitment to the use and sharing of public health data, this can be challenging in reality. No systematic framework or global operational guidelines have been created for data sharing in public health. Barriers at different levels have limited data sharing but have only been anecdotally discussed or in the context of specific case studies. Incomplete systematic evidence on the scope and variety of these barriers has limited opportunities to maximize the value and use of public health data for science and policy.

Methods

We conducted a systematic literature review of potential barriers to public health data sharing. Documents that described barriers to sharing of routinely collected public health data were eligible for inclusion and reviewed independently by a team of experts. We grouped identified barriers in a taxonomy for a focused international dialogue on solutions.

Results

Twenty potential barriers were identified and classified in six categories: technical, motivational, economic, political, legal and ethical. The first three categories are deeply rooted in well-known challenges of health information systems for which structural solutions have yet to be found; the last three have solutions that lie in an international dialogue aimed at generating consensus on policies and instruments for data sharing.

Conclusions

The simultaneous effect of multiple interacting barriers ranging from technical to intangible issues has greatly complicated advances in public health data sharing. A systematic framework of barriers to data sharing in public health will be essential to accelerate the use of valuable information for the global good.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2458-14-1144) contains supplementary material, which is available to authorized users.

A large-scale immuno-epidemiological simulation of influenza A epidemics

Background

Agent based models (ABM) are useful to explore population-level scenarios of disease spread and containment, but typically characterize infected individuals using simplified models of infection and symptoms dynamics. Adding more realistic models of individual infections and symptoms may help to create more realistic population level epidemic dynamics.

Methods

Using an equation-based, host-level mathematical model of influenza A virus infection, we develop a function that expresses the dependence of infectivity and symptoms of an infected individual on initial viral load, age, and viral strain phenotype. We incorporate this response function in a population-scale agent-based model of influenza A epidemic to create a hybrid multiscale modeling framework that reflects both population dynamics and individualized host response to infection.

Results

At the host level, we estimate parameter ranges using experimental data of H1N1 viral titers and symptoms measured in humans. By linearization of symptoms responses of the host-level model we obtain a map of the parameters of the model that characterizes clinical phenotypes of influenza infection and immune response variability over the population. At the population-level model, we analyze the effect of individualizing viral response in agent-based model by simulating epidemics across Allegheny County, Pennsylvania under both age-specific and age-independent severity assumptions.

Conclusions

We present a framework for multi-scale simulations of influenza epidemics that enables the study of population-level effects of individual differences in infections and symptoms, with minimal additional computational cost compared to the existing population-level simulations.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2458-14-1019) contains supplementary material, which is available to authorized users.

Dynamic simulation of crime perpetration and reporting to examine community intervention strategies

OBJECTIVE

To develop a conceptual computational agent-based model (ABM) to explore community-wide versus spatially focused crime reporting interventions to reduce community crime perpetrated by youth.

METHOD

Agents within the model represent individual residents and interact on a two-dimensional grid representing an abstract nonempirically grounded community setting. Juvenile agents are assigned initial random probabilities of perpetrating a crime and adults are assigned random probabilities of witnessing and reporting crimes. The agents' behavioral probabilities modify depending on the individual's experience with criminal behavior and punishment, and exposure to community crime interventions. Cost-effectiveness analyses assessed the impact of activating different percentages of adults to increase reporting and reduce community crime activity. Community-wide interventions were compared with spatially focused interventions, in which activated adults were focused in areas of highest crime prevalence.

RESULTS

The ABM suggests that both community-wide and spatially focused interventions can be effective in reducing overall offenses, but their relative effectiveness may depend on the intensity and cost of the interventions. Although spatially focused intervention yielded localized reductions in crimes, such interventions were shown to move crime to nearby communities. Community-wide interventions can achieve larger reductions in overall community crime offenses than spatially focused interventions, as long as sufficient resources are available.

CONCLUSION

The ABM demonstrates that community-wide and spatially focused crime strategies produce unique intervention dynamics influencing juvenile crime behaviors through the decisions and actions of community adults. It shows how such models might be used to investigate community-supported crime intervention programs by integrating community input and expertise and provides a simulated setting for assessing dimensions of cost comparison and intervention effect sustainability. ABM illustrates how intervention models might be used to investigate community-supported crime intervention programs.

A gorilla reservoir for human T-lymphotropic virus type 4

Of the seven known species of human retroviruses only one, human T-cell lymphotropic virus type 4 (HTLV-4), lacks a known animal reservoir. We report the largest screening for simian T-cell lymphotropic virus (STLV-4) to date in a wide range of captive and wild non-human primate (NHP) species from Cameroon. Among the 681 wild and 426 captive NHPs examined, we detected STLV-4 infection only among gorillas by using HTLV-4-specific quantitative polymerase chain reaction. The large number of samples analyzed, the diversity of NHP species examined, the geographic distribution of infected animals relative to the known HTLV-4 case, as well as detailed phylogenetic analyses on partial and full genomes, indicate that STLV-4 is endemic to gorillas, and that rather than being an ancient virus among humans, HTLV-4 emerged from a gorilla reservoir, likely through the hunting and butchering of wild gorillas. Our findings shed further light on the importance of gorillas as keystone reservoirs for the evolution and emergence of human infectious diseases and provide a clear course for preventing HTLV-4 emergence through management of human contact with wild gorillas, the development of improved assays for HTLV-4/STLV-4 detection and the ongoing monitoring of STLV-4 among gorillas and for HTLV-4 zoonosis among individuals exposed to gorilla populations.

Potential opportunities and perils of imperfect dengue vaccines

Dengue vaccine development efforts have focused on the development of tetravalent vaccines. However, a recent Phase IIb trial of a tetravalent vaccine indicates a protective effect against only 3 of the 4 serotypes. While vaccines effective against a subset of serotypes may reduce morbidity and mortality, particular profiles could result in an increased number of cases due to immune enhancement and other peculiarities of dengue epidemiology. Here, we use a compartmental transmission model to assess the impact of partially effective vaccines in a hyperendemic Thai population. Crucially, we evaluate the effects that certain serotype heterogeneities may have in the presence of mass-vaccination campaigns. In the majority of scenarios explored, partially effective vaccines lead to 50% or greater reductions in the number of cases. This is true even of vaccines that we would not expect to proceed to licensure due to poor or incomplete immune responses. Our results show that a partially effective vaccine can have significant impacts on serotype distribution and mean age of cases.

FRED (a Framework for Reconstructing Epidemic Dynamics): an open-source software system for modeling infectious diseases and control strategies using census-based populations

BACKGROUND

Mathematical and computational models provide valuable tools that help public health planners to evaluate competing health interventions, especially for novel circumstances that cannot be examined through observational or controlled studies, such as pandemic influenza. The spread of diseases like influenza depends on the mixing patterns within the population, and these mixing patterns depend in part on local factors including the spatial distribution and age structure of the population, the distribution of size and composition of households, employment status and commuting patterns of adults, and the size and age structure of schools. Finally, public health planners must take into account the health behavior patterns of the population, patterns that often vary according to socioeconomic factors such as race, household income, and education levels.

RESULTS

FRED (a Framework for Reconstructing Epidemic Dynamics) is a freely available open-source agent-based modeling system based closely on models used in previously published studies of pandemic influenza. This version of FRED uses open-access census-based synthetic populations that capture the demographic and geographic heterogeneities of the population, including realistic household, school, and workplace social networks. FRED epidemic models are currently available for every state and county in the United States, and for selected international locations.

CONCLUSIONS

State and county public health planners can use FRED to explore the effects of possible influenza epidemics in specific geographic regions of interest and to help evaluate the effect of interventions such as vaccination programs and school closure policies. FRED is available under a free open source license in order to contribute to the development of better modeling tools and to encourage open discussion of modeling tools being used to evaluate public health policies. We also welcome participation by other researchers in the further development of FRED.

Household transmission of influenza A and B in a school-based study of non-pharmaceutical interventions

The effect of school-based non-pharmaceutical interventions (NPIs) on influenza A and B transmission in children's households has not been estimated in published literature. We use data from a large school-based cluster randomized trial of improved hand and respiratory hygiene measures to explore the secondary transmission of influenza A and B in households of laboratory confirmed influenza cases. Data were taken from the Pittsburgh Influenza Prevention Project, a cluster-randomized trial of NPIs conducted in ten Pittsburgh, PA elementary schools during the 2007-2008 influenza season. We estimated two measures of influenza transmissibility in households; the susceptible infectious transmission probability, using variants of the Reed-Frost chain binomial model, and the secondary attack rate. We identified predictors of ILI using a logistic generalized estimating equation model. We estimate the secondary attack rates in intervention households to be 0.26 (95% confidence interval (CI) 0.19-0.34) compared to 0.30 (95% CI 0.23-0.38) in control households. Race and age were significant risk factors for secondary ILI acquisition in this study. We found no significant differences between the transmission probabilities for infectious individuals in intervention (0.19, 95% CI 0.14-0.25), and control households (0.22, 95% CI 0.16-0.29). Similarly, estimates for secondary attack rates and transmission probabilities for households with confirmed influenza A (0.31 and 0.22) were not significantly different from estimates from households with confirmed influenza B (0.25 and 0.20). While influenza A and B are thought to have different transmission characteristics, we find no significant differences in their transmissibility within households. Though our results suggest a potential effect, we found no statistically significant effect of school-based non-pharmaceutical interventions on transmission in symptomatic children's homes.

A model international partnership for community-based research on vaccine-preventable diseases: the Kamphaeng Phet-AFRIMS Virology Research Unit (KAVRU)

This paper describes an international collaboration to carry out studies that contributed to the understanding of pathogenesis, diagnosis, treatment, and prevention of several diseases of public health importance for Thailand and the United States. In Kamphaeng Phet Province, Thailand, febrile syndromes, including encephalitis, hepatitis, hemorrhagic fever, and influenza-like illnesses, occurred commonly and were clinically diagnosed, but the etiology was rarely confirmed. Since 1982, the Kamphaeng Phet Provincial Hospital, the Thai Ministry of Public Health, and the US Army Component of the Armed Forces Research Institute of Medical Sciences, along with vaccine manufacturers and universities, have collaborated on studies that evaluated and capitalized on improved diagnostic capabilities for infections caused by Japanese encephalitis, hepatitis A, dengue, and influenza viruses. The collaboration clarified clinical and epidemiological features of these infections and, in large clinical trials, demonstrated that vaccines against Japanese encephalitis and hepatitis A viruses were over 90% efficacious, supporting licensure of both vaccines. With the introduction of Japanese encephalitis vaccines in Thailand's Expanded Program on Immunization, reported encephalitis rates dropped substantially. Similarly, in the US, particularly in the military populations, rates of hepatitis A disease have dropped with the use of hepatitis A vaccine. Studies of the pathogenesis of dengue infections have increased understanding of the role of cellular immunity in responding to these infections, and epidemiological studies have prepared the province for studies of dengue vaccines. Approximately 80 publications resulted from this collaboration. Studies conducted in Kamphaeng Phet provided experience that contributed to clinical trials of hepatitis E and HIV vaccines, conducted elsewhere. To provide a base for continuing studies, The Kamphaeng Phet-AFRIMS Virology Research Unit (KAVRU) was established. This paper reviews the origins of the collaboration and the scientific observations made between 1982 and 2012.

Interactions between serotypes of dengue highlight epidemiological impact of cross-immunity

Dengue, a mosquito-borne virus of humans, infects over 50 million people annually. Infection with any of the four dengue serotypes induces protective immunity to that serotype, but does not confer long-term protection against infection by other serotypes. The immunological interactions between serotypes are of central importance in understanding epidemiological dynamics and anticipating the impact of dengue vaccines. We analysed a 38-year time series with 12 197 serotyped dengue infections from a hospital in Bangkok, Thailand. Using novel mechanistic models to represent different hypothesized immune interactions between serotypes, we found strong evidence that infection with dengue provides substantial short-term cross-protection against other serotypes (approx. 1-3 years). This is the first quantitative evidence that short-term cross-protection exists since human experimental infection studies performed in the 1950s. These findings will impact strategies for designing dengue vaccine studies, future multi-strain modelling efforts, and our understanding of evolutionary pressures in multi-strain disease systems.

Policies to reduce influenza in the workplace: impact assessments using an agent-based model

OBJECTIVES

We examined the impact of access to paid sick days (PSDs) and stay-at-home behavior on the influenza attack rate in workplaces.

METHODS

We used an agent-based model of Allegheny County, Pennsylvania, with PSD data from the US Bureau of Labor Statistics, standard influenza epidemic parameters, and the probability of staying home when ill. We compared the influenza attack rate among employees resulting from workplace transmission, focusing on the effects of presenteeism (going to work when ill).

RESULTS

In a simulated influenza epidemic (R0 = 1.4), the attack rate among employees owing to workplace transmission was 11.54%. A large proportion (72.00%) of this attack rate resulted from exposure to employees engaging in presenteeism. Universal PSDs reduced workplace infections by 5.86%. Providing 1 or 2 "flu days"-allowing employees with influenza to stay home-reduced workplace infections by 25.33% and 39.22%, respectively.

CONCLUSIONS

PSDs reduce influenza transmission owing to presenteeism and, hence, the burden of influenza illness in workplaces.

Molecular epidemiology of GB type C virus among individuals exposed to hepatitis C virus in Cameroon

GB Virus Type C (GBV-C), a blood-borne flavivirus currently infects about one sixth of the world's population. Its transmission has been reported through parenteral, sexual and vertical routes. Unusually for RNA viruses, it exhibits a high degree of conservation of the polyprotein sequence. The geographical distribution of GBV-C suggests an African origin and a long-term co-evolution in the human population but without any known pathogenicity. The aim of this study was to describe the different sub-types of this virus in Southern Cameroon. We studied the genetic epidemiology of GBV-C among rural populations where many HIV-1 and HCV genotypes have been identified. Plasma samples of 345 subjects with evidence of HCV exposure were tested for GBV-C infection. To detect GBV-C RNA, reverse transcription followed by a nested PCR of 5'UTR were performed. Direct sequencing and phylogenetic studies using PHYLIP, PAUP* and SimPlot were carried out. In total, 31 GBV-C RNA-positive samples were detected giving a prevalence of 9.0% among HCV-exposed individuals. Phylogenetic analysis of the 5'UTR showed two distinct clusters: Genotype 1 and Genotype 2. Twenty-eight isolates (8.0%) clustered with Genotype 1 and 3 (1.0%) with Genotype 2. More than one genotype of GBV-C is prevalent in Cameroon of which GBV-C Genotype 1 is more common, confirming reports in the literature. Studying the near full-length genome sequences of GBV-C isolates from primates in this region may provide clues of viral recombination, evolution and origin.

Assessment of serosurveys for H5N1

BACKGROUND

It has been suggested that the true case-fatality rate of human H5N1 influenza infection is appreciably less than the figure of approximately 60% that is based on official World Health Organization (WHO)-confirmed case reports because asymptomatic cases may have been missed. A number of seroepidemiologic studies have been conducted in an attempt to identify such missed cases.

METHODS

We conducted a comprehensive literature review of all English-language H5N1 human serology surveys with detailed attention to laboratory methodology used (including whether investigators used criteria set by the WHO to define positive cases), laboratory controls used, and the clades/genotypes involved.

RESULTS

Twenty-nine studies were included in the analysis. Few reported using unexposed control groups and one-third did not apply WHO criteria. Of studies that used WHO criteria, only 4 found any seropositive results to clades/genotypes of H5N1 that are currently circulating. No studies reported seropositive results to the clade 2/genotype Z viruses that have spread throughout Eurasia and Africa.

CONCLUSIONS

This review suggests that the frequency of positive H5 serology results is likely to be low; therefore, it is essential that future studies adhere to WHO criteria and include unexposed controls in their laboratory assays to limit the likelihood of false-positive results.

SIVagm infection in wild African green monkeys from South Africa: epidemiology, natural history, and evolutionary considerations

Pathogenesis studies of SIV infection have not been performed to date in wild monkeys due to difficulty in collecting and storing samples on site and the lack of analytical reagents covering the extensive SIV diversity. We performed a large scale study of molecular epidemiology and natural history of SIVagm infection in 225 free-ranging AGMs from multiple locations in South Africa. SIV prevalence (established by sequencing pol, env, and gag) varied dramatically between infant/juvenile (7%) and adult animals (68%) (p<0.0001), and between adult females (78%) and males (57%). Phylogenetic analyses revealed an extensive genetic diversity, including frequent recombination events. Some AGMs harbored epidemiologically linked viruses. Viruses infecting AGMs in the Free State, which are separated from those on the coastal side by the Drakensberg Mountains, formed a separate cluster in the phylogenetic trees; this observation supports a long standing presence of SIV in AGMs, at least from the time of their speciation to their Plio-Pleistocene migration. Specific primers/probes were synthesized based on the pol sequence data and viral loads (VLs) were quantified. VLs were of 10(4)-10(6) RNA copies/ml, in the range of those observed in experimentally-infected monkeys, validating the experimental approaches in natural hosts. VLs were significantly higher (10(7)-10(8) RNA copies/ml) in 10 AGMs diagnosed as acutely infected based on SIV seronegativity (Fiebig II), which suggests a very active transmission of SIVagm in the wild. Neither cytokine levels (as biomarkers of immune activation) nor sCD14 levels (a biomarker of microbial translocation) were different between SIV-infected and SIV-uninfected monkeys. This complex algorithm combining sequencing and phylogeny, VL quantification, serology, and testing of surrogate markers of microbial translocation and immune activation permits a systematic investigation of the epidemiology, viral diversity and natural history of SIV infection in wild African natural hosts.

School closure as an influenza mitigation strategy: how variations in legal authority and plan criteria can alter the impact

Background

States’ pandemic influenza plans and school closure statutes are intended to guide state and local officials, but most faced a great deal of uncertainty during the 2009 influenza H1N1 epidemic. Questions remained about whether, when, and for how long to close schools and about which agencies and officials had legal authority over school closures.

Methods

This study began with analysis of states’ school-closure statutes and pandemic influenza plans to identify the variations among them. An agent-based model of one state was used to represent as constants a population’s demographics, commuting patterns, work and school attendance, and community mixing patterns while repeated simulations explored the effects of variations in school closure authority, duration, closure thresholds, and reopening criteria.

Results

The results show no basis on which to justify statewide rather than school-specific or community-specific authority for school closures. Nor do these simulations offer evidence to require school closures promptly at the earliest stage of an epidemic. More important are criteria based on monitoring of local case incidence and on authority to sustain closure periods sufficiently to achieve epidemic mitigation.

Conclusions

This agent-based simulation suggests several ways to improve statutes and influenza plans. First, school closure should remain available to state and local authorities as an influenza mitigation strategy. Second, influenza plans need not necessarily specify the threshold for school closures but should clearly define provisions for early and ongoing local monitoring. Finally, school closure authority may be exercised at the statewide or local level, so long as decisions are informed by monitoring incidence in local communities and schools.

Local variations in spatial synchrony of influenza epidemics

Background

Understanding the mechanism of influenza spread across multiple geographic scales is not complete. While the mechanism of dissemination across regions and states of the United States has been described, understanding the determinants of dissemination between counties has not been elucidated. The paucity of high resolution spatial-temporal influenza incidence data to evaluate disease structure is often not available.

Methodology and Findings

We report on the underlying relationship between the spread of influenza and human movement between counties of one state. Significant synchrony in the timing of epidemics exists across the entire state and decay with distance (regional correlation = 62%). Synchrony as a function of population size display evidence of hierarchical spread with more synchronized epidemics occurring among the most populated counties. A gravity model describing movement between two populations is a stronger predictor of influenza spread than adult movement to and from workplaces suggesting that non-routine and leisure travel drive local epidemics.

Conclusions

These findings highlight the complex nature of influenza spread across multiple geographic scales.

Local spatial and temporal processes of influenza in Pennsylvania, USA: 2003-2009

Background

Influenza is a contagious respiratory disease responsible for annual seasonal epidemics in temperate climates. An understanding of how influenza spreads geographically and temporally within regions could result in improved public health prevention programs. The purpose of this study was to summarize the spatial and temporal spread of influenza using data obtained from the Pennsylvania Department of Health's influenza surveillance system.

Methodology and Findings

We evaluated the spatial and temporal patterns of laboratory-confirmed influenza cases in Pennsylvania, United States from six influenza seasons (2003–2009). Using a test of spatial autocorrelation, local clusters of elevated risk were identified in the South Central region of the state. Multivariable logistic regression indicated that lower monthly precipitation levels during the influenza season (OR = 0.52, 95% CI: 0.28, 0.94), fewer residents over age 64 (OR = 0.27, 95% CI: 0.10, 0.73) and fewer residents with more than a high school education (OR = 0.76, 95% CI: 0.61, 0.95) were significantly associated with membership in this cluster. In addition, time series analysis revealed a temporal lag in the peak timing of the influenza B epidemic compared to the influenza A epidemic.

Conclusions

These findings illustrate a distinct spatial cluster of cases in the South Central region of Pennsylvania. Further examination of the regional transmission dynamics within these clusters may be useful in planning public health influenza prevention programs.

Failure to detect simian immunodeficiency virus infection in a large Cameroonian cohort with high non-human primate exposure

Hunting and butchering of wildlife in Central Africa are known risk factors for a variety of human diseases, including HIV/AIDS. Due to the high incidence of human exposure to body fluids of non-human primates, the significant prevalence of simian immunodeficiency virus (SIV) in non-human primates, and hunting/butchering associated cross-species transmission of other retroviruses in Central Africa, it is possible that SIV is actively transmitted to humans from primate species other than mangabeys, chimpanzees, and/or gorillas. We evaluated SIV transmission to humans by screening 2,436 individuals that hunt and butcher non-human primates, a population in which simian foamy virus and simian T-lymphotropic virus were previously detected. We identified 23 individuals with high seroreactivity to SIV. Nucleic acid sequences of SIV genes could not be detected, suggesting that SIV infection in humans could occur at a lower frequency than infections with other retroviruses, including simian foamy virus and simian T-lymphotropic virus. Additional studies on human populations at risk for non-human primate zoonosis are necessary to determine whether these results are due to viral/host characteristics or are indicative of low SIV prevalence in primate species consumed as bushmeat as compared to other retroviruses in Cameroon.

A nonlinear programming approach for estimation of transmission parameters in childhood infectious disease using a continuous time model

Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.

Modeling Competing Infectious Pathogens from a Bayesian Perspective: Application to Influenza Studies with Incomplete Laboratory Results

In seasonal influenza epidemics, pathogens such as respiratory syncytial virus (RSV) often co-circulate with influenza and cause influenza-like illness (ILI) in human hosts. However, it is often impractical to test for each potential pathogen or to collect specimens for each observed ILI episode, making inference about influenza transmission difficult. In the setting of infectious diseases, missing outcomes impose a particular challenge because of the dependence among individuals. We propose a Bayesian competing-risk model for multiple co-circulating pathogens for inference on transmissibility and intervention efficacies under the assumption that missingness in the biological confirmation of the pathogen is ignorable. Simulation studies indicate a reasonable performance of the proposed model even if the number of potential pathogens is misspecified. They also show that a moderate amount of missing laboratory test results has only a small impact on inference about key parameters in the setting of close contact groups. Using the proposed model, we found that a non-pharmaceutical intervention is marginally protective against transmission of influenza A in a study conducted in elementary schools.