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1.  PREDICTIVE MODELING OF CHOLERA OUTBREAKS IN BANGLADESH 
The annals of applied statistics  2016;10(2):575-595.
Despite seasonal cholera outbreaks in Bangladesh, little is known about the relationship between environmental conditions and cholera cases. We seek to develop a predictive model for cholera outbreaks in Bangladesh based on environmental predictors. To do this, we estimate the contribution of environmental variables, such as water depth and water temperature, to cholera outbreaks in the context of a disease transmission model. We implement a method which simultaneously accounts for disease dynamics and environmental variables in a Susceptible-Infected-Recovered-Susceptible (SIRS) model. The entire system is treated as a continuous-time hidden Markov model, where the hidden Markov states are the numbers of people who are susceptible, infected, or recovered at each time point, and the observed states are the numbers of cholera cases reported. We use a Bayesian framework to fit this hidden SIRS model, implementing particle Markov chain Monte Carlo methods to sample from the posterior distribution of the environmental and transmission parameters given the observed data. We test this method using both simulation and data from Mathbaria, Bangladesh. Parameter estimates are used to make short-term predictions that capture the formation and decline of epidemic peaks. We demonstrate that our model can successfully predict an increase in the number of infected individuals in the population weeks before the observed number of cholera cases increases, which could allow for early notification of an epidemic and timely allocation of resources.
doi:10.1214/16-AOAS908
PMCID: PMC5061460  PMID: 27746850
2.  The First Reported Outbreak of Chikungunya in the U.S. Virgin Islands, 2014–2015 
The chikungunya virus (CHIKV) epidemic in the Americas is of significant public health importance due to the lack of effective control and prevention strategies, severe disease morbidity among susceptible populations, and potential for persistent arthralgia and long-term impaired physical functionality. Using surveillance data of suspected CHIKV cases, we describe the first reported outbreak in the U.S. Virgin Islands. CHIKV incidence was highest among individuals aged 55–64 years (13.1 cases per 1,000 population) and lowest among individuals aged 0–14 years (1.8 cases per 1,000 population). Incidence was higher among women compared to men (6.6 and 5.0 cases per 1,000 population, respectively). More than half of reported laboratory-positive cases experienced fever lasting 2–7 days, chills/rigor, myalgia, anorexia, and headache. No clinical symptoms apart from the suspected case definition of fever ≥ 38°C and arthralgia were significantly associated with being a reported laboratory-positive case. These results contribute to our knowledge of demographic risk factors and clinical manifestations of CHIKV disease and may aid in mitigating future CHIKV outbreaks in the Caribbean.
doi:10.4269/ajtmh.16-0288
PMCID: PMC5062794  PMID: 27402523
3.  One versus two doses: what is the best use of vaccine in an influenza pandemic? 
Epidemics  2015;13:17-27.
Avian influenza A (H7N9), emerged in China in April 2013, sparking fears of a new, highly pathogenic, influenza pandemic. In addition, avian influenza A (H5N1) continues to circulate and remains a threat. Currently, influenza H7N9 vaccines are being tested to be stockpiled along with H5N1 vaccines. These vaccines require two doses, 21 days apart, for maximal protection. We developed a mathematical model to evaluate two possible strategies for allocating limited vaccine supplies: a one-dose strategy, where a larger number of people are vaccinated with a single dose, or a two-dose strategy, where half as many people are vaccinated with two doses. We prove that there is a threshold in the level of protection obtained after the first dose, below which vaccinating with two doses results in a lower illness attack rate than with the one-dose strategy; but above the threshold, the one-dose strategy would be better. For reactive vaccination, we show that the optimal use of vaccine depends on several parameters, with the most important one being the level of protection obtained after the first dose. We describe how these vaccine dosing strategies can be integrated into effective pandemic control plans.
doi:10.1016/j.epidem.2015.06.001
PMCID: PMC4664891  PMID: 26616038
influenza; influenza vaccine; mathematical model; infectious disease modeling
4.  Containing Ebola at the Source with Ring Vaccination 
PLoS Neglected Tropical Diseases  2016;10(11):e0005093.
Interim results from the Guinea Ebola ring vaccination trial suggest high efficacy of the rVSV-ZEBOV vaccine. These findings open the door to the use of ring vaccination strategies in which the contacts and contacts of contacts of each index case are promptly vaccinated to contain future Ebola virus disease outbreaks. To provide a numerical estimate of the effectiveness of ring vaccination strategies we introduce a spatially explicit agent-based model to simulate Ebola outbreaks in the Pujehun district, Sierra Leone, structurally similar to previous modelling approaches. We find that ring vaccination can successfully contain an outbreak for values of the effective reproduction number up to 1.6. Through an extensive sensitivity analysis of parameters characterising the readiness and capacity of the health care system, we identify interventions that, alongside ring vaccination, could increase the likelihood of containment. In particular, shortening the time from symptoms onset to hospitalisation to 2–3 days on average through improved contact tracing procedures, adding a 2km spatial component to the vaccination ring, and decreasing human mobility by quarantining affected areas might contribute increase our ability to contain outbreaks with effective reproduction number up to 2.6. These results have implications for future control of Ebola and other emerging infectious disease threats.
Author Summary
When the 2014–15 Ebola outbreak in West Africa began, no licensed vaccines for the disease were available. The rVSV-ZEBOV vaccine was developed during the course of the epidemic and underwent a clinical trial demonstrating 100% efficacy when vaccinating contacts and contacts of contacts of confirmed Ebola cases (an approach called ring vaccination). However, the trial did not provide any understanding on whether this vaccination strategy can be effective in containing future Ebola virus disease outbreaks. Through a modelling study on a region of Sierra Leone, we provide numerical estimates for the effectiveness of ring vaccination: we show that outbreaks with moderate transmission potential, with no more than 1.6 secondary cases generated by an index case on average, can be successfully contained; more extensive vaccination(e.g., including spatial rings around index cases) and reinforcement of the healthcare system would increase the likelihood of containment even if the virus were more transmissible than in the past. Our results provide implications for control plans of possible future Ebola outbreaks.
doi:10.1371/journal.pntd.0005093
PMCID: PMC5091901  PMID: 27806049
5.  Spatiotemporal dynamics of the Ebola epidemic in Guinea and implications for vaccination and disease elimination: a computational modeling analysis 
BMC Medicine  2016;14(1):130.
Background
Among the three countries most affected by the Ebola virus disease outbreak in 2014–2015, Guinea presents an unusual spatiotemporal epidemic pattern, with several waves and a long tail in the decay of the epidemic incidence.
Methods
Here, we develop a stochastic agent-based model at the level of a single household that integrates detailed data on Guinean demography, hospitals, Ebola treatment units, contact tracing, and safe burial interventions. The microsimulation-based model is used to assess the effect of each control strategy and the probability of elimination of the epidemic according to different intervention scenarios, including ring vaccination with the recombinant vesicular stomatitis virus-vectored vaccine.
Results
The numerical results indicate that the dynamics of the Ebola epidemic in Guinea can be quantitatively explained by the timeline of the implemented interventions. In particular, the early availability of Ebola treatment units and the associated isolation of cases and safe burials helped to limit the number of Ebola cases experienced by Guinea. We provide quantitative evidence of a strong negative correlation between the time series of cases and the number of traced contacts. This result is confirmed by the computational model that suggests that contact tracing effort is a key determinant in the control and elimination of the disease. In data-driven microsimulations, we find that tracing at least 5–10 contacts per case is crucial in preventing epidemic resurgence during the epidemic elimination phase. The computational model is used to provide an analysis of the ring vaccination trial highlighting its potential effect on disease elimination.
Conclusions
We identify contact tracing as one of the key determinants of the epidemic’s behavior in Guinea, and we show that the early availability of Ebola treatment unit beds helped to limit the number of Ebola cases in Guinea.
Electronic supplementary material
The online version of this article (doi:10.1186/s12916-016-0678-3) contains supplementary material, which is available to authorized users.
doi:10.1186/s12916-016-0678-3
PMCID: PMC5013652  PMID: 27600737
Computational modeling; Intervention strategies; Ebola epidemiology
6.  The Dengue Vaccine Pipeline: Implications for the Future of Dengue Control 
Vaccine  2015;33(29):3293-3298.
Dengue has become the most rapidly expanding mosquito-borne infectious disease on the planet, surpassing malaria and infecting at least 390 million people per year. There is no effective treatment for dengue illness other than supportive care, especially for severe cases. Symptoms can be mild or life-threatening as in dengue hemorrhagic fever and dengue shock syndrome. Vector control has been only partially successful in decreasing dengue transmission. The potential use of safe and effective tetravalent dengue vaccines is an attractive addition to prevent disease or minimize the possibility of epidemics. There are currently no licensed dengue vaccines. This review summarizes the current status of all dengue vaccine candidates in clinical evaluation. Currently five candidate vaccines are in human clinical trials. One has completed two Phase III trials, two are in Phase II trials, and three are in Phase I testing.
doi:10.1016/j.vaccine.2015.05.010
PMCID: PMC4470297  PMID: 25989449
dengue virus; dengue vaccine; vaccine; efficacy; clinical trial
7.  THE CASE FOR A TYPHOID VACCINE PROBE STUDY AND OVERVIEW OF DESIGN ELEMENTS 
Vaccine  2015;33(0 3):C30-C35.
Recent advances in typhoid vaccine, and consideration of support from Gavi, the Vaccine Alliance, raise the possibility that some endemic countries will introduce typhoid vaccine into public immunization programs. This decision, however, is limited by lack of definitive information on disease burden. We propose use of a vaccine probe study approach. This approach would more clearly assess the total burden of typhoid across different syndromic groups and account for lack of access to care, poor diagnostics, incomplete laboratory testing, lack of mortality and intestinal perforation surveillance, and increasing antibiotic resistance. We propose a cluster randomized trial design using a mass immunization campaign among all age groups, with monitoring over a 4-year period of a variety of outcomes. The primary outcome would be the vaccine preventable disease incidence of prolonged fever hospitalization. Sample size calculations suggest that such a study would be feasible over a reasonable set of assumptions.
doi:10.1016/j.vaccine.2015.03.085
PMCID: PMC4633310  PMID: 25912286
clinical trial; disease burden; trial design; typhoid; typhoid vaccine; vaccine; vaccine probe study
8.  Projected Impact of Dengue Vaccination in Yucatán, Mexico 
PLoS Neglected Tropical Diseases  2016;10(5):e0004661.
Dengue vaccines will soon provide a new tool for reducing dengue disease, but the effectiveness of widespread vaccination campaigns has not yet been determined. We developed an agent-based dengue model representing movement of and transmission dynamics among people and mosquitoes in Yucatán, Mexico, and simulated various vaccine scenarios to evaluate effectiveness under those conditions. This model includes detailed spatial representation of the Yucatán population, including the location and movement of 1.8 million people between 375,000 households and 100,000 workplaces and schools. Where possible, we designed the model to use data sources with international coverage, to simplify re-parameterization for other regions. The simulation and analysis integrate 35 years of mild and severe case data (including dengue serotype when available), results of a seroprevalence survey, satellite imagery, and climatological, census, and economic data. To fit model parameters that are not directly informed by available data, such as disease reporting rates and dengue transmission parameters, we developed a parameter estimation toolkit called AbcSmc, which we have made publicly available. After fitting the simulation model to dengue case data, we forecasted transmission and assessed the relative effectiveness of several vaccination strategies over a 20 year period. Vaccine efficacy is based on phase III trial results for the Sanofi-Pasteur vaccine, Dengvaxia. We consider routine vaccination of 2, 9, or 16 year-olds, with and without a one-time catch-up campaign to age 30. Because the durability of Dengvaxia is not yet established, we consider hypothetical vaccines that confer either durable or waning immunity, and we evaluate the use of booster doses to counter waning. We find that plausible vaccination scenarios with a durable vaccine reduce annual dengue incidence by as much as 80% within five years. However, if vaccine efficacy wanes after administration, we find that there can be years with larger epidemics than would occur without any vaccination, and that vaccine booster doses are necessary to prevent this outcome.
Author Summary
Dengue is a mosquito-transmitted viral disease that is common throughout the tropics. Despite a long history in humans and extensive efforts to control dengue transmission in many countries, the number, severity, and geographic range of reported cases is increasing. Most control efforts have focused on controlling mosquito populations, but the main vector, Aedes aegypti, flourishes in human-disturbed and indoor environments. Because the mosquitoes prefer to bite during the day when people are active and potentially moving around high-risk locations, fixed barriers like bed nets are not effective. Several dengue vaccines are being actively developed and may become valuable tools in dengue control. Using historical dengue data from Yucatán, Mexico, we fit a detailed simulation of human and mosquito populations to project future transmission, then used efficacy data from vaccine trials to evaluate the benefit of potential vaccination deployment strategies in the region. For a durable vaccine, we find that population-level, annual vaccine effectiveness approaches 65% by the end of the 20-year forecast period. For waning vaccines, however, effectiveness is greatly reduced–and sometimes negative–unless booster vaccinations are used.
doi:10.1371/journal.pntd.0004661
PMCID: PMC4882069  PMID: 27227883
9.  Molecular Infectious Disease Epidemiology: Survival Analysis and Algorithms Linking Phylogenies to Transmission Trees 
PLoS Computational Biology  2016;12(4):e1004869.
Recent work has attempted to use whole-genome sequence data from pathogens to reconstruct the transmission trees linking infectors and infectees in outbreaks. However, transmission trees from one outbreak do not generalize to future outbreaks. Reconstruction of transmission trees is most useful to public health if it leads to generalizable scientific insights about disease transmission. In a survival analysis framework, estimation of transmission parameters is based on sums or averages over the possible transmission trees. A phylogeny can increase the precision of these estimates by providing partial information about who infected whom. The leaves of the phylogeny represent sampled pathogens, which have known hosts. The interior nodes represent common ancestors of sampled pathogens, which have unknown hosts. Starting from assumptions about disease biology and epidemiologic study design, we prove that there is a one-to-one correspondence between the possible assignments of interior node hosts and the transmission trees simultaneously consistent with the phylogeny and the epidemiologic data on person, place, and time. We develop algorithms to enumerate these transmission trees and show these can be used to calculate likelihoods that incorporate both epidemiologic data and a phylogeny. A simulation study confirms that this leads to more efficient estimates of hazard ratios for infectiousness and baseline hazards of infectious contact, and we use these methods to analyze data from a foot-and-mouth disease virus outbreak in the United Kingdom in 2001. These results demonstrate the importance of data on individuals who escape infection, which is often overlooked. The combination of survival analysis and algorithms linking phylogenies to transmission trees is a rigorous but flexible statistical foundation for molecular infectious disease epidemiology.
Author Summary
Recent work has attempted to use whole-genome sequence data from pathogens to reconstruct the transmission trees linking infectors and infectees in outbreaks. However, transmission trees from one outbreak do not generalize to future outbreaks. Reconstruction of transmission trees is most useful to public health if it leads to generalizable scientific insights about disease transmission. Accurate estimates of transmission parameters can help identify risk factors for transmission and aid the design and evaluation of public health interventions for emerging infections. Using statistical methods for time-to-event data (survival analysis), estimation of transmission parameters is based on sums or averages over the possible transmission trees. By providing partial information about who infected whom, a pathogen phylogeny can reduce the set of possible transmission trees and increase the precision of transmission parameter estimates. We derive algorithms that enumerate the transmission trees consistent with a pathogen phylogeny and epidemiologic data, show how to calculate likelihoods for transmission data with a phylogeny, and apply these methods to a foot and mouth disease outbreak in the United Kingdom in 2001. These methods will allow pathogen genetic sequences to be incorporated into the analysis of outbreak investigations, vaccine trials, and other studies of infectious disease transmission.
doi:10.1371/journal.pcbi.1004869
PMCID: PMC4829193  PMID: 27070316
10.  Invited Commentary: Evaluating Vaccination Programs Using Genetic Sequence Data 
American Journal of Epidemiology  2009;170(12):1464-1466.
Genomic data will become an increasingly important component of epidemiologic studies in coming years. The authors of the accompanying Journal article, van Ballegooijen et al. (Am J Epidemiol. 2009;170(12):1455–1463), are to be commended for attempting to use the coalescent analysis of viral sequence data to evaluate a hepatitis B vaccination program. Coalescent theory attempts to link the phylogenetic history of populations with rates of population growth and decline. In particular, under certain assumptions, a reduction in genetic diversity can be interpreted as a reduction in disease incidence. However, the authors of this commentary contend that van Ballegooijen et al.’s interpretation of changes in viral genetic diversity as a measure of hepatitis B vaccine effectiveness has major limitations. Because of the potential use of these methods in future vaccination studies, the authors discuss the utility of these methods and the data requirements needed for them to be convincing. First, data sets should be large enough to provide sufficient epidemiologic-scale resolution. Second, data need to reflect sufficiently fine-grained temporal sampling. Third, other processes that can potentially influence genetic diversity and confuse demographic inferences should be considered.
doi:10.1093/aje/kwp366
PMCID: PMC2800275  PMID: 19910381
communicable diseases; disease notification; disease transmission, infectious; genetic variation; hepatitis B virus; molecular sequence data; vaccination
11.  Spatio-temporal spread of the Ebola 2014 outbreak in Liberia and the effectiveness of non-pharmaceutical interventions: a computational modelling analysis 
The Lancet. Infectious diseases  2015;15(2):204-211.
Summary
Background
The 2014 Ebola epidemic in West Africa defines an unprecedented health threat. We developed a model of Ebola transmission that integrates detailed geographical and demographic data from Liberia to overcome the limitations of non-spatial approaches in projecting the disease dynamics and assessing non-pharmaceutical control interventions.
Methods
We use a spatial agent-based model calibrated using a Markov chain Monte Carlo approach. The model is used to estimate Ebola transmission parameters and investigate the effectiveness of interventions such as availability of Ebola Treatment Units, safe burials procedures and household protection kits.
Findings
Through August 16, 2014, we estimate that 38·3% (95%CI 17·4-76·4) of infections were acquired in hospitals, 30·7% (95%CI 14·1-46·4) in households, and 8·9% (95%CI 3·3-11·8) while participating in funerals. The movement and mixing of Ebola and non-Ebola patients in hospitals at the early stage of the epidemic is found to be a sufficient driver of the observed pattern of spatial spread. The subsequent decrease of incidence at country and county level is ascribable to the increasing availability of Ebola treatment units – which in turn contributed to drastically decrease hospital transmission – safe burials, and distribution of household protection kits.
Interpretation
The model allows evaluating intervention options and disentangling their role in the decrease of incidence observed since September 7, 2014. High-quality data - e.g. to estimate household secondary attack rate, contact patterns within hospitals, and effects of ongoing interventions - are needed to reduce uncertainty in model estimates.
doi:10.1016/S1473-3099(14)71074-6
PMCID: PMC4409131  PMID: 25575618
14.  A Pathway EM-Algorithm for Estimating Vaccine E cacy with a Non-Monotone Validation Set 
Biometrics  2014;70(3):568-578.
Summary
Here we consider time-to-event data where individuals can experience two or more types of events that are not distinguishable from one another without further confirmation, perhaps by laboratory test. The event type of primary interest can occur only once. The other types of events can recur. If the type of a portion of the events is identified, this forms a validation set. However, even if a random sample of events are tested, confirmations can be missing nonmonotonically, creating uncertainty about whether an individual is still at risk for the event of interest. For example, in a study to estimate e cacy of an influenza vaccine, an individual may experience a sequence of symptomatic respiratory illnesses caused by various pathogens over the season. Often only a limited number of these episodes are confirmed in the laboratory to be influenza-related or not. We propose two novel methods to estimate covariate e ects in this survival setting, and subsequently vaccine e cacy. The first is a pathway Expectation-Maximization (EM) algorithm that takes into account all pathways of event types in an individual compatible with that individual’s test outcomes. The pathway EM iteratively estimates baseline hazards that are used to weight possible event types. The second method is a non-iterative pathway piecewise validation method that does not estimate the baseline hazards. These methods are compared with a previous simpler method. Simulation studies suggest mean squared error is lower in the e cacy estimates when the baseline hazards are estimated, especially at higher hazard rates. We use the pathway EM-algorithm to reevaluate the e cacy of a trivalent live-attenuated influenza vaccine during the 2003-2004 influenza season in Temple-Belton, Texas, and compare our results with a previously published analysis.
doi:10.1111/biom.12173
PMCID: PMC4209209  PMID: 24766139
EM algorithm; Missing data; Vaccine efficacy; Validation set
15.  Assessing Effects of Cholera Vaccination in the Presence of Interference 
Biometrics  2014;70(3):731-741.
Summary
Interference occurs when the treatment of one person affects the outcome of another. For example, in infectious diseases, whether one individual is vaccinated may affect whether another individual becomes infected or develops disease. Quantifying such indirect (or spillover) effects of vaccination could have important public health or policy implications. In this paper we use recently developed inverse-probability weighted (IPW) estimators of treatment effects in the presence of interference to analyze an individually-randomized, placebo-controlled trial of cholera vaccination that targeted 121,982 individuals in Matlab, Bangladesh. Because these IPW estimators have not been employed previously, a simulation study was also conducted to assess the empirical behavior of the estimators in settings similar to the cholera vaccine trial. Simulation study results demonstrate the IPW estimators can yield unbiased estimates of the direct, indirect, total and overall effects of vaccination when there is interference provided the untestable no unmeasured confounders assumption holds and the group-level propensity score model is correctly specified. Application of the IPW estimators to the cholera vaccine trial indicates the presence of interference. For example, the IPW estimates suggest on average 5.29 fewer cases of cholera per 1000 person-years (95% confidence interval 2.61, 7.96) will occur among unvaccinated individuals within neighborhoods with 60% vaccine coverage compared to neighborhoods with 32% coverage. Our analysis also demonstrates how not accounting for interference can render misleading conclusions about the public health utility of vaccination.
doi:10.1111/biom.12184
PMCID: PMC4239215  PMID: 24845800
Causal inference; Interference; Inverse-probability weighted estimators; Spillover effect; Two-stage randomization; Vaccine
16.  Comparing Bounds for Vaccine Effects on Infectiousness 
Epidemiology (Cambridge, Mass.)  2012;23(6):931-932.
doi:10.1097/EDE.0b013e31826d0741
PMCID: PMC3482261  PMID: 23038122
Causal inference; infectious disease; infectiousness; interference; principal stratification; vaccine efficacy
17.  Economic evaluation of influenza pandemic mitigation strategies in the us using a stochastic microsimulation transmission model 
Objectives
To project the potential economic impact of pandemic influenza mitigation strategies from a societal perspective in the United States.
Methods
We use a stochastic agent-based model to simulate pandemic influenza in the community. We compare 17 strategies: targeted antiviral prophylaxis (TAP) alone and in combination with school closure as well as prevaccination.
Results
In the absence of intervention, we predict a 50% attack rate with an economic impact of $187 per capita as loss to society. Full TAP is the most effective single strategy, reducing number of cases by 54% at the lowest cost to society ($127 per capita). Prevaccination reduces number of cases by 48% and is the second least costly alternative ($140 per capita). Adding school closure to full TAP or prevaccination further improves health outcomes, but increases total cost to society by approximately $2700 per capita.
Conclusion
Full targeted antiviral prophylaxis is an effective and cost-saving measure for mitigating pandemic influenza.
doi:10.1111/j.1524-4733.2008.00437.x
PMCID: PMC3710126  PMID: 18671770
Influenza; Human Disease Outbreaks; Cost-Benefit Analysis; Economics; Pharmaceutical Models; Theoretical; Computer Simulation
18.  Assessing the impact of travel restrictions on international spread of the 2014 West African Ebola epidemic 
The quick spread of an Ebola outbreak in West Africa has led a number of countries and airline companies to issue travel bans to the affected areas. Considering data up to 31 Aug 2014, we assess the impact of the resulting traffic reductions with detailed numerical simulations of the international spread of the epidemic. Traffic reductions are shown to delay by only a few weeks the risk that the outbreak extends to new countries.
PMCID: PMC4415609  PMID: 25358040
19.  Emerging, evolving, and established infectious diseases and interventions 
Science (New York, N.Y.)  2014;345(6202):1292-1294.
doi:10.1126/science.1254166
PMCID: PMC4408765  PMID: 25214617
20.  Causal Inference for Vaccine Effects on Infectiousness 
The International Journal of Biostatistics  2012;8(2):10.2202/1557-4679.1354 /j/ijb.2012.8.issue-2/1557-4679.1354/1557-4679.1354.xml.
If a vaccine does not protect individuals completely against infection, it could still reduce infectiousness of infected vaccinated individuals to others. Typically, vaccine efficacy for infectiousness is estimated based on contrasts between the transmission risk to susceptible individuals from infected vaccinated individuals compared with that from infected unvaccinated individuals. Such estimates are problematic, however, because they are subject to selection bias and do not have a causal interpretation. Here, we develop causal estimands for vaccine efficacy for infectiousness for four different scenarios of populations of transmission units of size two. These causal estimands incorporate both principal stratification, based on the joint potential infection outcomes under vaccine and control, and interference between individuals within transmission units. In the most general scenario, both individuals can be exposed to infection outside the transmission unit and both can be assigned either vaccine or control. The three other scenarios are special cases of the general scenario where only one individual is exposed outside the transmission unit or can be assigned vaccine. The causal estimands for vaccine efficacy for infectiousness are well defined only within certain principal strata and, in general, are identifiable only with strong unverifiable assumptions. Nonetheless, the observed data do provide some information, and we derive large sample bounds on the causal vaccine efficacy for infectiousness estimands. An example of the type of data observed in a study to estimate vaccine efficacy for infectiousness is analyzed in the causal inference framework we developed.
doi:10.2202/1557-4679.1354
PMCID: PMC3348179  PMID: 22499732
causal inference; principal stratification; interference; infectious disease; vaccine
21.  Interference and Sensitivity Analysis 
Causal inference with interference is a rapidly growing area. The literature has begun to relax the “no-interference” assumption that the treatment received by one individual does not affect the outcomes of other individuals. In this paper we briefly review the literature on causal inference in the presence of interference when treatments have been randomized. We then consider settings in which causal effects in the presence of interference are not identified, either because randomization alone does not suffice for identification, or because treatment is not randomized and there may be unmeasured confounders of the treatment-outcome relationship. We develop sensitivity analysis techniques for these settings. We describe several sensitivity analysis techniques for the infectiousness effect which, in a vaccine trial, captures the effect of the vaccine of one person on protecting a second person from infection even if the first is infected. We also develop two sensitivity analysis techniques for causal effects in the presence of unmeasured confounding which generalize analogous techniques when interference is absent. These two techniques for unmeasured confounding are compared and contrasted.
doi:10.1214/14-STS479
PMCID: PMC4300555  PMID: 25620841
Causal inference; infectiousness effect; interference; sensitivity analysis; spillover effect; stable unit treatment value assumption; vaccine trial
22.  School-Located Influenza Vaccination Reduces Community Risk for Influenza and Influenza-Like Illness Emergency Care Visits 
PLoS ONE  2014;9(12):e114479.
Background
School-located influenza vaccination (SLIV) programs can substantially enhance the sub-optimal coverage achieved under existing delivery strategies. Randomized SLIV trials have shown these programs reduce laboratory-confirmed influenza among both vaccinated and unvaccinated children. This work explores the effectiveness of a SLIV program in reducing the community risk of influenza and influenza-like illness (ILI) associated emergency care visits.
Methods
For the 2011/12 and 2012/13 influenza seasons, we estimated age-group specific attack rates (AR) for ILI from routine surveillance and census data. Age-group specific SLIV program effectiveness was estimated as one minus the AR ratio for Alachua County versus two comparison regions: the 12 county region surrounding Alachua County, and all non-Alachua counties in Florida.
Results
Vaccination of ∼50% of 5–17 year-olds in Alachua reduced their risk of ILI-associated visits, compared to the rest of Florida, by 79% (95% confidence interval: 70, 85) in 2011/12 and 71% (63, 77) in 2012/13. The greatest indirect effectiveness was observed among 0–4 year-olds, reducing AR by 89% (84, 93) in 2011/12 and 84% (79, 88) in 2012/13. Among all non-school age residents, the estimated indirect effectiveness was 60% (54, 65) and 36% (31, 41) for 2011/12 and 2012/13. The overall effectiveness among all age-groups was 65% (61, 70) and 46% (42, 50) for 2011/12 and 2012/13.
Conclusion
Wider implementation of SLIV programs can significantly reduce the influenza-associated public health burden in communities.
doi:10.1371/journal.pone.0114479
PMCID: PMC4260868  PMID: 25489850
23.  Comparative Effectiveness of Different Strategies of Oral Cholera Vaccination in Bangladesh: A Modeling Study 
Background
Killed, oral cholera vaccines have proven safe and effective, and several large-scale mass cholera vaccination efforts have demonstrated the feasibility of widespread deployment. This study uses a mathematical model of cholera transmission in Bangladesh to examine the effectiveness of potential vaccination strategies.
Methods & Findings
We developed an age-structured mathematical model of cholera transmission and calibrated it to reproduce the dynamics of cholera in Matlab, Bangladesh. We used the model to predict the effectiveness of different cholera vaccination strategies over a period of 20 years. We explored vaccination programs that targeted one of three increasingly focused age groups (the entire vaccine-eligible population of age one year and older, children of ages 1 to 14 years, or preschoolers of ages 1 to 4 years) and that could occur either as campaigns recurring every five years or as continuous ongoing vaccination efforts. Our modeling results suggest that vaccinating 70% of the population would avert 90% of cholera cases in the first year but that campaign and continuous vaccination strategies differ in effectiveness over 20 years. Maintaining 70% coverage of the population would be sufficient to prevent sustained transmission of endemic cholera in Matlab, while vaccinating periodically every five years is less effective. Selectively vaccinating children 1–14 years old would prevent the most cholera cases per vaccine administered in both campaign and continuous strategies.
Conclusions
We conclude that continuous mass vaccination would be more effective against endemic cholera than periodic campaigns. Vaccinating children averts more cases per dose than vaccinating all age groups, although vaccinating only children is unlikely to control endemic cholera in Bangladesh. Careful consideration must be made before generalizing these results to other regions.
Author Summary
Bangladesh has a high burden of cholera and may become the first country to use cholera vaccine on a large scale. Mass cholera vaccination may be hard to justify to international funding agencies because of the modest efficacy of existing vaccines and their limited duration of protection. However, mass cholera vaccination can induce high levels of indirect protection in a population, i.e., protecting even unvaccinated individuals by lowering cholera incidence, and a case for cost-effective cholera vaccination could be made. Mathematical modeling is one way to predict the magnitude of indirect protection conferred by a proposed vaccination program. Here, we predict the effectiveness of various mass cholera vaccination strategies in Bangladesh using a mathematical model. We found that maintaining high levels of vaccination coverage in children could be very effective in reducing the burden of cholera, and secondary transmission of cholera would virtually stop when 70% of the population is vaccinated. Mathematical modeling may play a key role in planning widespread cholera vaccination efforts in Bangladesh and other countries.
doi:10.1371/journal.pntd.0003343
PMCID: PMC4256212  PMID: 25473851
24.  Household Transmission of Vibrio cholerae in Bangladesh 
Background
Vibrio cholerae infections cluster in households. This study's objective was to quantify the relative contribution of direct, within-household exposure (for example, via contamination of household food, water, or surfaces) to endemic cholera transmission. Quantifying the relative contribution of direct exposure is important for planning effective prevention and control measures.
Methodology/Principal Findings
Symptom histories and multiple blood and fecal specimens were prospectively collected from household members of hospital-ascertained cholera cases in Bangladesh from 2001–2006. We estimated the probabilities of cholera transmission through 1) direct exposure within the household and 2) contact with community-based sources of infection. The natural history of cholera infection and covariate effects on transmission were considered. Significant direct transmission (p-value<0.0001) occurred among 1414 members of 364 households. Fecal shedding of O1 El Tor Ogawa was associated with a 4.9% (95% confidence interval: 0.9%–22.8%) risk of infection among household contacts through direct exposure during an 11-day infectious period (mean length). The estimated 11-day risk of O1 El Tor Ogawa infection through exposure to community-based sources was 2.5% (0.8%–8.0%). The corresponding estimated risks for O1 El Tor Inaba and O139 infection were 3.7% (0.7%–16.6%) and 8.2% (2.1%–27.1%) through direct exposure, and 3.4% (1.7%–6.7%) and 2.0% (0.5%–7.3%) through community-based exposure. Children under 5 years-old were at elevated risk of infection. Limitations of the study may have led to an underestimation of the true risk of cholera infection. For instance, available covariate data may have incompletely characterized levels of pre-existing immunity to cholera infection. Transmission via direct exposure occurring outside of the household was not considered.
Conclusions
Direct exposure contributes substantially to endemic transmission of symptomatic cholera in an urban setting. We provide the first estimate of the transmissibility of endemic cholera within prospectively-followed members of households. The role of direct transmission must be considered when planning cholera control activities.
Author Summary
Since John Snow's ground-breaking investigations of the devastating outbreaks in 19th-century London, cholera has been considered the quintessential waterborne human infection, transmitting via fecal contamination of environmental water sources. Recently, renewed interest has been paid to the potential importance of transmission through direct exposure within close-contact groups, such as, via fecal contamination of surfaces, food, or drinking water within households. Significant direct transmission of cholera within close contact groups would represent a new target for innovative prevention and control strategies. We estimated the probability of transmission 1) via direct contact within 364 urban households located in an endemic cholera setting (Dhaka, Bangladesh) and 2) via exposure to sources located outside of these households. In this setting we estimated a 4 to 8 percent probability of becoming infected with cholera via direct exposure within households in this setting versus a 2 to 3 percent likelihood of infection due to exposure to external sources over a comparable time period. Our results demonstrate that direct (within-household) transmission is a significant component of endemic cholera transmission, suggesting that biomedical and behavioral-modification interventions specifically targeting this mode of transmission could substantially reduce the cholera burden in this type of setting.
doi:10.1371/journal.pntd.0003314
PMCID: PMC4238997  PMID: 25411971
25.  Assessing the International Spreading Risk Associated with the 2014 West African Ebola Outbreak 
PLoS Currents  2014;6:ecurrents.outbreaks.cd818f63d40e24aef769dda7df9e0da5.
Background: The 2014 West African Ebola Outbreak is so far the largest and deadliest recorded in history. The affected countries, Sierra Leone, Guinea, Liberia, and Nigeria, have been struggling to contain and to mitigate the outbreak. The ongoing rise in confirmed and suspected cases, 2615 as of 20 August 2014, is considered to increase the risk of international dissemination, especially because the epidemic is now affecting cities with major commercial airports. Method: We use the Global Epidemic and Mobility Model to generate stochastic, individual based simulations of epidemic spread worldwide, yielding, among other measures, the incidence and seeding events at a daily resolution for 3,362 subpopulations in 220 countries. The mobility model integrates daily airline passenger traffic worldwide and the disease model includes the community, hospital, and burial transmission dynamic. We use a multimodel inference approach calibrated on data from 6 July to the date of 9 August 2014. The estimates obtained were used to generate a 3-month ensemble forecast that provides quantitative estimates of the local transmission of Ebola virus disease in West Africa and the probability of international spread if the containment measures are not successful at curtailing the outbreak. Results: We model the short-term growth rate of the disease in the affected West African countries and estimate the basic reproductive number to be in the range 1.5 − 2.0 (interval at the 1/10 relative likelihood). We simulated the international spreading of the outbreak and provide the estimate for the probability of Ebola virus disease case importation in countries across the world. Results indicate that the short-term (3 and 6 weeks) probability of international spread outside the African region is small, but not negligible. The extension of the outbreak is more likely occurring in African countries, increasing the risk of international dissemination on a longer time scale.
doi:10.1371/currents.outbreaks.cd818f63d40e24aef769dda7df9e0da5
PMCID: PMC4169359  PMID: 25642360
2014WA; disease model; disease outbreak; EVD; infectious disease

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