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1.  Characterizing the Transmission Dynamics and Control of Ebola Virus Disease 
PLoS Biology  2015;13(1):e1002057.
Carefully calibrated transmission models have the potential to guide public health officials on the nature and scale of the interventions required to control the ongoing Ebola virus disease epidemic in West Africa.
Carefully calibrated transmission models have the potential to guide public health officials on the nature and scale of the interventions required to control epidemics. In the context of the ongoing Ebola virus disease (EVD) epidemic in Liberia, Drake and colleagues, in this issue of PLOS Biology, employed an elegant modeling approach to capture the distributions of the number of secondary cases that arise in the community and health care settings in the context of changing population behaviors and increasing hospital capacity. Their findings underscore the role of increasing the rate of safe burials and the fractions of infectious individuals who seek hospitalization together with hospital capacity to achieve epidemic control. However, further modeling efforts of EVD transmission and control in West Africa should utilize the spatial-temporal patterns of spread in the region by incorporating spatial heterogeneity in the transmission process. Detailed datasets are urgently needed to characterize temporal changes in population behaviors, contact networks at different spatial scales, population mobility patterns, adherence to infection control measures in hospital settings, and hospitalization and reporting rates.
doi:10.1371/journal.pbio.1002057
PMCID: PMC4301953  PMID: 25607595
2.  Years of Life Lost in the First Wave of the 2009 Influenza A(H1N1) Pandemic in Hong Kong 
American Journal of Epidemiology  2013;178(8):1313-1318.
The impact of influenza pandemics might be overestimated; the published studies of years of life lost (YLL) have typically ignored the presence of underlying chronic conditions or health risk behaviors in most deaths. We used data on deaths involving laboratory-confirmed 2009 influenza A(H1N1) virus infection that occurred between April 2009 and May 2010 in Hong Kong, China, to adjust for these underlying risk factors. Life expectancy was corrected with hazard-based modifications to the life tables. The excess hazards posed by underlying risk factors were added to the “baseline” age-specific hazards in the local life tables to reflect the life expectancy associated with each underlying risk factor. Of 72 deceased persons with laboratory-confirmed 2009 influenza A(H1N1) virus infection, 56% had underlying risk factors. We estimated that the 2009 pandemic was associated with 1,540 (95% confidence interval: 1,350, 1,630) YLL after adjustment for age and underlying risk factors. This figure is approximately 25% lower than the YLL estimate of 2,080 derived after adjustment for age but not for risk factors. Our analysis demonstrates the potential scale of bias in YLL estimation if underlying risk factors are ignored. The estimation of YLL with correction for underlying risk factors in addition to age could also provide a framework for similar calculations elsewhere.
doi:10.1093/aje/kwt120
PMCID: PMC3792731  PMID: 23978528
influenza; pandemics; underlying risk factors; years of life lost
3.  Transmission dynamics and control of Ebola virus disease (EVD): a review 
BMC Medicine  2014;12(1):196.
The complex and unprecedented Ebola epidemic ongoing in West Africa has highlighted the need to review the epidemiological characteristics of Ebola Virus Disease (EVD) as well as our current understanding of the transmission dynamics and the effect of control interventions against Ebola transmission. Here we review key epidemiological data from past Ebola outbreaks and carry out a comparative review of mathematical models of the spread and control of Ebola in the context of past outbreaks and the ongoing epidemic in West Africa. We show that mathematical modeling offers useful insights into the risk of a major epidemic of EVD and the assessment of the impact of basic public health measures on disease spread. We also discuss the critical need to collect detailed epidemiological data in real-time during the course of an ongoing epidemic, carry out further studies to estimate the effectiveness of interventions during past outbreaks and the ongoing epidemic, and develop large-scale modeling studies to study the spread and control of viral hemorrhagic fevers in the context of the highly heterogeneous economic reality of African countries.
doi:10.1186/s12916-014-0196-0
PMCID: PMC4207625  PMID: 25300956
Ebola Virus Disease; Transmission model; Control interventions; Basic reproduction number; West Africa; Incubation; Serial interval; Case fatality ratio; Isolation; Behavior change
4.  Modes of Transmission of Influenza B Virus in Households 
PLoS ONE  2014;9(9):e108850.
Introduction
While influenza A and B viruses can be transmitted via respiratory droplets, the importance of small droplet nuclei “aerosols” in transmission is controversial.
Methods and Findings
In Hong Kong and Bangkok, in 2008–11, subjects were recruited from outpatient clinics if they had recent onset of acute respiratory illness and none of their household contacts were ill. Following a positive rapid influenza diagnostic test result, subjects were randomly allocated to one of three household-based interventions: hand hygiene, hand hygiene plus face masks, and a control group. Index cases plus their household contacts were followed for 7–10 days to identify secondary infections by reverse transcription polymerase chain reaction (RT-PCR) testing of respiratory specimens. Index cases with RT-PCR-confirmed influenza B were included in the present analyses. We used a mathematical model to make inferences on the modes of transmission, facilitated by apparent differences in clinical presentation of secondary infections resulting from aerosol transmission. We estimated that approximately 37% and 26% of influenza B virus transmission was via the aerosol mode in households in Hong Kong and Bangkok, respectively. In the fitted model, influenza B virus infections were associated with a 56%–72% risk of fever plus cough if infected via aerosol route, and a 23%–31% risk of fever plus cough if infected via the other two modes of transmission.
Conclusions
Aerosol transmission may be an important mode of spread of influenza B virus. The point estimates of aerosol transmission were slightly lower for influenza B virus compared to previously published estimates for influenza A virus in both Hong Kong and Bangkok. Caution should be taken in interpreting these findings because of the multiple assumptions inherent in the model, including that there is limited biological evidence to date supporting a difference in the clinical features of influenza B virus infection by different modes.
doi:10.1371/journal.pone.0108850
PMCID: PMC4182555  PMID: 25268241
6.  The epidemiological and public health research response to 2009 pandemic influenza A(H1N1): experiences from Hong Kong 
Background
In recent years Hong Kong has invested in research infrastructure to appropriately respond to novel infectious disease epidemics. Research from Hong Kong made a strong contribution to the international response to the 2009 influenza A(H1N1) pandemic (pH1N1). Summarizing, describing and reviewing the Hong Kong's response to the 2009 pandemic, this article aimed to identify key elements of a real-time research response.
Methods
A systematic search in PubMed and EMBASE for research into the infection dynamics and natural history, impact or control of pH1N1 in Hong Kong. Eligible articles were analyzed according to their scope.
Results
55 articles were included in the review. Transmissibility of pH1N1 was similar in Hong Kong to elsewhere, and only a small fraction of infections were associated with severe disease. School closures were effective in reducing pH1N1 transmission, oseltamivir was effective for treatment of severe cases while convalescent plasma therapy has the potential to mitigate future pandemics.
Conclusions
There was a rapid and comprehensive research response to pH1N1 in Hong Kong, providing important information on the epidemiology of the novel virus with relevance internationally as well as locally. The scientific knowledge gained through these detailed studies of pH1N1 is now being used to revise and update pandemic plans. The experiences of the research response in Hong Kong could provide a template for the research response to future emerging and reemerging disease epidemics.
doi:10.1111/j.1750-2659.2012.00420.x
PMCID: PMC3705741  PMID: 22883352
7.  Heterogeneity in Viral Shedding Among Individuals With Medically Attended Influenza A Virus Infection 
The Journal of Infectious Diseases  2013;207(8):1281-1285.
Compared with the average transmissibility of human influenza A virus, much less attention has been paid to the potential variability in its transmissibility. We considered viral shedding as a proxy for infectiousness and explored the heterogeneity of infectiousness among patients with medically attended seasonal influenza A virus infection. The analysis revealed that viral shedding is more heterogeneous in children than in adults. The top 20% most infectious children and adults were estimated to be responsible for 89%–96% and 78%–82%, respectively, of the total infectiousness in each age group. Further investigation is required to correlate the substantial variations in viral shedding with heterogeneity in actual transmissibility.
doi:10.1093/infdis/jit034
PMCID: PMC3603536  PMID: 23382573
influenza; viral shedding; infectiousness
8.  Infection Fatality Risk of the Pandemic A(H1N1)2009 Virus in Hong Kong 
American Journal of Epidemiology  2013;177(8):834-840.
One measure of the severity of a pandemic influenza outbreak at the individual level is the risk of death among people infected by the new virus. However, there are complications in estimating both the numerator and denominator. Regarding the numerator, statistical estimates of the excess deaths associated with influenza virus infections tend to exceed the number of deaths associated with laboratory-confirmed infection. Regarding the denominator, few infections are laboratory confirmed, while differences in case definitions and approaches to case ascertainment can lead to wide variation in case fatality risk estimates. Serological surveillance can be used to estimate the cumulative incidence of infection as a denominator that is more comparable across studies. We estimated that the first wave of the influenza A(H1N1)pdm09 virus in 2009 was associated with approximately 232 (95% confidence interval: 136, 328) excess deaths of all ages in Hong Kong, mainly among the elderly. The point estimates of the risk of death on a per-infection basis increased substantially with age, from below 1 per 100,000 infections in children to 1,099 per 100,000 infections in those 60–69 years of age. Substantial variation in the age-specific infection fatality risk complicates comparison of the severity of different influenza strains.
doi:10.1093/aje/kws314
PMCID: PMC3658096  PMID: 23459950
death; human influenza; severity
9.  Estimating the Risk of Parvovirus B19 Infection in Blood Donors and Pregnant Women in Japan 
PLoS ONE  2014;9(3):e92519.
Background
Seroepidemiological study of parvovirus B19 has not taken place for some 20 years in Japan. To estimate the risk of parvovirus B19 infection in Japan among blood donors and pregnant women in this century, a seroepidemiological survey and statistical modeling of the force of infection were conducted.
Methodology/Principal Findings
The time- and age-specific seroprevalence data were suggestive of strong age-dependency in the risk of infection. Employing a piecewise constant model, the highest forces of infection of 0.05 and 0.12 per year were observed among those aged 0–4 and 5–9 years, respectively, while estimates among older individuals were less than 0.01 per year. Analyzing the antigen detection data among blood donors, the age-specific proportion positive was highest among those aged 30–39 years, agreeing with the presence of dip in seroprevalence in this age-group. Among pregnant women, up to 107 fetal deaths and 21 hydrops fetalis were estimated to have occurred annually across Japan.
Conclusions
Seroepidemiological profiles of PVB19 infection in Japan was characterized with particular emphasis on the risk of infection in blood donors and the burden of infection among pregnant women. When a vaccine becomes available in the future, a similar seroepidemiological study is expected to play a key role in planning the appropriate immunization policy.
doi:10.1371/journal.pone.0092519
PMCID: PMC3962423  PMID: 24658180
10.  Cost-effective length and timing of school closure during an influenza pandemic depend on the severity 
Background
There has been a variation in published opinions toward the effectiveness of school closure which is implemented reactively when substantial influenza transmissions are seen at schools. Parameterizing an age-structured epidemic model using published estimates of the pandemic H1N1-2009 and accounting for the cost effectiveness, we examined if the timing and length of school closure could be optimized.
Methods
Age-structured renewal equation was employed to describe the epidemic dynamics of an influenza pandemic. School closure was assumed to take place only once during the course of the pandemic, abruptly reducing child-to-child transmission for a fixed length of time and also influencing the transmission between children and adults. Public health effectiveness was measured by reduction in the cumulative incidence, and cost effectiveness was also examined by calculating the incremental cost effectiveness ratio and adopting a threshold of 1.0 × 107 Japanese Yen/life-year.
Results
School closure at the epidemic peak appeared to yield the largest reduction in the final size, while the time of epidemic peak was shown to depend on the transmissibility. As the length of school closure was extended, we observed larger reduction in the cumulative incidence. Nevertheless, the cost effectiveness analysis showed that the cost of our school closure scenario with the parameters derived from H1N1-2009 was not justifiable. If the risk of death is three times or greater than that of H1N1-2009, the school closure could be regarded as cost effective.
Conclusions
There is no fixed timing and duration of school closure that can be recommended as universal guideline for different types of influenza viruses. The effectiveness of school closure depends on the transmission dynamics of a particular influenza virus strain, especially the virulence (i.e. the infection fatality risk).
doi:10.1186/1742-4682-11-5
PMCID: PMC3901768  PMID: 24447310
11.  Excess Mortality Associated With Influenza A and B Virus in Hong Kong, 1998–2009 
The Journal of Infectious Diseases  2012;206(12):1862-1871.
Background. Although deaths associated with laboratory-confirmed influenza virus infections are rare, the excess mortality burden of influenza estimated from statistical models may more reliably quantify the impact of influenza in a population.
Methods. We applied age-specific multiple linear regression models to all-cause and cause-specific mortality rates in Hong Kong from 1998 through 2009. The differences between estimated mortality rates in the presence or absence of recorded influenza activity were used to estimate influenza-associated excess mortality.
Results. The annual influenza-associated all-cause excess mortality rate was 11.1 (95% confidence interval [CI], 7.2–14.6) per 100 000 person-years. We estimated an average of 751 (95% CI, 488–990) excess deaths associated with influenza annually from 1998 through 2009, with 95% of the excess deaths occurring in persons aged ≥65 years. Most of the influenza-associated excess deaths were from respiratory (53%) and cardiovascular (18%) causes. Influenza A(H3N2) epidemics were associated with more excess deaths than influenza A(H1N1) or B during the study period.
Conclusions. Influenza was associated with a substantial number of excess deaths each year, mainly among the elderly, in Hong Kong in the past decade. The influenza-associated excess mortality rates were generally similar in Hong Kong and the United States.
doi:10.1093/infdis/jis628
PMCID: PMC3502382  PMID: 23045622
12.  Theoretical Biology and Medical Modelling: ensuring continued growth and future leadership 
Theoretical biology encompasses a broad range of biological disciplines ranging from mathematical biology and biomathematics to philosophy of biology. Adopting a broad definition of "biology", Theoretical Biology and Medical Modelling, an open access journal, considers original research studies that focus on theoretical ideas and models associated with developments in biology and medicine.
doi:10.1186/1742-4682-10-43
PMCID: PMC3710265  PMID: 23842034
13.  Household transmission of 2009 pandemic influenza A(H1N1): a systematic review and meta-analysis 
Epidemiology (Cambridge, Mass.)  2012;23(4):531-542.
Background
During the 2009 influenza A(H1N1) pandemic, household transmission studies were implemented to understand better the characteristics of the transmission of the novel virus in a confined setting.
Methods
We conducted a systematic review and meta-analysis to assess and summarize the findings of these studies. We identified 27 articles, around half of which reported studies conducted in May and June 2009.
Results
In 13 of the 27 studies (48%) that collected respiratory specimens from household contacts, point estimates of the risk of secondary infection ranged from 3 to 38%, with substantial heterogeneity. Meta-regression analyses revealed that a part of the heterogeneity reflected varying case ascertainment and study designs. The estimates of symptomatic secondary infection risk, based on 20 studies identifying febrile acute respiratory illness among household contacts, also showed substantial variability, with point estimates ranging from 4% to 37%.
Conclusions
Transmission of the 2009 pandemic virus in households appeared to vary in different countries and settings, with differences in estimates of the secondary infection risk also partly due to differences in study designs.
doi:10.1097/EDE.0b013e31825588b8
PMCID: PMC3367058  PMID: 22561117
14.  Aerosol transmission is an important mode of influenza A virus spread 
Nature communications  2013;4:1935.
Influenza A viruses are believed to spread between humans through contact, large respiratory droplets and small particle droplet nuclei (aerosols), but the relative importance of each of these modes of transmission is unclear. Volunteer studies suggest that infections via aerosol transmission may have a higher risk of febrile illness. Here we apply a mathematical model to data from randomized controlled trials of hand hygiene and surgical face masks in Hong Kong and Bangkok households. In these particular environments, inferences on the relative importance of modes of transmission are facilitated by information on the timing of secondary infections and apparent differences in clinical presentation of secondary infections resulting from aerosol transmission. We find that aerosol transmission accounts for approximately half of all transmission events. This implies that measures to reduce transmission by contact or large droplets may not be sufficient to control influenza A virus transmission in households.
doi:10.1038/ncomms2922
PMCID: PMC3682679  PMID: 23736803
15.  Increased Risk of Noninfluenza Respiratory Virus Infections Associated With Receipt of Inactivated Influenza Vaccine 
We randomized 115 children to trivalent inactivated influenza vaccine (TIV) or placebo. Over the following 9 months, TIV recipients had an increased risk of virologically-confirmed non-influenza infections (relative risk: 4.40; 95% confidence interval: 1.31-14.8). Being protected against influenza, TIV recipients may lack temporary non-specific immunity that protected against other respiratory viruses.
doi:10.1093/cid/cis307
PMCID: PMC3404712  PMID: 22423139
16.  How to interpret the transmissibility of novel influenza A(H7N9): an analysis of initial epidemiological data of human cases from China 
Background
As the human infections with novel influenza A(H7N9) virus have been reported from several different provinces in China, the pandemic potential of the virus has been questioned. The presence of human-to-human transmission has not been demonstrated, but the absence of demonstration does not guarantee that there is no such transmission.
Methods
A mathematical model of cluster size distribution is devised without imposing an assumption of subcriticality of the reproduction number and accounting for right censoring of new clusters. The proportion of cases with a history of bird contact is analytically derived, permitting us to fit the model to the observed data of confirmed cases. Using contact history with bird among confirmed cases (n = 129), we estimate the reproduction number of the novel influenza A(H7N9) from human to human.
Results
Analysing twenty confirmed cases with known exposure, the reproduction number for human-to-human transmission was estimated at 0.28 (95% CI: 0.11, 0.45). Sensitivity analysis indicated that the reproduction number is substantially below unity.
Conclusions
It is unlikely to observe an immediate pandemic of novel influenza A(H7N9) virus with human to human transmission. Continued monitoring of cases and animals would be the key to elucidate additional epidemiological characteristics of the virus.
doi:10.1186/1742-4682-10-30
PMCID: PMC3655037  PMID: 23642092
17.  The Impact of Model Building on the Transmission Dynamics under Vaccination: Observable (Symptom-Based) versus Unobservable (Contagiousness-Dependent) Approaches 
PLoS ONE  2013;8(4):e62062.
Background
The way we formulate a mathematical model of an infectious disease to capture symptomatic and asymptomatic transmission can greatly influence the likely effectiveness of vaccination in the presence of vaccine effect for preventing clinical illness. The present study aims to assess the impact of model building strategy on the epidemic threshold under vaccination.
Methodology/Principal Findings
We consider two different types of mathematical models, one based on observable variables including symptom onset and recovery from clinical illness (hereafter, the “observable model”) and the other based on unobservable information of infection event and infectiousness (the “unobservable model”). By imposing a number of modifying assumptions to the observable model, we let it mimic the unobservable model, identifying that the two models are fully consistent only when the incubation period is identical to the latent period and when there is no pre-symptomatic transmission. We also computed the reproduction numbers with and without vaccination, demonstrating that the data generating process of vaccine-induced reduction in symptomatic illness is consistent with the observable model only and examining how the effective reproduction number is differently calculated by two models.
Conclusions
To explicitly incorporate the vaccine effect in reducing the risk of symptomatic illness into the model, it is fruitful to employ a model that directly accounts for disease progression. More modeling studies based on observable epidemiological information are called for.
doi:10.1371/journal.pone.0062062
PMCID: PMC3625221  PMID: 23593507
18.  Modeling the obesity epidemic: social contagion and its implications for control 
Background
As an obesity epidemic has grown worldwide, a variety of intervention programs have been considered, but a scientific approach to comparatively assessing the control programs has still to be considered. The present study aims to describe an obesity epidemic by employing a simple mathematical model that accounts for both social contagion and non-contagious hazards of obesity, thereby comparing the effectiveness of different types of interventions.
Methods
An epidemiological model is devised to describe the time- and age-dependent risk of obesity, the hazard of which is dealt with as both dependent on and independent of obesity prevalence, and parameterizing the model using empirically observed data. The equilibrium prevalence is investigated as our epidemiological outcome, assessing its sensitivity to different parameters that regulate the impact of intervention programs and qualitatively comparing the effectiveness. We compare the effectiveness of different types of interventions, including those directed to never-obese individuals (i.e. primary prevention) and toward obese and ex-obese individuals (i.e. secondary prevention).
Results
The optimal choice of intervention programs considerably varies with the transmission coefficient of obesity, and a limited transmissibility led us to favour preventing weight gain among never-obese individuals. An abrupt decline in the prevalence is expected when the hazards of obesity through contagious and non-contagious routes fall into a particular parameter space, with a high sensitivity to the transmission potential of obesity from person to person. When a combination of two control strategies can be selected, primary and secondary preventions yielded similar population impacts and the superiority of the effectiveness depends on the strength of the interventions at an individual level.
Conclusions
The optimality of intervention programs depends on the contagiousness of obesity. Filling associated data gaps of obesity transmission would help systematically understand the epidemiological dynamics and consider required control programs.
doi:10.1186/1742-4682-10-17
PMCID: PMC3599605  PMID: 23497183
19.  Swine Influenza in Sri Lanka 
Emerging Infectious Diseases  2013;19(3):481-484.
To study influenza viruses in pigs in Sri Lanka,we examined samples from pigs at slaughterhouses. Influenza (H3N2) and A(H1N1)pdm09 viruses were prevalent during 2004–2005 and 2009–2012, respectively. Genetic and epidemiologic analyses of human and swine influenza viruses indicated 2 events of A(H1N1)pdm09 virus spillover from humans to pigs.
doi:10.3201/eid1903.120945
PMCID: PMC3647653  PMID: 23621918
swine influenza; Sri Lanka; epidemiology; viruses; spillover; ecology; A(H1N1)pdm09; influenza
20.  Vaccination and Clinical Severity: Is the Effectiveness of Contact Tracing and Case Isolation Hampered by Past Vaccination? 
While contact tracing and case isolation are considered as the first choice of interventions against a smallpox bioterrorist event, their effectiveness under vaccination is questioned, because not only susceptibility of host and infectiousness of case but also the risk of severe clinical manifestations among cases is known to be reduced by vaccine-induced immunity, thereby potentially delaying the diagnosis and increasing mobility among vaccinated cases. We employed a multi-type stochastic epidemic model, aiming to assess the feasibility of contact tracing and case isolation in a partially vaccinated population and identify data gaps. We computed four epidemiological outcome measures, i.e., (i) the threshold of a major epidemic under the interventions; (ii) the expected total number of cases; (iii) the probability of extinction, and (iv) the expected duration of an outbreak, demonstrating that all of these outcomes critically depend on the clinical impact of past vaccination on the diagnosis and movement of vaccinated cases. We discuss that, even in the absence of smallpox in the present day, one should consider the way to empirically quantify the delay in case detection and an increase in the frequency of contacts among previously vaccinated cases compared to unvaccinated during the early stage of an epidemic so that the feasibility of contact tracing and case isolation in a vaccinated population can be explicitly assessed.
doi:10.3390/ijerph10030816
PMCID: PMC3709287  PMID: 23446821
symptom; immunization; epidemiology; mathematical model; contact tracing
21.  Age-Dependent Estimates of the Epidemiological Impact of Pandemic Influenza (H1N1-2009) in Japan 
The total number of influenza cases with medical attendance has been estimated from sentinel surveillance data in Japan under a random sampling assumption of sentinel medical institutions among the total medical institutions. The 2009 pandemic offered a research opportunity to validate the sentinel-based estimation method using the estimated proportion of infections measured by the population-wide seroepidemiological survey employing hemagglutinin inhibition (HI) assay. For the entire population, we estimated the age-standardized proportion of infections at 28.5% and 23.5% using cut-off values of HI titer at 1 : 20 and 1 : 40, respectively. Investigating the age profiles, we show that the estimated influenza-like illness (ILI) cases with medical attendance exceeded the estimated infections among those aged from 0 to 19 years, indicating an overestimation of the magnitude by sentinel-based estimation method. The ratio of estimated cases to estimated infections decreased as a function of age. Examining the geographic distributions, no positive correlation was identified between the estimated cases and infections. Our findings indicate a serious technical limitation of the so-called multiplier method in appropriately quantifying the risk of influenza due to limited specificity of ILI and reporting bias. A seroepidemiological study should be planned in advance of a pandemic.
doi:10.1155/2013/637064
PMCID: PMC3594908  PMID: 23509599
22.  Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks 
Use of the final size distribution of minor outbreaks for the estimation of the reproduction numbers of supercritical epidemic processes has yet to be considered. We used a branching process model to derive the final size distribution of minor outbreaks, assuming a reproduction number above unity, and applying the method to final size data for pneumonic plague. Pneumonic plague is a rare disease with only one documented major epidemic in a spatially limited setting. Because the final size distribution of a minor outbreak needs to be normalized by the probability of extinction, we assume that the dispersion parameter (k) of the negative-binomial offspring distribution is known, and examine the sensitivity of the reproduction number to variation in dispersion. Assuming a geometric offspring distribution with k = 1, the reproduction number was estimated at 1.16 (95% confidence interval: 0.97–1.38). When less dispersed with k = 2, the maximum likelihood estimate of the reproduction number was 1.14. These estimates agreed with those published from transmission network analysis, indicating that the human-to-human transmission potential of the pneumonic plague is not very high. Given only minor outbreaks, transmission potential is not sufficiently assessed by directly counting the number of offspring. Since the absence of a major epidemic does not guarantee a subcritical process, the proposed method allows us to conservatively regard epidemic data from minor outbreaks as supercritical, and yield estimates of threshold values above unity.
doi:10.1016/j.jtbi.2011.10.039
PMCID: PMC3249525  PMID: 22079419
Basic reproduction number; Branching process; Statistical model; Likelihood function; Confidence interval
23.  Sample Size Considerations for One-to-One Animal Transmission Studies of the Influenza A Viruses 
PLoS ONE  2013;8(1):e55358.
Background
Animal transmission studies can provide important insights into host, viral and environmental factors affecting transmission of viruses including influenza A. The basic unit of analysis in typical animal transmission experiments is the presence or absence of transmission from an infectious animal to a susceptible animal. In studies comparing two groups (e.g. two host genetic variants, two virus strains, or two arrangements of animal cages), differences between groups are evaluated by comparing the proportion of pairs with successful transmission in each group. The present study aimed to discuss the significance and power to estimate transmissibility and identify differences in the transmissibility based on one-to-one trials. The analyses are illustrated on transmission studies of influenza A viruses in the ferret model.
Methodology/Principal Findings
Employing the stochastic general epidemic model, the basic reproduction number, R0, is derived from the final state of an epidemic and is related to the probability of successful transmission during each one-to-one trial. In studies to estimate transmissibility, we show that 3 pairs of infectious/susceptible animals cannot demonstrate a significantly higher transmissibility than R0 = 1, even if infection occurs in all three pairs. In comparisons between two groups, at least 4 pairs of infectious/susceptible animals are required in each group to ensure high power to identify significant differences in transmissibility between the groups.
Conclusions
These results inform the appropriate sample sizes for animal transmission experiments, while relating the observed proportion of infected pairs to R0, an interpretable epidemiological measure of transmissibility. In addition to the hypothesis testing results, the wide confidence intervals of R0 with small sample sizes also imply that the objective demonstration of difference or similarity should rest on firmly calculated sample size.
doi:10.1371/journal.pone.0055358
PMCID: PMC3561278  PMID: 23383167
24.  Identifying Transmission Cycles at the Human-Animal Interface: The Role of Animal Reservoirs in Maintaining Gambiense Human African Trypanosomiasis 
PLoS Computational Biology  2013;9(1):e1002855.
Many infections can be transmitted between animals and humans. The epidemiological roles of different species can vary from important reservoirs to dead-end hosts. Here, we present a method to identify transmission cycles in different combinations of species from field data. We used this method to synthesise epidemiological and ecological data from Bipindi, Cameroon, a historical focus of gambiense Human African Trypanosomiasis (HAT, sleeping sickness), a disease that has often been considered to be maintained mainly by humans. We estimated the basic reproduction number of gambiense HAT in Bipindi and evaluated the potential for transmission in the absence of human cases. We found that under the assumption of random mixing between vectors and hosts, gambiense HAT could not be maintained in this focus without the contribution of animals. This result remains robust under extensive sensitivity analysis. When using the distributions of species among habitats to estimate the amount of mixing between those species, we found indications for an independent transmission cycle in wild animals. Stochastic simulation of the system confirmed that unless vectors moved between species very rarely, reintroduction would usually occur shortly after elimination of the infection from human populations. This suggests that elimination strategies may have to be reconsidered as targeting human cases alone would be insufficient for control, and reintroduction from animal reservoirs would remain a threat. Our approach is broadly applicable and could reveal animal reservoirs critical to the control of other infectious diseases.
Author Summary
Gambiense sleeping sickness is a disease transmitted by tsetse flies that mostly affects rural populations in sub-Saharan Africa. Although the parasite that causes the disease can be found in many different wild and domestic animal species, the disease has often been claimed to be maintained mostly by humans. Currently, fewer than 10,000 human cases are reported per year across Africa, and it has been suggested that elimination of gambiense sleeping sickness is feasible. We analysed human and animal case data from a well-known endemic focus of sleeping sickness in Cameroon, to quantify the contribution of the different species to the circulation of the parasite. In a wide range of scenarios, we found that animals are crucial for maintenance in the disease. When informing our model by the distribution of species among habitats as measured in the field, we found indications for independent transmission cycles in animals. This suggests that a risk of reintroduction from animal into human populations would remain even if the disease were eliminated from those human populations.
doi:10.1371/journal.pcbi.1002855
PMCID: PMC3547827  PMID: 23341760
25.  Effectiveness of antiviral prophylaxis coupled with contact tracing in reducing the transmission of the influenza A (H1N1-2009): a systematic review 
Background
During the very early stage of the 2009 pandemic, mass chemoprophylaxis was implemented as part of containment measure. The purposes of the present study were to systematically review the retrospective studies that investigated the effectiveness of antiviral prophylaxis during the 2009 pandemic, and to explicitly estimate the effectiveness by employing a mathematical model.
Methods
A systematic review identified 17 articles that clearly defined the cases and identified exposed individuals based on contact tracing. Analysing a specific school-driven outbreak, we estimated the effectiveness of antiviral prophylaxis using a renewal equation model. Other parameters, including the reproduction number and the effectiveness of antiviral treatment and school closure, were jointly estimated.
Results
Based on the systematic review, median secondary infection risks (SIRs) among exposed individuals with and without prophylaxis were estimated at 2.1% (quartile: 0, 12.2) and 16.6% (quartile: 8.4, 32.4), respectively. A very high heterogeneity in the SIR was identified with an estimated I2 statistic at 71.8%. From the outbreak data in Madagascar, the effectiveness of mass chemoprophylaxis in reducing secondary transmissions was estimated to range from 92.8% to 95.4% according to different model assumptions and likelihood functions, not varying substantially as compared to other parameters.
Conclusions
Only based on the meta-analysis of retrospective studies with different study designs and exposure settings, it was not feasible to estimate the effectiveness of antiviral prophylaxis in reducing transmission. However, modelling analysis of a single outbreak successfully yielded an estimate of the effectiveness that appeared to be robust to model assumptions. Future studies should fill the data gap that has existed in observational studies and allow mathematical models to be used for the analysis of meta-data.
doi:10.1186/1742-4682-10-4
PMCID: PMC3563494  PMID: 23324555

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