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1.  The Effect of Age on Transmission of 2009 Pandemic Influenza A (H1N1) in a Camp and Associated Households 
Epidemiology (Cambridge, Mass.)  2011;22(2):10.1097/EDE.0b013e3182060ca5.
A major portion of influenza disease burden during the 2009 pandemic was observed among young people.
We examined the effect of age on the transmission of influenza-like illness associated with the 2009 pandemic influenza A (H1N1) virus (pH1N1) for an April–May 2009 outbreak among youth-camp participants and household contacts in Washington State.
An influenza-like illness attack rate of 51% was found among 96 camp participants. We observed a cabin secondary attack rate of 42% (95% confidence interval = 21%–66%) and a camp local reproductive number of 2.7 (1.7–4.1) for influenza-like illness among children (less than 18 years old). Among the 136 contacts in the 41 households with an influenza-like illness index case who attended the camp, the influenza-like illness secondary attack rate was 11% for children (5%–21%) and 4% for adults (2%–8%). The odds ratio for influenza-like illness among children versus adults was 3.1 (1.3–7.3).
The strong age effect, combined with the low number of susceptible children per household (1.2), plausibly explains the lower-than-expected household secondary attack rate for influenza-like illness, illustrating the importance of other venues where children congregate for sustaining community transmission. Quantifying the effects of age on pH1N1 transmission is important for informing effective intervention strategies.
PMCID: PMC3755879  PMID: 21233714
2.  Critical immune and vaccination thresholds for determining multiple influenza epidemic waves 
Epidemics  2011;4(1):22-32.
Previous influenza pandemics (1918, 1957, and 1968) have all had multiple waves. The 2009 pandemic influenza A(H1N1) (pandemic H1N1) started in April 2009 and was followed, in the United States (US) and temperate Northern Hemisphere, by a second wave during the fall of 2009. The ratio of susceptible and immune individuals in a population at the end of a wave determines the potential and magnitude of a subsequent wave. As influenza vaccines are not completely protective, there was a combined immunity in the population at the beginning of 2010 (due to vaccination and due to previous natural infection), and it was uncertain if this mixture of herd immunity was enough to prevent a third wave of pandemic influenza during the winter of 2010. Motivated by this problem, we developed a mathematical deterministic two-group epidemic model with vaccination and calibrated it for the 2009 pandemic H1N1. Then, applying methods from mathematical epidemiology we developed a scheme that allowed us to determine critical thresholds for vaccine-induced and natural immunity that would prevent the spread of influenza. Finally, we estimated the level of combined immunity in the US during winter 2010. Our results suggest that a third wave was unlikely if the basic reproduction number R0 were below 1.6, plausible if the original R0 was 1.6, and likely if the original R0 was 1.8 or higher. Given that the estimates for the basic reproduction number for pandemic influenza place it in the range between 1.4 and 1.6 [1, 2, 3, 4, 5, 6, 7], our approach accurately predicted the absence of a third wave of influenza in the US during the winter of 2010. We also used this scheme to accurately predict the second wave of pandemic influenza in London and the West Midlands, UK during the fall of 2009.
PMCID: PMC3703471  PMID: 22325011
influenza; mathematical modelling; epidemic wave; influenza vaccine
3.  Planning for the Control of Pandemic Influenza A (H1N1) in Los Angeles County and the United States 
American Journal of Epidemiology  2011;173(10):1121-1130.
Mathematical and computer models can provide guidance to public health officials by projecting the course of an epidemic and evaluating control measures. The authors built upon an existing collaboration between an academic research group and the Los Angeles County, California, Department of Public Health to plan for and respond to the first and subsequent years of pandemic influenza A (H1N1) circulation. The use of models allowed the authors to 1) project the timing and magnitude of the epidemic in Los Angeles County and the continental United States; 2) predict the effect of the influenza mass vaccination campaign that began in October 2009 on the spread of pandemic H1N1 in Los Angeles County and the continental United States; and 3) predict that a third wave of pandemic influenza in the winter or spring of 2010 was unlikely to occur. The close collaboration between modelers and public health officials during pandemic H1N1 spread in the fall of 2009 helped Los Angeles County officials develop a measured and appropriate response to the unfolding pandemic and establish reasonable goals for mitigation of pandemic H1N1.
PMCID: PMC3121321  PMID: 21427173
communicable disease control; influenza, human; influenza vaccines; mass vaccination
4.  The Effects of Vector Movement and Distribution in a Mathematical Model of Dengue Transmission 
PLoS ONE  2013;8(10):e76044.
Mathematical models have been used to study the dynamics of infectious disease outbreaks and predict the effectiveness of potential mass vaccination campaigns. However, models depend on simplifying assumptions to be tractable, and the consequences of making such assumptions need to be studied. Two assumptions usually incorporated by mathematical models of vector-borne disease transmission is homogeneous mixing among the hosts and vectors and homogeneous distribution of the vectors.
Methodology/Principal Findings
We explored the effects of mosquito movement and distribution in an individual-based model of dengue transmission in which humans and mosquitoes are explicitly represented in a spatial environment. We found that the limited flight range of the vector in the model greatly reduced its ability to transmit dengue among humans. A model that does not assume a limited flight range could yield similar attack rates when transmissibility of dengue was reduced by 39%. A model in which mosquitoes are distributed uniformly across locations behaves similarly to one in which the number of mosquitoes per location is drawn from an exponential distribution with a slightly higher mean number of mosquitoes per location. When the models with different assumptions were calibrated to have similar human infection attack rates, mass vaccination had nearly identical effects.
Small changes in assumptions in a mathematical model of dengue transmission can greatly change its behavior, but estimates of the effectiveness of mass dengue vaccination are robust to some simplifying assumptions typically made in mathematical models of vector-borne disease.
PMCID: PMC3804532  PMID: 24204590
5.  Have the explosive HIV epidemics in sub-Saharan Africa been driven by higher community viral load? 
AIDS (London, England)  2013;27(6):981-989.
The HIV epidemic has carved contrasting trajectories around the world with sub-Saharan Africa (SSA) being most affected. We hypothesized that mean HIV-1 plasma RNA viral loads (VL) are higher in SSA than other areas, and that these elevated levels may contribute to the scale of epidemics in this region.
Design and Methods
To evaluate this hypothesis, we constructed a database of means of 71,668 VL measurements from 44 cohorts in seven regions of the world. We used linear regression statistical models to estimate differences in VL between regions. We also constructed and analyzed a mathematical model to describe the impact of the regional VL differences on HIV epidemic trajectory.
We found substantial regional VL heterogeneity. The mean VL in SSA was 0.58 log10 copies/mL higher than in North America (95% CI: 0.45 to 0.71); this represents about a 4-fold increase. The highest mean VLs were found in Southern and East Africa, while in Asia, Europe, North America, and South America, mean VLs were comparable. Mathematical modeling indicated that conservatively 14% of HIV infections in a representative population in Kenya could be attributed to the enhanced infectiousness of subjects with heightened VL.
We conclude that community VL appears to be higher in SSA than in other regions and this may be a central driver of the massive HIV epidemics in this region. The elevated VLs in SSA may reflect, among other factors, the high burden of co-infections or the preponderance of HIV-1 subtype C infection.
PMCID: PMC3725236  PMID: 23196933
HIV; viral load; co-infection; epidemic; sub-Saharan Africa; mathematical model
6.  Strategies for Pandemic and Seasonal Influenza Vaccination of Schoolchildren in the United States 
American Journal of Epidemiology  2009;170(6):679-686.
Vaccinating school-aged children against influenza can reduce age-specific and population-level illness attack rates. Using a stochastic simulation model of influenza transmission, the authors assessed strategies for vaccinating children in the United States, varying the vaccine type, coverage level, and reproductive number R (average number of secondary cases produced by a typical primary case). Results indicated that vaccinating children can substantially reduce population-level illness attack rates over a wide range of scenarios. The greatest absolute reduction in influenza illness cases per season occurred at R values ranging from 1.2 to 1.6 for a given vaccine coverage level. The indirect, total, and overall effects of vaccinating children were strong when transmission intensity was low to intermediate. The indirect effects declined rapidly as transmission intensity increased. In a mild influenza season (R = 1.1), approximately 19 million influenza cases could be prevented by vaccinating 70% of children. At most, nearly 100 million cases of influenza illness could be prevented, depending on the proportion of children vaccinated and the transmission intensity. Given the current worldwide threat of novel influenza A (H1N1), with an estimated R of 1.4–1.6, health officials should consider strategies for vaccinating children against novel influenza A (H1N1) as well as seasonal influenza.
PMCID: PMC2737588  PMID: 19679750
communicable disease control; influenza, human; influenza vaccines; mass immunization
7.  Economic evaluation of influenza pandemic mitigation strategies in the us using a stochastic microsimulation transmission model 
To project the potential economic impact of pandemic influenza mitigation strategies from a societal perspective in the United States.
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.
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.
Full targeted antiviral prophylaxis is an effective and cost-saving measure for mitigating pandemic influenza.
PMCID: PMC3710126  PMID: 18671770
Influenza; Human Disease Outbreaks; Cost-Benefit Analysis; Economics; Pharmaceutical Models; Theoretical; Computer Simulation
8.  Estimating Influenza Vaccine Efficacy From Challenge and Community-based Study Data 
American Journal of Epidemiology  2008;168(12):1343-1352.
In this paper, the authors provide estimates of 4 measures of vaccine efficacy for live, attenuated and inactivated influenza vaccine based on secondary analysis of 5 experimental influenza challenge studies in seronegative adults and community-based vaccine trials. The 4 vaccine efficacy measures are for susceptibility (VES), symptomatic illness given infection (VEP), infection and illness (VESP), and infectiousness (VEI). The authors also propose a combined (VEC) measure of the reduction in transmission in the entire population based on all of the above efficacy measures. Live influenza vaccine and inactivated vaccine provided similar protection against laboratory-confirmed infection (for live vaccine: VES  = 41%, 95% confidence interval (CI): 15, 66; for inactivated vaccine: VES  = 43%, 95% CI: 8, 79). Live vaccine had a higher efficacy for illness given infection (VEP  = 67%, 95% CI: 24, 100) than inactivated vaccine (VEP  = 29%, 95% CI: −19, 76), although the difference was not statistically significant. VESP for the live vaccine was higher than for the inactivated vaccine. VEI estimates were particularly low for these influenza vaccines. VESP and VEC can remain high for both vaccines, even when VEI is relatively low, as long as the other 2 measures of vaccine efficacy are relatively high.
PMCID: PMC2638553  PMID: 18974084
communicable disease control; immunization; influenza, human; influenza vaccines; models, theoretical; research design
9.  Detecting Human-to-Human Transmission of Avian Influenza A (H5N1) 
Emerging Infectious Diseases  2007;13(9):1348-1353.
Effective surveillance, containment response, and field evaluation are essential to contain potential pandemic strains
Highly pathogenic avian influenza A (HPAI) subtype H5N1 has caused family case clusters, mostly in Southeast Asia, that could be due to human-to-human transmission. Should this virus, or another zoonotic influenza virus, gain the ability of sustained human-to-human transmission, an influenza pandemic could result. We used statistical methods to test whether observed clusters of HPAI (H5N1) illnesses in families in northern Sumatra, Indonesia, and eastern Turkey were due to human-to-human transmission. Given that human-to-human transmission occurs, we estimate the infection secondary attack rates (SARs) and the local basic reproductive number, R0. We find statistical evidence of human-to-human transmission (p = 0.009) in Sumatra but not in Turkey (p = 0.114). For Sumatra, the estimated household SAR was 29% (95% confidence interval [CI] 15%–51%). The estimated lower limit on the local R0 was 1.14 (95% CI 0.61–2.14). Effective HPAI (H5N1) surveillance, containment response, and field evaluation are essential to monitor and contain potential pandemic strains.
PMCID: PMC2857285  PMID: 18252106
human influenza; outbreaks; surveillance; control; data analysis; mathematical model; research
10.  The global spread of drug-resistant influenza 
Resistance to oseltamivir, the most widely used influenza antiviral drug, spread to fixation in seasonal influenza A(H1N1) between 2006 and 2009. This sudden rise in resistance seemed puzzling given the low overall level of the oseltamivir usage and the lack of a correlation between local rates of resistance and oseltamivir usage. We used a stochastic simulation model and deterministic approximations to examine how such events can occur, and in particular to determine how the rate of fixation of the resistant strain depends both on its fitness in untreated hosts as well as the frequency of antiviral treatment. We found that, for the levels of antiviral usage in the population, the resistant strain will eventually spread to fixation, if it is not attenuated in transmissibility relative to the drug-sensitive strain, but not at the speed observed in seasonal H1N1. The extreme speed with which the resistance spread in seasonal H1N1 suggests that the resistant strain had a transmission advantage in untreated hosts, and this could have arisen from genetic hitchhiking, or from the mutations responsible for resistance and compensation. Importantly, our model also shows that resistant virus will fail to spread if it is even slightly less transmissible than its sensitive counterpart—a finding of relevance given that resistant pandemic influenza (H1N1) 2009 may currently suffer from a small, but nonetheless experimentally perceptible reduction in transmissibility.
PMCID: PMC3284134  PMID: 21865253
influenza; antiviral agents; mathematical model
11.  Optimal Vaccine Allocation for the Early Mitigation of Pandemic Influenza 
PLoS Computational Biology  2013;9(3):e1002964.
With new cases of avian influenza H5N1 (H5N1AV) arising frequently, the threat of a new influenza pandemic remains a challenge for public health. Several vaccines have been developed specifically targeting H5N1AV, but their production is limited and only a few million doses are readily available. Because there is an important time lag between the emergence of new pandemic strain and the development and distribution of a vaccine, shortage of vaccine is very likely at the beginning of a pandemic. We coupled a mathematical model with a genetic algorithm to optimally and dynamically distribute vaccine in a network of cities, connected by the airline transportation network. By minimizing the illness attack rate (i.e., the percentage of people in the population who become infected and ill), we focus on optimizing vaccine allocation in a network of 16 cities in Southeast Asia when only a few million doses are available. In our base case, we assume the vaccine is well-matched and vaccination occurs 5 to 10 days after the beginning of the epidemic. The effectiveness of all the vaccination strategies drops off as the timing is delayed or the vaccine is less well-matched. Under the best assumptions, optimal vaccination strategies substantially reduced the illness attack rate, with a maximal reduction in the attack rate of 85%. Furthermore, our results suggest that cooperative strategies where the resources are optimally distributed among the cities perform much better than the strategies where the vaccine is equally distributed among the network, yielding an illness attack rate 17% lower. We show that it is possible to significantly mitigate a more global epidemic with limited quantities of vaccine, provided that the vaccination campaign is extremely fast and it occurs within the first weeks of transmission.
Author Summary
In the past, the emergence of new strains of influenza has been sometimes responsible for large and deadly pandemics. With a very high mortality rate, (i.e., about 60% of the reported cases), H5N1AV influenza, commonly known as bird flu, is thought to be an important potential threat for a new pandemic. Because of this, several vaccines have been developed, but only a few million doses are readily available. Other zoonotic influenza strains, particularly in pigs, also threaten, and vaccines are being produced for them as well. In the event of an influenza pandemic, utilizing these resources optimally could make the difference between dealing with a serious infectious disease at a global scale and reducing it to a highly localized and controlled outbreak. In this paper, we address this issue by developing a mathematical model of influenza transmission on a network of cities. We couple the model with an optimization algorithm to allocate vaccine in time and space through the network. We find that our optimal allocation strategies can mitigate a pandemic, provided that vaccination occurs quickly, within the first weeks of a potential pandemic. In addition, our analysis highlights the importance of cooperative and coordinated vaccine distribution, if we want to mitigate a pandemic.
PMCID: PMC3605056  PMID: 23555207
Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools, and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than non-friends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network. We then compare a targeted antiviral prophylaxis intervention strategy and a grade closure intervention strategy under random mixing and network-based mixing. We find that random mixing overestimates the effect of targeted antiviral prophylaxis on the probability of an epidemic when the probability of transmission in 10 minutes of contact is less than 0.004 and underestimates it when this transmission probability is greater than 0.004. We found the same pattern for the final size of an epidemic, with a threshold transmission probability of 0.005. We also find random mixing overestimates the effect of a grade closure intervention on the probability of an epidemic and final size for all transmission probabilities. Our findings have implications for policy recommendations based on models assuming random mixing, and can inform further development of network-based models.
PMCID: PMC3359895  PMID: 22639701
contact network; epidemic model; influenza; simulation model; social network
13.  A Hybrid EM and Monte Carlo EM Algorithm and Its Application to Analysis of Transmission of Infectious Diseases 
Biometrics  2012;68(4):1238-1249.
In epidemics of infectious diseases such as influenza, an individual may have one of four possible final states: prior immune, escaped from infection, infected with symptoms, and infected asymptomatically. The exact state is often not observed. In addition, the unobserved transmission times of asymptomatic infections further complicate analysis. Under the assumption of missing at random, data-augmentation techniques can be used to integrate out such uncertainties. We adapt an importance-sampling-based Monte Carlo EM (MCEM) algorithm to the setting of an infectious disease transmitted in close contact groups. Assuming the independence between close contact groups, we propose a hybrid EM-MCEM algorithm that applies the MCEM or the traditional EM algorithms to each close contact group depending on the dimension of missing data in that group, and discuss the variance estimation for this practice. In addition, we propose a bootstrap approach to assess the total Monte Carlo error and factor that error into the variance estimation. The proposed methods are evaluated using simulation studies. We use the hybrid EM-MCEM algorithm to analyze two influenza epidemics in the late 1970s to assess the effects of age and pre-season antibody levels on the transmissibility and pathogenicity of the viruses.
PMCID: PMC3402623  PMID: 22506893
Data augmentation; EM algorithm; Infectious disease; Missing data; Monte Carlo
14.  Hand, Foot and Mouth Disease in China: Patterns of Spread and Transmissibility during 2008-2009 
Epidemiology (Cambridge, Mass.)  2011;22(6):781-792.
Large outbreaks of hand, foot and mouth disease (HFMD) were observed in both 2008 and 2009 in China.
Using the national surveillance data since May 2, 2008, epidemiological characteristics of the outbreaks are summarized, and the transmissibility of the disease and the effects of potential risk factors were evaluated via a susceptible-infectious-recovered transmission model.
Children of 1.0–2.9 years were the most susceptible group to HFMD (odds ratios [OR] > 2.3 as compared to other age groups). Infant cases had the highest incidences of severe disease (ORs > 1.4) and death (ORs > 2.4), as well as the longest delay from symptom onset to diagnosis (2.3 days). Males were more susceptible to HFMD than females (OR=1.56 [95% confidence interval=1.56, 1.57]). An one day delay in diagnosis was associated with increases in the odds of severe disease by 40.3% [38.7%, 41.9%] and in the odds of death by 53.7% [43.6%, 64.5%]. Compared to Coxsackie A16, enterovirus (EV) 71 is more strongly associated with severe disease (OR=15.6 [13.4, 18.1]) and death (OR=40.7 [13.0, 127.3]). The estimated local effective reproductive numbers among prefectures ranged from 1.4 to 1.6 (median=1.4) in spring and stayed below 1.2 in other seasons. A higher risk of transmission was associated with temperatures in the range of 70-80F, higher relative humidity, wind speed, precipitation, population density, and the periods in which schools were open.
HFMD is a moderately transmittable infectious disease, mainly among pre-school children. EV71 was responsible for most severe cases and fatalities. Mixing of asymptomatically infected children in schools might have contributed to the spread of HFMD. Timely diagnosis may be a key to reducing the high mortality rate in infants.
PMCID: PMC3246273  PMID: 21968769
15.  Controlling Dengue with Vaccines in Thailand 
Dengue is a mosquito-borne infectious disease that constitutes a growing global threat with the habitat expansion of its vectors Aedes aegyti and A. albopictus and increasing urbanization. With no effective treatment and limited success of vector control, dengue vaccines constitute the best control measure for the foreseeable future. With four interacting dengue serotypes, the development of an effective vaccine has been a challenge. Several dengue vaccine candidates are currently being tested in clinical trials. Before the widespread introduction of a new dengue vaccine, one needs to consider how best to use limited supplies of vaccine given the complex dengue transmission dynamics and the immunological interaction among the four dengue serotypes.
Methodology/Principal Findings
We developed an individual-level (including both humans and mosquitoes), stochastic simulation model for dengue transmission and control in a semi-rural area in Thailand. We calibrated the model to dengue serotype-specific infection, illness and hospitalization data from Thailand. Our simulations show that a realistic roll-out plan, starting with young children then covering progressively older individuals in following seasons, could reduce local transmission of dengue to low levels. Simulations indicate that this strategy could avert about 7,700 uncomplicated dengue fever cases and 220 dengue hospitalizations per 100,000 people at risk over a ten-year period.
Vaccination will have an important role in controlling dengue. According to our modeling results, children should be prioritized to receive vaccine, but adults will also need to be vaccinated if one wants to reduce community-wide dengue transmission to low levels.
Author Summary
An estimated 40% of the world's population is at risk of infection with dengue, a mosquito-borne disease that can lead to hospitalization or death. Dengue vaccines are currently being tested in clinical trials and at least one product will likely be available within a couple of years. Before widespread deployment, one should plan how best to use limited supplies of vaccine. We developed a mathematical model of dengue transmission in semi-rural Thailand to help evaluate different vaccination strategies. Our modeling results indicate that children should be prioritized to receive vaccine to reduce dengue-related morbidity, but adults will also need to be vaccinated if one wants to eliminate local dengue transmission. Dengue is a challenging disease to study because of its four interacting serotypes, seasonality of its transmission, and pre-existing immunity in a population. Models such as this one are useful coherent framework for synthesizing these complex issues and evaluating potential public health interventions such as mass vaccination.
PMCID: PMC3493390  PMID: 23145197
16.  Design and Evaluation of Prophylactic Interventions Using Infectious Disease Incidence Data from Close Contact Groups 
Prophylaxis of contacts of infectious cases such as household members and treatment of infectious cases are methods to prevent spread of infectious diseases. We develop a method based on maximum likelihood to estimate the efficacy of such interventions and the transmission probabilities. We consider both the design with prospective follow-up of close contact groups and the design with ascertainment of close contact groups by an index case as well as randomization by groups and by individuals. We compare the designs using simulations. We estimate the efficacy of the influenza antiviral agent oseltamivir in reducing susceptibility and infectiousness in two case-ascertained household trials.
PMCID: PMC3312606  PMID: 22457545
Antiviral agent; Community trial; Infectious disease; Intervention efficacy; Left truncation
The annals of applied statistics  2011;5(3):1816-1838.
Acute respiratory diseases are transmitted over networks of social contacts. Large-scale simulation models are used to predict epidemic dynamics and evaluate the impact of various interventions, but the contact behavior in these models is based on simplistic and strong assumptions which are not informed by survey data. These assumptions are also used for estimating transmission measures such as the basic reproductive number and secondary attack rates. Development of methodology to infer contact networks from survey data could improve these models and estimation methods. We contribute to this area by developing a model of within-household social contacts and using it to analyze the Belgian POLYMOD data set, which contains detailed diaries of social contacts in a 24-hour period. We model dependency in contact behavior through a latent variable indicating which household members are at home. We estimate age-specific probabilities of being at home and age-specific probabilities of contact conditional on two members being at home. Our results differ from the standard random mixing assumption. In addition, we find that the probability that all members contact each other on a given day is fairly low: 0.49 for households with two 0–5 year olds and two 19–35 year olds, and 0.36 for households with two 12–18 year olds and two 36+ year olds. We find higher contact rates in households with 2–3 members, helping explain the higher influenza secondary attack rates found in households of this size.
PMCID: PMC3306235  PMID: 22427793
18.  School opening dates predict pandemic influenza A (H1N1) epidemics in the USA 
The Journal of infectious diseases  2010;202(6):877-880.
The opening of schools in late summer of 2009 may have triggered the fall wave of pandemic influenza A(H1N1) in the United States. We found that elevated percent of outpatient visits for influenza-like illness (ILI%) occurred an average of 14 days after schools opened in a state in the fall of 2009. The timing of these events was highly correlated (Spearman’s correlation coefficient=0.62, p < 1.0 × 10−5). This result provides evidence that transmission in schools catalyzes community-wide transmission. School opening dates can be useful for future pandemic planning, and influenza mitigation strategies should be targeted at school populations before the influenza season.
PMCID: PMC2939723  PMID: 20704486
Children; Epidemics; Human Influenza; Pandemics
19.  The Global Transmission and Control of Influenza 
PLoS ONE  2011;6(5):e19515.
New strains of influenza spread around the globe via the movement of infected individuals. The global dynamics of influenza are complicated by different patterns of influenza seasonality in different regions of the world. We have released an open-source stochastic mathematical model of the spread of influenza across 321 major, strategically located cities of the world. Influenza is transmitted between cities via infected airline passengers. Seasonality is simulated by increasing the transmissibility in each city at the times of the year when influenza has been observed to be most prevalent. The spatiotemporal spread of pandemic influenza can be understood through clusters of global transmission and links between them, which we identify using the epidemic percolation network (EPN) of the model. We use the model to explain the observed global pattern of spread for pandemic influenza A(H1N1) 2009–2010 (pandemic H1N1 2009) and to examine possible global patterns of spread for future pandemics depending on the origin of pandemic spread, time of year of emergence, and basic reproductive number (). We also use the model to investigate the effectiveness of a plausible global distribution of vaccine for various pandemic scenarios. For pandemic H1N1 2009, we show that the biggest impact of vaccination was in the temperate northern hemisphere. For pandemics starting in the temperate northern hemisphere in May or April, vaccination would have little effect in the temperate southern hemisphere and a small effect in the tropics. With the increasing interconnectedness of the world's population, we must take a global view of infectious disease transmission. Our open-source, computationally simple model can help public health officials plan for the next pandemic as well as deal with interpandemic influenza.
PMCID: PMC3089626  PMID: 21573121
20.  Population level impact of an imperfect prophylactic HSV-2 vaccine 
Sexually transmitted diseases  2010;37(5):290-297.
The continuation of developing HSV-2 prophylactic vaccines requires parallel mathematical modeling to quantify the impact on the population of these vaccines.
Using mathematical modeling we derived three summary measures for the population impact of imperfect HSV-2 vaccines as a function of their efficacies in reducing susceptibility (VES), genital shedding (VEP), and infectivity during shedding (VEI). In addition, we studied the population level impact of vaccine intervention using representative vaccine efficacies.
A vaccine with limited efficacy of reducing shedding frequency (VEP =10%) and infectivity (VEI =0%) would need to reduce susceptibility by 75% (VES =75%) to substantially reduce the sustainability of HSV-2 infection in a population. No reduction in susceptibility would be required to reach this target in a vaccine that decreased shedding by 75% (VES =0%, VEP =75%, VEI =0%). Mass vaccination using a vaccine with imperfect efficacies (VES =30%, VEP =75%, and VEI =0%) in Kisumu, Kenya in 2010 would decrease prevalence and incidence in 2020 by 7% and 30% respectively. For lower prevalence settings, vaccination is predicted to have a lower impact on prevalence.
A vaccine with substantially high efficacy of reducing HSV-2 shedding frequency would have a desirable impact at the population level. The vaccine’s short-term impact in a high prevalence setting in Africa would be a substantial decrease in incidence, whereas its immediate impact on prevalence would be small and would increase slowly over time.
PMCID: PMC2860045  PMID: 20351622
Keywords: Herpes simplex virus; mathematical modeling; prophylactic vaccines; summary measures; vaccine efficacy
21.  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.
PMCID: PMC3070363  PMID: 21472041
Missing data; MCMC; Infectious disease; Competing risks; Intervention efficacy
22.  Towards a quantitative understanding of the within-host dynamics of influenza A infections 
Although the influenza A virus has been extensively studied, a quantitative understanding of the infection dynamics is still lacking. To make progress in this direction, we designed several mathematical models and compared them with data from influenza A infections of mice. We find that the immune response (IR) plays an important part in the infection dynamics. Both an innate and an adaptive IR are required to provide adequate explanation of the data. In contrast, regrowth of epithelial cells did not seem to be an important mechanism on the time scale of the infection. We also find that different model variants for both innate and adaptive responses fit the data well, indicating the need for additional data to allow further model discrimination.
PMCID: PMC2839376  PMID: 19474085
infectious disease; mathematical modelling; theoretical immunology
23.  Optimizing Vaccine Allocation at Different Points in Time during an Epidemic 
PLoS ONE  2010;5(11):e13767.
Pandemic influenza A(H1N1) 2009 began spreading around the globe in April of 2009 and vaccination started in October of 2009. In most countries, by the time vaccination started, the second wave of pandemic H1N1 2009 was already under way. With limited supplies of vaccine, we are left to question whether it may be a good strategy to vaccinate the high-transmission groups earlier in the epidemic, but it might be a better use of resources to protect instead the high-risk groups later in the epidemic. To answer this question, we develop a deterministic epidemic model with two age-groups (children and adults) and further subdivide each age group in low and high risk.
Methods and Findings
We compare optimal vaccination strategies started at various points in time in two different settings: a population in a developed country where children account for 24% of the population, and a population in a less developed country where children make up the majority of the population, 55%. For each of these populations, we minimize mortality or hospitalizations and we find an optimal vaccination strategy that gives the best vaccine allocation given a starting vaccination time and vaccine coverage level. We find that population structure is an important factor in determining the optimal vaccine distribution. Moreover, the optimal policy is dynamic as there is a switch in the optimal vaccination strategy at some time point just before the peak of the epidemic. For instance, with 25% vaccine coverage, it is better to protect the high-transmission groups before this point, but it is optimal to protect the most vulnerable groups afterward.
Choosing the optimal strategy before or early in the epidemic makes an important difference in minimizing the number of influenza infections, and consequently the number of influenza deaths or hospitalizations, but the optimal strategy makes little difference after the peak.
PMCID: PMC2978681  PMID: 21085686
24.  Intervention strategies for an influenza pandemic taking into account secondary bacterial infections 
Epidemics  2009;1(3):185-195.
Influenza infections often predispose individuals to consecutive bacterial infections. Both during seasonal and pandemic influenza outbreaks, morbidity and mortality due to secondary bacterial infections can be substantial. With the help of a mathematical model, we investigate the potential impact of such bacterial infections during an influenza pandemic, and we analyze how antiviral and antibacterial treatment or prophylaxis affect morbidity and mortality. We consider different scenarios for the spread of bacteria, the emergence of antiviral resistance, and different levels of severity for influenza infections (1918-like and 2009-like). We find that while antibacterial intervention strategies are unlikely to play an important role in reducing the overall number of cases, such interventions can lead to a significant reduction in mortality and in the number of bacterial infections. Antibacterial interventions become even more important if one considers the – very likely – scenario that during a pandemic outbreak, influenza strains resistant to antivirals emerge. Overall, our study suggests that pandemic preparedness plans should consider intervention strategies based on antibacterial treatment or prophylaxis through drugs or vaccines as part of the overall control strategy. A major caveat for our results is the lack of data that would allow precise estimation of many of the model parameters. As our results show, this leads to very large uncertainty in model outcomes. As we discuss, precise assessment of the impact of antibacterial strategies during an influenza pandemic will require the collection of further data to better estimate key parameters, especially those related to the bacterial infections and the impact of antibacterial intervention strategies.
PMCID: PMC2796779  PMID: 20161493
25.  Efficacy of Trivalent, Cold-Adapted, Influenza Virus Vaccine Against Influenza A (Fujian), a Drift Variant, during 2003–2004 
Vaccine  2007;25(20):4038-4045.
In the 2003–2004 influenza season, the predominant circulating influenza A (H3N2) virus in the United States was similar antigenically to A/Fujian/411/2002 (H3N2), a drift variant of A/Panama/2007/99 (H3N2), the vaccine strain. That year, a field study of trivalent live-attenuated influenza vaccine (LAIV-T) was conducted in Temple-Belton, Texas, as part of a larger community-based, non-randomized, open-label study in three communities that began in August 1998 [1, 2, 3]. Participants were healthy children aged 5 – 18 years. The analysis here concerns 6,403 children in the Scott & White Health Plan (SWHP) database living within zip codes of the Temple-Belton area, of whom 1,706 received LAIV-T and 548 received trivalent inactivated vaccine (TIV) in 2003, 983 had been previously vaccinated in 1998–2001, but not in 2002–2003 or 2003, and 3,166 had never been vaccinated. The main outcome measure was medically-attended acute respiratory illness (MAARI). Surveillance culture results were incorporated into the analysis to estimate efficacy against culture-confirmed influenza illness. Vaccine effectiveness of LAIV-T against MAARI was 26% (95% confidence interval (CI) 11,39). Vaccine efficacy of LAIV-T against culture-confirmed influenza illness including surveillance cultures of children in the SWHP database in the validation calculation was 56% (95% CI 24,84). LAIV-T was cross-protective with a drift variant strain in 2003–2004, evidence that such vaccines could be important for preparing for a pandemic and for annual influenza.
PMCID: PMC2883284  PMID: 17395338
efficacy; influenza; surveillance; vaccine

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