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1.  Middle East respiratory syndrome coronavirus: quantification of the extent of the epidemic, surveillance biases, and transmissibility 
The Lancet Infectious Diseases  2014;14(1):50-56.
The novel Middle East respiratory syndrome coronavirus (MERS-CoV) had, as of Aug 8, 2013, caused 111 virologically confirmed or probable human cases of infection worldwide. We analysed epidemiological and genetic data to assess the extent of human infection, the performance of case detection, and the transmission potential of MERS-CoV with and without control measures.
We assembled a comprehensive database of all confirmed and probable cases from public sources and estimated the incubation period and generation time from case cluster data. Using data of numbers of visitors to the Middle East and their duration of stay, we estimated the number of symptomatic cases in the Middle East. We did independent analyses, looking at the growth in incident clusters, the growth in viral population, the reproduction number of cluster index cases, and cluster sizes to characterise the dynamical properties of the epidemic and the transmission scenario.
The estimated number of symptomatic cases up to Aug 8, 2013, is 940 (95% CI 290–2200), indicating that at least 62% of human symptomatic cases have not been detected. We find that the case-fatality ratio of primary cases detected via routine surveillance (74%; 95% CI 49–91) is biased upwards because of detection bias; the case-fatality ratio of secondary cases was 20% (7–42). Detection of milder cases (or clinical management) seemed to have improved in recent months. Analysis of human clusters indicated that chains of transmission were not self-sustaining when infection control was implemented, but that R in the absence of controls was in the range 0·8–1·3. Three independent data sources provide evidence that R cannot be much above 1, with an upper bound of 1·2–1·5.
By showing that a slowly growing epidemic is underway either in human beings or in an animal reservoir, quantification of uncertainty in transmissibility estimates, and provision of the first estimates of the scale of the epidemic and extent of case detection biases, we provide valuable information for more informed risk assessment.
Medical Research Council, Bill & Melinda Gates Foundation, EU FP7, and National Institute of General Medical Sciences.
PMCID: PMC3895322  PMID: 24239323
2.  Transmission Dynamics, Border Entry Screening, and School Holidays during the 2009 Influenza A (H1N1) Pandemic, China 
Emerging Infectious Diseases  2012;18(5):758-766.
Screening delayed spread by <4 days; autumn school holidays reduced the effective reproduction number by ≈40%.
Pandemic influenza A (H1N1) 2009 virus spread rapidly around the world in 2009. We used multiple data sources from surveillance systems and specific investigations to characterize the transmission patterns of this virus in China during May–November 2009 and analyze the effectiveness of border entry screening and holiday-related school closures on transmission. In China, age distribution and transmission dynamic characteristics were similar to those in Northern Hemisphere temperate countries. The epidemic was focused in children, with an effective reproduction number of ≈1.2–1.3. The 8 days of national holidays in October reduced the effective reproduction number by 37% (95% credible interval 28%–45%) and increased underreporting by ≈20%–30%. Border entry screening detected at most 37% of international travel–related cases, with most (89%) persons identified as having fever at time of entry. These findings suggest that border entry screening was unlikely to have delayed spread in China by >4 days.
PMCID: PMC3358060  PMID: 22515989
transmission; school closure; border screening; influenza A; pandemic (H1N1) 2009; People’s Republic of China; influenza; viruses
3.  Estimating Potential Incidence of MERS-CoV Associated with Hajj Pilgrims to Saudi Arabia, 2014 
PLoS Currents  2014;6:ecurrents.outbreaks.c5c9c9abd636164a9b6fd4dbda974369.
Between March and June 2014 the Kingdom of Saudi Arabia (KSA) had a large outbreak of MERS-CoV, renewing fears of a major outbreak during the Hajj this October. Using KSA Ministry of Health data, the MERS-CoV Scenario and Modeling Working Group forecast incidence under three scenarios. In the expected incidence scenario, we estimate 6.2 (95% Prediction Interval [PI]: 1–17) pilgrims will develop MERS-CoV symptoms during the Hajj, and 4.0 (95% PI: 0–12) foreign pilgrims will be infected but return home before developing symptoms. In the most pessimistic scenario, 47.6 (95% PI: 32–66) cases will develop symptoms during the Hajj, and 29.0 (95% PI: 17–43) will be infected but return home asymptomatic. Large numbers of MERS-CoV cases are unlikely to occur during the 2014 Hajj even under pessimistic assumptions, but careful monitoring is still needed to detect possible mass infection events and minimize introductions into other countries.  
PMCID: PMC4323406
infectious disease; MERS-coronavirus
4.  Contrasting benefits of different artemisinin combination therapies as first-line malaria treatments using model-based cost-effectiveness analysis 
Nature Communications  2014;5:5606.
There are currently several recommended drug regimens for uncomplicated falciparum malaria in Africa. Each has different properties that determine its impact on disease burden. Two major antimalarial policy options are artemether–lumefantrine (AL) and dihydroartemisinin–piperaquine (DHA–PQP). Clinical trial data show that DHA–PQP provides longer protection against reinfection, while AL is better at reducing patient infectiousness. Here we incorporate pharmacokinetic-pharmacodynamic factors, transmission-reducing effects and cost into a mathematical model and simulate malaria transmission and treatment in Africa, using geographically explicit data on transmission intensity and seasonality, population density, treatment access and outpatient costs. DHA–PQP has a modestly higher estimated impact than AL in 64% of the population at risk. Given current higher cost estimates for DHA–PQP, there is a slightly greater cost per case averted, except in areas with high, seasonally varying transmission where the impact is particularly large. We find that a locally optimized treatment policy can be highly cost effective for reducing clinical malaria burden.
Several drug combinations with different properties are used for malaria treatment. Here, Okell et al. use a mathematical model to simulate malaria transmission and treatment with two drug combinations in Africa, and find that locally optimized policies can be highly cost effective for reducing malaria burden.
PMCID: PMC4263185  PMID: 25425081
5.  A New Framework and Software to Estimate Time-Varying Reproduction Numbers During Epidemics 
American Journal of Epidemiology  2013;178(9):1505-1512.
The quantification of transmissibility during epidemics is essential to designing and adjusting public health responses. Transmissibility can be measured by the reproduction number R, the average number of secondary cases caused by an infected individual. Several methods have been proposed to estimate R over the course of an epidemic; however, they are usually difficult to implement for people without a strong background in statistical modeling. Here, we present a ready-to-use tool for estimating R from incidence time series, which is implemented in popular software including Microsoft Excel (Microsoft Corporation, Redmond, Washington). This tool produces novel, statistically robust analytical estimates of R and incorporates uncertainty in the distribution of the serial interval (the time between the onset of symptoms in a primary case and the onset of symptoms in secondary cases). We applied the method to 5 historical outbreaks; the resulting estimates of R are consistent with those presented in the literature. This tool should help epidemiologists quantify temporal changes in the transmission intensity of future epidemics by using surveillance data.
PMCID: PMC3816335  PMID: 24043437
incidence; influenza; measles; reproduction number; SARS; smallpox; software
6.  Optimizing the Precision of Case Fatality Ratio Estimates Under the Surveillance Pyramid Approach 
American Journal of Epidemiology  2014;180(10):1036-1046.
In the management of emerging infectious disease epidemics, precise and accurate estimation of severity indices, such as the probability of death after developing symptoms—the symptomatic case fatality ratio (sCFR)—is essential. Estimation of the sCFR may require merging data gathered through different surveillance systems and surveys. Since different surveillance strategies provide different levels of precision and accuracy, there is need for a theory to help investigators select the strategy that maximizes these properties. Here, we study the precision of sCFR estimators that combine data from several levels of the severity pyramid. We derive a formula for the standard error, which helps us find the estimator with the best precision given fixed resources. We further propose rules of thumb for guiding the choice of strategy: For example, should surveillance of a particular severity level be started? Which level should be preferred? We derive a formula for the optimal allocation of resources between chosen surveillance levels and provide a simple approximation that can be used in thinking more heuristically about planning surveillance. We illustrate these concepts with numerical examples corresponding to 3 influenza pandemic scenarios. Finally, we review the equally important issue of accuracy.
PMCID: PMC4240167  PMID: 25255809
case fatality ratio; emerging infectious diseases; influenza; pandemics; statistical planning; surveillance protocol
7.  Determinants of Influenza Transmission in South East Asia: Insights from a Household Cohort Study in Vietnam 
PLoS Pathogens  2014;10(8):e1004310.
To guide control policies, it is important that the determinants of influenza transmission are fully characterized. Such assessment is complex because the risk of influenza infection is multifaceted and depends both on immunity acquired naturally or via vaccination and on the individual level of exposure to influenza in the community or in the household. Here, we analyse a large household cohort study conducted in 2007–2010 in Vietnam using innovative statistical methods to ascertain in an integrative framework the relative contribution of variables that influence the transmission of seasonal (H1N1, H3N2, B) and pandemic H1N1pdm09 influenza. Influenza infection was diagnosed by haemagglutination-inhibition (HI) antibody assay of paired serum samples. We used a Bayesian data augmentation Markov chain Monte Carlo strategy based on digraphs to reconstruct unobserved chains of transmission in households and estimate transmission parameters. The probability of transmission from an infected individual to another household member was 8% (95% CI, 6%, 10%) on average, and varied with pre-season titers, age and household size. Within households of size 3, the probability of transmission from an infected member to a child with low pre-season HI antibody titers was 27% (95% CI 21%–35%). High pre-season HI titers were protective against infection, with a reduction in the hazard of infection of 59% (95% CI, 44%–71%) and 87% (95% CI, 70%–96%) for intermediate (1∶20–1∶40) and high (≥1∶80) HI titers, respectively. Even after correcting for pre-season HI titers, adults had half the infection risk of children. Twenty six percent (95% CI: 21%, 30%) of infections may be attributed to household transmission. Our results highlight the importance of integrated analysis by influenza sub-type, age and pre-season HI titers in order to infer influenza transmission risks in and outside of the household.
Author Summary
Influenza causes an estimated three to five million severe illnesses worldwide each year. In order to guide control policies it is important to determine the key risk factors for transmission. This is often done by studying transmission in households but in the past, analysis of such data has suffered from important simplifying assumptions (for example not being able to account for the effect of biological markers of protection like pre-season antibody titers). We have developed new statistical methods that address these limitations and applied them to a large household cohort study conducted in 2007–2010 in Vietnam. By comparing a large range of model variants, we have obtained unique insights into the patterns and determinants of transmission of seasonal (H1N1, H3N2, B) and pandemic H1N1pdm09 influenza in South East Asia. This includes estimating the proportion of cases attributed to household transmission, the average household transmission probability, the protection afforded by pre-season HI titers, and the effect of age on infection risk after correcting for pre-season HI titers.
PMCID: PMC4140851  PMID: 25144780
8.  Estimates of the changing age-burden of Plasmodium falciparum malaria disease in sub-Saharan Africa 
Nature communications  2014;5:3136.
Estimating the changing burden of malaria disease remains difficult due to limitations in health reporting systems. Here, we use a transmission model incorporating acquisition and loss of immunity to capture age-specific patterns of disease at different transmission intensities. The model is fitted to age-stratified data from 23 sites in Africa, and we then produce maps and estimates of disease burden. We estimate that in 2010 there were 252 (95% credible interval: 171-353) million cases of malaria in sub-Saharan Africa that active case finding would detect. However, only 34% (12%-86%) of these cases would be observed through passive case detection. We estimate that the proportion of all cases of clinical malaria which are in under-fives varies from above 60% at high transmission to below 20% at low transmission. The focus of some interventions towards young children may need to be re-considered, and should be informed by the current local transmission intensity.
PMCID: PMC3923296  PMID: 24518518
9.  Multiple Contributory Factors to the Age Distribution of Disease Cases: A Modeling Study in the Context of Influenza A(H3N2v) 
Background. In late 2011 and early 2012, 13 cases of human influenza resulted from infection with a novel triple reassortant swine-origin influenza virus, influenza A (H3N2) variant. This variant was notable for its inclusion of the matrix gene from the 2009 influenza A(H1N1) pandemic virus. While most of these confirmed cases were among children, the transmission potential and likely age-dependent susceptibility to the virus was unknown. Preliminary serologic studies indicated that very young children have less protection than older children and adults.
Methods. We construct a mathematical transmission model of influenza transmission that allows for external zoonotic exposure to infection and show how exposure and susceptibility-related factors contribute to the observed case distribution.
Results and Conclusions. Age-dependent susceptibility to infection strongly influences epidemic dynamics. The result is that the risk of an outbreak in a highly susceptible age group may be substantially higher than in an older age group with less susceptibility, but exposure-related factors must also be accounted for when interpreting case data.
PMCID: PMC3689451  PMID: 23794728
novel influenza; emerging infection; modeling; zoonosis
10.  Transmission dynamics of the 2009 influenza A (H1N1) pandemic in India: The impact of holiday-related school closure 
Epidemics  2013;5(4):157-163.
The role of social-distancing measures, such as school closures, is a controversial aspect of pandemic mitigation planning. However, the timing of 2009 pandemic provides a natural experiment for evaluating the impact of school closure during holidays on influenza transmission.
To quantify the transmission intensity of the influenza A (H1N1) pdm’09 in India, by estimating the time varying reproduction number (Rt) and correlating the temporal changes in the estimates of Rt for different regions of India with the timing of school holidays. We used daily lab-confirmed case reports of influenza A (H1N1) pdm’09 in India (during 17 May’09 to 17 May’10), stratified by regions. We estimated the transmissibility of the pandemic for different regions from these time-series, using Bayesian methods applied to a branching process model of disease spread and correlated the resulting estimates with the timing of school holidays in each region.
The North-west region experienced two notable waves, with the peak of the first wave coinciding with the start of a 4 week school holiday (September-October’09). In the southern region the two waves were less clear cut, though again the first peak of the first wave coincided with the start of school holidays – albeit of less than 2 weeks duration (August’09). Our analysis suggests that the school holidays had a significant influence on the epidemiology of the 2009 pandemic in India. We estimate that school holidays reduced the reproduction number by 14%–27% in different regions of India, relative to levels seen outside holiday periods. The estimates of the reproduction number obtained (with peak R values below 1.5) are compatible with those reported from other regions of the world. This work reinforces past studies showing the significant impact of school holidays on spread of 2009 pandemic virus, and by inference the role of contact patterns in children on transmission.
PMCID: PMC4088951  PMID: 24267871
Influenza; mathematical models; reproduction number; school holidays; India
11.  Within-host viral dynamics of dengue serotype 1 infection 
Dengue, the most common mosquito-borne viral infection of humans, is endemic across much of the world, including much of tropical Asia and is increasing in its geographical range. Here, we present a mathematical model of dengue virus dynamics within infected individuals, detailing the interaction between virus and a simple immune response. We fit this model to measurements of plasma viral titre from cases of primary and secondary DENV 1 infection in Vietnam. We show that variation in model parameters governing the immune response is sufficient to create the observed variation in virus dynamics between individuals. Estimating model parameter values, we find parameter differences between primary and secondary cases consistent with the theory of antibody-dependent enhancement (namely enhanced rates of viral entry to target cells in secondary cases). Finally, we use our model to examine the potential impact of an antiviral drug on the within-host dynamics of dengue. We conclude that the impact of antiviral therapy on virus dynamics is likely to be limited if therapy is only started at the onset of symptoms, owing to the typically late stage of viral pathogenesis reached by the time symptoms are manifested and thus treatment is started.
PMCID: PMC4032531  PMID: 24829280
dengue; virus dynamics; within-host modelling
12.  Yellow Fever in Africa: Estimating the Burden of Disease and Impact of Mass Vaccination from Outbreak and Serological Data 
PLoS Medicine  2014;11(5):e1001638.
Neil Ferguson and colleagues estimate the disease burden of yellow fever in Africa, as well as the impact of mass vaccination campaigns.
Please see later in the article for the Editors' Summary
Yellow fever is a vector-borne disease affecting humans and non-human primates in tropical areas of Africa and South America. While eradication is not feasible due to the wildlife reservoir, large scale vaccination activities in Africa during the 1940s to 1960s reduced yellow fever incidence for several decades. However, after a period of low vaccination coverage, yellow fever has resurged in the continent. Since 2006 there has been substantial funding for large preventive mass vaccination campaigns in the most affected countries in Africa to curb the rising burden of disease and control future outbreaks. Contemporary estimates of the yellow fever disease burden are lacking, and the present study aimed to update the previous estimates on the basis of more recent yellow fever occurrence data and improved estimation methods.
Methods and Findings
Generalised linear regression models were fitted to a dataset of the locations of yellow fever outbreaks within the last 25 years to estimate the probability of outbreak reports across the endemic zone. Environmental variables and indicators for the surveillance quality in the affected countries were used as covariates. By comparing probabilities of outbreak reports estimated in the regression with the force of infection estimated for a limited set of locations for which serological surveys were available, the detection probability per case and the force of infection were estimated across the endemic zone.
The yellow fever burden in Africa was estimated for the year 2013 as 130,000 (95% CI 51,000–380,000) cases with fever and jaundice or haemorrhage including 78,000 (95% CI 19,000–180,000) deaths, taking into account the current level of vaccination coverage. The impact of the recent mass vaccination campaigns was assessed by evaluating the difference between the estimates obtained for the current vaccination coverage and for a hypothetical scenario excluding these vaccination campaigns. Vaccination campaigns were estimated to have reduced the number of cases and deaths by 27% (95% CI 22%–31%) across the region, achieving up to an 82% reduction in countries targeted by these campaigns. A limitation of our study is the high level of uncertainty in our estimates arising from the sparseness of data available from both surveillance and serological surveys.
With the estimation method presented here, spatial estimates of transmission intensity can be combined with vaccination coverage levels to evaluate the impact of past or proposed vaccination campaigns, thereby helping to allocate resources efficiently for yellow fever control. This method has been used by the Global Alliance for Vaccines and Immunization (GAVI Alliance) to estimate the potential impact of future vaccination campaigns.
Please see later in the article for the Editors' Summary
Editors' Summary
Yellow fever is a flavivirus infection that is transmitted to people and to non-human primates through the bites of infected mosquitoes. This serious viral disease affects people living in and visiting tropical regions of Africa and Central and South America. In rural areas next to forests, the virus typically causes sporadic cases or even small-scale epidemics (outbreaks) but, if it is introduced into urban areas, it can cause large explosive epidemics that are hard to control. Although many people who contract yellow fever do not develop any symptoms, some have mild flu-like symptoms, and others develop a high fever with jaundice (yellowing of the skin and eyes) or hemorrhaging (bleeding) from the mouth, nose, eyes, or stomach. Half of patients who develop these severe symptoms die. Because of this wide spectrum of symptoms, which overlap with those of other tropical diseases, it is hard to diagnose yellow fever from symptoms alone. However, serological tests that detect antibodies to the virus in the blood can help in diagnosis. There is no specific antiviral treatment for yellow fever but its symptoms can be treated.
Why Was This Study Done?
Eradication of yellow fever is not feasible because of the wildlife reservoir for the virus but there is a safe, affordable, and highly effective vaccine against the disease. Large-scale vaccination efforts during the 1940s, 1950s, and 1960s reduced the yellow fever burden for several decades but, after a period of low vaccination coverage, the number of cases rebounded. In 2005, the Yellow Fever Initiative—a collaboration between the World Health Organization (WHO) and the United Nations Children Fund supported by the Global Alliance for Vaccines and Immunization (GAVI Alliance)—was launched to create a vaccine stockpile for use in epidemics and to implement preventive mass vaccination campaigns in the 12 most affected countries in West Africa. Campaigns have now been implemented in all these countries except Nigeria. However, without an estimate of the current yellow fever burden, it is hard to determine the impact of these campaigns. Here, the researchers use recent yellow fever occurrence data, serological survey data, and improved estimation methods to update estimates of the yellow fever burden and to determine the impact of mass vaccination on this burden.
What Did the Researchers Do and Find?
The researchers developed a generalized linear statistical model and used data on the locations where yellow fever was reported between 1987 and 2011 in Africa, force of infection estimates for a limited set of locations where serological surveys were available (the force of infection is the rate at which susceptible individuals acquire a disease), data on vaccination coverage, and demographic and environmental data for their calculations. They estimate that about 130,000 yellow fever cases with fever and jaundice or hemorrhage occurred in Africa in 2013 and that about 78,000 people died from the disease. By evaluating the difference between this estimate, which takes into account the current vaccination coverage, and a hypothetical scenario that excluded the mass vaccination campaigns, the researchers estimate that these campaigns have reduced the burden of disease by 27% across Africa and by up to 82% in the countries targeted by the campaigns (an overall reduction of 57% in the 12 targeted countries).
What Do These Findings Mean?
These findings provide a contemporary estimate of the burden of yellow fever in Africa. This estimate is broadly similar to the historic estimate of 200,000 cases and 30,000 deaths annually, which was based on serological survey data obtained from children in Nigeria between 1945 and 1971. Notably, both disease burden estimates are several hundred-fold higher than the average number of yellow fever cases reported annually to WHO, which reflects the difficulties associated with the diagnosis of yellow fever. Importantly, these findings also provide an estimate of the impact of recent mass vaccination campaigns. All these findings have a high level of uncertainty, however, because of the lack of data from both surveillance and serological surveys. Other assumptions incorporated in the researchers' model may also affect the accuracy of these findings. Nevertheless, the framework for burden estimation developed here provides essential new information about the yellow fever burden and the impact of vaccination campaigns and should help the partners of the Yellow Fever Initiative estimate the potential impact of future vaccination campaigns and ensure the efficient allocation of resources for yellow fever control.
Additional Information
Please access these websites via the online version of this summary at
The World Health Organization provides detailed information about yellow fever (in several languages), including photo stories about vaccination campaigns in the Sudan and Mali; it also provides information about the Yellow Fever Initiative (in English and French)
The GAVI Alliance website includes detailed of its support for yellow fever vaccination
The US Centers for Disease Control and Prevention provides information about yellow fever for the public, travelers, and health care providers
The UK National Health Service Choices website also has information about yellow fever
Wikipedia has a page on yellow fever that includes information about the history of the disease (note that Wikipedia is a free online encyclopedia that anyone can edit; available in several languages)
PMCID: PMC4011853  PMID: 24800812
13.  Parameters for the Mathematical Modelling of Clostridium difficile Acquisition and Transmission: A Systematic Review 
PLoS ONE  2013;8(12):e84224.
Mathematical modelling of Clostridium difficile infection dynamics could contribute to the optimisation of strategies for its prevention and control. The objective of this systematic review was to summarise the available literature specifically identifying the quantitative parameters required for a compartmental mathematical model of Clostridium difficile transmission.
Six electronic healthcare databases were searched and all screening, data extraction and study quality assessments were undertaken in duplicate. Results were synthesised using a narrative approach.
Fifty-four studies met the inclusion criteria. Reproduction numbers for hospital based epidemics were described in two studies with a range from 0.55 to 7. Two studies provided consistent data on incubation periods. For 62% of cases, symptoms occurred in less than 4 weeks (3-28 days) after infection. Evidence on contact patterns was identified in four studies but with limited data reported for populating a mathematical model. Two studies, including one without clinically apparent donor-recipient pairs, provided information on serial intervals for household or ward contacts, showing transmission intervals of <1 week in ward based contacts compared to up to 2 months for household contacts. Eight studies reported recovery rates of between 75% - 100% for patients who had been treated with either metronidazole or vancomycin. Forty-nine studies gave recurrence rates of between 3% and 49% but were limited by varying definitions of recurrence. No study was found which specifically reported force of infection or net reproduction numbers.
There is currently scant literature overtly citing estimates of the parameters required to inform the quantitative modelling of Clostridium difficile transmission. Further high quality studies to investigate transmission parameters are required, including through review of published epidemiological studies where these quantitative estimates may not have been explicitly estimated, but that nonetheless contain the relevant data to allow their calculation. [Systematic review reference: CRD42012003081]
PMCID: PMC3869946  PMID: 24376797
14.  Household Transmission of 2009 Pandemic Influenza A (H1N1) Virus in the United States 
The New England journal of medicine  2009;361(27):10.1056/NEJMoa0905498.
As of June 11, 2009, a total of 17,855 probable or confirmed cases of 2009 pandemic influenza A (H1N1) had been reported in the United States. Risk factors for transmission remain largely uncharacterized. We characterize the risk factors and describe the transmission of the virus within households.
Probable and confirmed cases of infection with the 2009 H1N1 virus in the United States were reported to the Centers for Disease Control and Prevention with the use of a standardized case form. We investigated transmission of infection in 216 households — including 216 index patients and their 600 household contacts — in which the index patient was the first case patient and complete information on symptoms and age was available for all household members.
An acute respiratory illness developed in 78 of 600 household contacts (13%). In 156 households (72% of the 216 households), an acute respiratory illness developed in none of the household contacts; in 46 households (21%), illness developed in one contact; and in 14 households (6%), illness developed in more than one contact. The proportion of household contacts in whom acute respiratory illness developed decreased with the size of the household, from 28% in two-member households to 9% in six-member households. Household contacts 18 years of age or younger were twice as susceptible as those 19 to 50 years of age (relative susceptibility, 1.96; Bayesian 95% credible interval, 1.05 to 3.78; P = 0.005), and household contacts older than 50 years of age were less susceptible than those who were 19 to 50 years of age (relative susceptibility, 0.17; 95% credible interval, 0.02 to 0.92; P = 0.03). Infectivity did not vary with age. The mean time between the onset of symptoms in a case patient and the onset of symptoms in the household contacts infected by that patient was 2.6 days (95% credible interval, 2.2 to 3.5).
The transmissibility of the 2009 H1N1 influenza virus in households is lower than that seen in past pandemics. Most transmissions occur soon before or after the onset of symptoms in a case patient.
PMCID: PMC3840270  PMID: 20042753
15.  Feature Selection Methods for Identifying Genetic Determinants of Host Species in RNA Viruses 
PLoS Computational Biology  2013;9(10):e1003254.
Despite environmental, social and ecological dependencies, emergence of zoonotic viruses in human populations is clearly also affected by genetic factors which determine cross-species transmission potential. RNA viruses pose an interesting case study given their mutation rates are orders of magnitude higher than any other pathogen – as reflected by the recent emergence of SARS and Influenza for example. Here, we show how feature selection techniques can be used to reliably classify viral sequences by host species, and to identify the crucial minority of host-specific sites in pathogen genomic data. The variability in alleles at those sites can be translated into prediction probabilities that a particular pathogen isolate is adapted to a given host. We illustrate the power of these methods by: 1) identifying the sites explaining SARS coronavirus differences between human, bat and palm civet samples; 2) showing how cross species jumps of rabies virus among bat populations can be readily identified; and 3) de novo identification of likely functional influenza host discriminant markers.
Author Summary
Moving away from genome scan methods used for human GWAS (ultimately inappropriate for the short highly polymorphic genomes of RNA viruses), our work shows the power and potential of multi-class machine learning algorithms in inferring the functional genetic changes associated with phenotypic change (e.g. crossing a species barrier). We show that even distantly related viruses within a viral family share highly conserved genetic signatures of host specificity; reinforce how fitness landscapes of host adaptation are shaped by host phylogeny; and highlight the evolutionary trajectories of RNA viruses in rapid expansion and under great evolutionary pressure. We do so by (for each dataset) unveiling a set of phenotype characteristic mutations which are shown to be functionally relevant, thus providing new insights into phenotypic relationships between RNA viruses. These methods also provide a solid statistical framework with which the degree of host adaptation can be inferred, thus serving as a valuable tool for studying host transition events with particular relevance for emerging infectious diseases. These methods can then serve as rigorous tools of emergence potential assessment, specifically in scenarios where rapid host classification of newly emerging viruses can be more important than identifying putative functional sites.
PMCID: PMC3794897  PMID: 24130470
16.  Epidemic growth rate and household reproduction number in communities of households, schools and workplaces 
Journal of mathematical biology  2010;63(4):691-734.
In this paper we present a novel and coherent modelling framework for the characterisation of the real-time growth rate in SIR models of epidemic spread in populations with social structures of increasing complexity. Known results about homogeneous mixing and multitype models are included in the framework, which is then extended to models with households and models with households and schools/workplaces.
Efficient methods for the exact computation of the real-time growth rate are presented for the standard SIR model with constant infection and recovery rates (Markovian case). Approximate methods are described for a large class of models with time-varying infection rates (non-Markovian case). The quality of the approximation is assessed via comparison with results from individual-based stochastic simulations.
The methodology is then applied to the case of influenza in models with households and schools/workplaces, to provide an estimate of a household-to-household reproduction number and thus asses the effort required to prevent an outbreak by targeting control policies at the level of households. The results highlight the risk of underestimating such effort when the additional presence of schools/workplaces is neglected.
Our framework increases the applicability of models of epidemic spread in socially structured population by linking earlier theoretical results, mainly focused on time-independent key epidemiological parameters (e.g. reproduction numbers, critical vaccination coverage, epidemic final size) to new results on the epidemic dynamics.
PMCID: PMC3786716  PMID: 21120484
Stochastic epidemic models; Real-time growth rate; Household reproduction number; Structured populations; Two levels of mixing; Epidemic dynamics
17.  Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings 
Science (New York, N.Y.)  2009;324(5934):1557-1561.
A novel influenza A (H1N1) virus has spread rapidly across the globe. Judging its pandemic potential is difficult with limited data, but nevertheless essential to inform appropriate health responses. By analyzing the outbreak in Mexico, early data on international spread, and viral genetic diversity, we make an early assessment of transmissibility and severity. Our estimates suggest that 23,000 (range 6000 to 32,000) individuals had been infected in Mexico by late April, giving an estimated case fatality ratio (CFR) of 0.4% (range: 0.3 to 1.8%) based on confirmed and suspected deaths reported to that time. In a community outbreak in the small community of La Gloria, Veracruz, no deaths were attributed to infection, giving an upper 95% bound on CFR of 0.6%. Thus, although substantial uncertainty remains, clinical severity appears less than that seen in the 1918 influenza pandemic but comparable with that seen in the 1957 pandemic. Clinical attack rates in children in La Gloria were twice that in adults (<15 years of age: 61%; ≥15 years: 29%). Three different epidemiological analyses gave basic reproduction number (R0) estimates in the range of 1.4 to 1.6, whereas a genetic analysis gave a central estimate of 1.2. This range of values is consistent with 14 to 73 generations of human-to-human transmission having occurred in Mexico to late April. Transmissibility is therefore substantially higher than that of seasonal flu, and comparable with lower estimates of R0 obtained from previous influenza pandemics.
PMCID: PMC3735127  PMID: 19433588
18.  Using Routine Surveillance Data to Estimate the Epidemic Potential of Emerging Zoonoses: Application to the Emergence of US Swine Origin Influenza A H3N2v Virus 
PLoS Medicine  2013;10(3):e1001399.
Using a novel method to assess the risks of outbreaks and epidemics, Simon Cauchemez and colleagues provide insight into a simple tool that allows for more robust monitoring of the epidemic potential of zoonoses.
Prior to emergence in human populations, zoonoses such as SARS cause occasional infections in human populations exposed to reservoir species. The risk of widespread epidemics in humans can be assessed by monitoring the reproduction number R (average number of persons infected by a human case). However, until now, estimating R required detailed outbreak investigations of human clusters, for which resources and expertise are not always available. Additionally, existing methods do not correct for important selection and under-ascertainment biases. Here, we present simple estimation methods that overcome many of these limitations.
Methods and Findings
Our approach is based on a parsimonious mathematical model of disease transmission and only requires data collected through routine surveillance and standard case investigations. We apply it to assess the transmissibility of swine-origin influenza A H3N2v-M virus in the US, Nipah virus in Malaysia and Bangladesh, and also present a non-zoonotic example (cholera in the Dominican Republic). Estimation is based on two simple summary statistics, the proportion infected by the natural reservoir among detected cases (G) and among the subset of the first detected cases in each cluster (F). If detection of a case does not affect detection of other cases from the same cluster, we find that R can be estimated by 1−G; otherwise R can be estimated by 1−F when the case detection rate is low. In more general cases, bounds on R can still be derived.
We have developed a simple approach with limited data requirements that enables robust assessment of the risks posed by emerging zoonoses. We illustrate this by deriving transmissibility estimates for the H3N2v-M virus, an important step in evaluating the possible pandemic threat posed by this virus.
Please see later in the article for the Editors' Summary
Editors' Summary
When a virus emerges in the human population, such viruses can cause global epidemics potentially harming large numbers of people. Zoonotic viruses are viruses that are transmissible from animals to humans; the global health threat of zoonotic viruses was recently demonstrated by the 2009 H1N1 influenza pandemic and the SARS epidemic in 2003. Many zoonotic viruses are transmitted by means of an infected vector, while others can be transmitted by inhalation, contact with infected excretions, or by direct contact with an infected animal. Zoonotic viruses primarily cause occasional infections in human populations exposed to reservoir species (the animal species harboring the virus) because the pathogens are usually poorly adapted for sustained human-to-human transmission. However, zoonotic viruses are under strong selective pressure to acquire the ability for human-to-human transmission.
Why Was This Study Done?
The highly pathogenic H5N1 avian influenza epidemic was alarming to many because of the high mortality rate in humans and its rapid spread in avian populations. Public health response to outbreaks such as those of H5N1 avian influenza and SARS required reliable estimates of transmissibility (how easily it spreads between people) and severity (the proportion of infected people who needed hospital treatment). For efficient prevention and control of the emerging epidemic, quantitative and rigorous assessment of the associated risks is needed. Specifically, health officials and researchers need fast, reliable methods for estimating the extent to which a virus has acquired the ability to transmit from person to person. In this study, the authors developed a novel method to estimate a standard measure of transmissibility, the human-to-human reproduction number R (average number of persons infected by a human case) of a zoonotic virus, which overcomes many of the limitations of existing methods.
What Did the Researchers Do and Find?
The authors developed a simple method to estimate the reproduction number of emerging zoonoses from routine surveillance data. By using two simple summary statistics, the proportion infected by the natural reservoir among detected cases (G) and among the subset of the first detected cases in each cluster (F), the authors estimated R, the reproduction number of zoonoses in humans. The authors then applied their new approach to assess the human-to-human transmissibility of swine-origin influenza A variant (H1N1v, H1N2v, and H3N2v) virus, in particular that of the H3N2v-M virus, from US surveillance data for the period December 2005–December 2011, Nipah virus in Malaysia and Bangladesh, as well as to a non-zoonotic pathogen Vibrio Cholerae in the Dominican Republic. This study demonstrates the applicability of this novel approach to estimating R during zoonotic and certain non-zoonotic outbreaks.
What Do These Findings Mean?
Cauchemez and colleagues show that their new approach will be useful in assessing human-to-human transmissions during zoonotic outbreaks. The authors show that their new method does not require as much of an investigation effort as existing methods, the statistical treatment of the data is extremely simple, and the robustness of the method is demonstrated even if larger clusters are more likely to be detected and if the ability to detect all cases in a cluster once a cluster is identified is low. This method of estimating R is designed for the context of subcritical outbreaks, i.e., R<1. However if R≥1, other estimation methods will be needed.
Additional Information
Please access these Web sites via the online version of this summary at 10.1371/journal.pmed.1001399.
The US Centers for Disease Control and Prevention's (CDC) National Center for Emerging and Zoonotic Infectious Diseases provides information on infectious disease
The CDC also has resources for pandemic flu and H3N2v
The University of Wisconsin's School of Veterinary medicine has an online tutorial on zoonotic diseases
The European Food Safety Authority (EFSA) also provides comprehensive information on zoonotic diseases
PMCID: PMC3589342  PMID: 23472057
19.  Estimating Air Temperature and Its Influence on Malaria Transmission across Africa 
PLoS ONE  2013;8(2):e56487.
Malaria transmission is strongly influenced by climatic conditions which determine the abundance and seasonal dynamics of the Anopheles vector. In particular, water temperature influences larval development rates whereas air temperature determines adult longevity as well as the rate of parasite development within the adult mosquito. Although data on land surface temperature exist at a spatial resolution of approximately 1 km globally with four time steps per day, comparable data are not currently available for air temperature. In order to address this gap and demonstrate the importance of using the right type of temperature data, we fitted simple models of the relationship between land-surface and air temperature at lower resolution to obtain a high resolution estimate of air temperature across Africa. We then used these estimates to calculate some crucial malaria transmission parameters that strongly depend on air temperatures. Our results demonstrate substantial differences between air and surface temperatures that impact temperature-based maps of areas suitable for transmission. We present high resolution maps of the malaria transmission parameters driven by air temperature and their seasonal variation. The fitted air temperature datasets are made publicly available alongside this publication.
PMCID: PMC3577915  PMID: 23437143
20.  Influenza Infection Rates, Measurement Errors and the Interpretation of Paired Serology 
PLoS Pathogens  2012;8(12):e1003061.
Serological studies are the gold standard method to estimate influenza infection attack rates (ARs) in human populations. In a common protocol, blood samples are collected before and after the epidemic in a cohort of individuals; and a rise in haemagglutination-inhibition (HI) antibody titers during the epidemic is considered as a marker of infection. Because of inherent measurement errors, a 2-fold rise is usually considered as insufficient evidence for infection and seroconversion is therefore typically defined as a 4-fold rise or more. Here, we revisit this widely accepted 70-year old criterion. We develop a Markov chain Monte Carlo data augmentation model to quantify measurement errors and reconstruct the distribution of latent true serological status in a Vietnamese 3-year serological cohort, in which replicate measurements were available. We estimate that the 1-sided probability of a 2-fold error is 9.3% (95% Credible Interval, CI: 3.3%, 17.6%) when antibody titer is below 10 but is 20.2% (95% CI: 15.9%, 24.0%) otherwise. After correction for measurement errors, we find that the proportion of individuals with 2-fold rises in antibody titers was too large to be explained by measurement errors alone. Estimates of ARs vary greatly depending on whether those individuals are included in the definition of the infected population. A simulation study shows that our method is unbiased. The 4-fold rise case definition is relevant when aiming at a specific diagnostic for individual cases, but the justification is less obvious when the objective is to estimate ARs. In particular, it may lead to large underestimates of ARs. Determining which biological phenomenon contributes most to 2-fold rises in antibody titers is essential to assess bias with the traditional case definition and offer improved estimates of influenza ARs.
Author Summary
Each year, seasonal influenza is responsible for about three to five million severe illnesses and about 250,000 to 500,000 deaths worldwide. In order to assess the burden of disease and guide control policies, it is important to quantify the proportion of people infected by an influenza virus each year. Since infection usually leaves a “signature” in the blood of infected individuals (namely a rise in antibodies), a standard protocol consists in collecting blood samples in a cohort of subjects and determining the proportion of those who experienced such rise. However, because of inherent measurement errors, only large rises are accounted for in the standard 4-fold rise case definition. Here, we revisit this 70 year old and widely accepted and applied criterion. We present innovative statistical techniques to better capture the impact of measurement errors and improve our interpretation of the data. Our analysis suggests that the number of people infected by an influenza virus each year might be substantially larger than previously thought, with important implications for our understanding of the transmission and evolution of influenza – and the nature of infection.
PMCID: PMC3521724  PMID: 23271967
21.  Evaluating the Adequacy of Gravity Models as a Description of Human Mobility for Epidemic Modelling 
PLoS Computational Biology  2012;8(10):e1002699.
Gravity models have a long history of use in describing and forecasting the movements of people as well as goods and services, making them a natural basis for disease transmission rates over distance. In agent-based micro-simulations, gravity models can be directly used to represent movement of individuals and hence disease. In this paper, we consider a range of gravity models as fits to movement data from the UK and the US. We examine the ability of synthetic networks generated from fitted models to match those from the data in terms of epidemic behaviour; in particular, times to first infection. For both datasets, best fits are obtained with a two-piece ‘matched’ power law distance distribution. Epidemics on synthetic UK networks match well those on data networks across all but the smallest nodes for a range of aggregation levels. We derive an expression for time to infection between nodes in terms of epidemiological and network parameters which illuminates the influence of network clustering in spread across networks and suggests an approximate relationship between the log-likelihood deviance of model fit and the match times to infection between synthetic and data networks. On synthetic US networks, the match in epidemic behaviour is initially poor and sensitive to the initially infected node. Analysis of times to infection indicates a failure of models to capture infrequent long-range contact between large nodes. An assortative model based on node population size captures this heterogeneity, considerably improving the epidemiological match between synthetic and data networks.
Author Summary
An accurate representation of disease transmission between spatially-distinct regions is an essential part of modelling epidemic behaviour on a national or international scale. Gravity models, which describe movement fluxes between regions in terms of their populations and distance from each other, have a history of successful use in the geography and economics and are increasingly used in epidemiology. We look at the ability of a range of gravity models to fit human movement data from the UK and the US. In particular, we compare the behaviour of a simple flu-like epidemic model on synthetic networks generated by fitted gravity models and on the original network present in the data, using time to first infection. For UK data, epidemic behaviour on synthetic networks matches that on the original data quite closely. For US movement data, synthetic networks perform much worse. We develop an analytic expression for infection time between two regions which indicates that our gravity models fail to capture long range connections between large populations. A model with assortative mixing based on population size greatly improves the match between synthetic and data networks.
PMCID: PMC3475681  PMID: 23093917
23.  Influenza Transmission in Households During the 1918 Pandemic 
American Journal of Epidemiology  2011;174(5):505-514.
Analysis of historical data has strongly shaped our understanding of the epidemiology of pandemic influenza and informs analysis of current and future epidemics. Here, the authors analyzed previously unpublished documents from a large household survey of the “Spanish” H1N1 influenza pandemic, conducted in 1918, for the first time quantifying influenza transmissibility at the person-to-person level during that most lethal of pandemics. The authors estimated a low probability of person-to-person transmission relative to comparable estimates from seasonal influenza and other directly transmitted infections but similar to recent estimates from the 2009 H1N1 pandemic. The authors estimated a very low probability of asymptomatic infection, a previously unknown parameter for this pandemic, consistent with an unusually virulent virus. The authors estimated a high frequency of prior immunity that they attributed to a largely unreported influenza epidemic in the spring of 1918 (or perhaps to cross-reactive immunity). Extrapolating from this finding, the authors hypothesize that prior immunity partially protected some populations from the worst of the fall pandemic and helps explain differences in attack rates between populations. Together, these analyses demonstrate that the 1918 influenza virus, though highly virulent, was only moderately transmissible and thus in a modern context would be considered controllable.
PMCID: PMC3695637  PMID: 21749971
disease transmission, infectious; epidemics; history of medicine; influenza, human; Orthomyxoviridae; pandemics; virulence
24.  Inferring pandemic growth rates from sequence data 
Using sequence data to infer population dynamics is playing an increasing role in the analysis of outbreaks. The most common methods in use, based on coalescent inference, have been widely used but not extensively tested against simulated epidemics. Here, we use simulated data to test the ability of both parametric and non-parametric methods for inference of effective population size (coded in the popular BEAST package) to reconstruct epidemic dynamics. We consider a range of simulations centred on scenarios considered plausible for pandemic influenza, but our conclusions are generic for any exponentially growing epidemic. We highlight systematic biases in non-parametric effective population size estimation. The most prominent such bias leads to the false inference of slowing of epidemic spread in the recent past even when the real epidemic is growing exponentially. We suggest some sampling strategies that could reduce (but not eliminate) some of the biases. Parametric methods can correct for these biases if the infected population size is large. We also explore how some poor sampling strategies (e.g. that over-represent epidemiologically linked clusters of cases) could dramatically exacerbate bias in an uncontrolled manner. Finally, we present a simple diagnostic indicator, based on coalescent density and which can easily be applied to reconstructed phylogenies, that identifies time-periods for which effective population size estimates are less likely to be biased. We illustrate this with an application to the 2009 H1N1 pandemic.
PMCID: PMC3385754  PMID: 22337627
phylodynamics; epidemics; simulation
25.  Serial Intervals and the Temporal Distribution of Secondary Infections within Households of 2009 Pandemic Influenza A (H1N1): Implications for Influenza Control Recommendations 
A critical issue during the 2009 influenza A (H1N1) pandemic was determining the appropriate duration of time individuals with influenza-like illness (ILI) should remain isolated to reduce onward transmission while limiting societal disruption. Ideally this is based on knowledge of the relative infectiousness of ill individuals at each point during the course of the infection. Data on 261 clinically apparent pH1N1 infector-infectee pairs in households, from 7 epidemiological studies conducted in the United States early in 2009, were analyzed to estimate the distribution of times from symptom onset in an infector to symptom onset in the household contacts they infect (mean, 2.9 days, not correcting for tertiary transmission). Only 5% of transmission events were estimated to take place >3 days after the onset of clinical symptoms among those ill with pH1N1 virus. These results will inform future recommendations on duration of isolation of individuals with ILI.
PMCID: PMC3106264  PMID: 21342883

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