Estimating the potential for global dissemination of pandemic pathogens using the global airline network and healthcare development indices.

Pandemics have the potential to incur significant health and economic impacts, and can reach a large number of countries from their origin within weeks. Early identification and containment of a newly emerged pandemic within the source country is key for minimising global impact. To identify a country's potential to control and contain a pathogen with pandemic potential, we compared the quality of a country's healthcare system against its global airline connectivity. Healthcare development was determined using three multi-factorial indices, while detailed airline passenger data was used to identify the global connectivity of all countries. Proximities of countries to a putative 'Worst Case Scenario' (extreme high-connectivity and low-healthcare development) were calculated. We found a positive relationship between a country's connectivity and healthcare metrics. We also identified countries that potentially pose the greatest risk for pandemic dissemination, notably Dominican Republic, India and Pakistan. China and Mexico, both sources of recent influenza and coronavirus pandemics were also identified as among the highest risk countries. Collectively, lower-middle and upper-middle income countries represented the greatest risk, while high income countries represented the lowest risk. Our analysis represents an alternative approach to identify countries where increased within-country disease surveillance and pandemic preparedness may benefit global health.

Dispersion of Legionella bacteria in atmosphere: A practical source location estimation method.

Legionnaires' disease, a form of pneumonia which can be fatal, is transmitted via the inhalation of water droplets containing Legionella bacteria. These droplets can be dispersed in the atmosphere several kilometers from their source. The most common such sources are contaminated water within cooling towers and other air-conditioning systems but other sources such as ornamental fountains and spa pools have also caused outbreaks of the disease in the past. There is an obvious need to locate and eliminate any such sources as quickly as possible. Here a maximum likelihood model estimating the source of an outbreak from case location data has been developed and implemented. Unlike previous models, the average dose exposure sub-model is formulated using a atmospheric dispersion model. How the uncertainty in inferred parameters can be estimated is discussed. The model is applied to the 2012 Edinburgh Legionnaires' disease outbreak.

Methods for calculating credible intervals for ratios of beta distributions with application to relative risks of death during the second plague pandemic.

Employing historical records we are able to estimate the risk of premature death during the second plague pandemic, and identify the Black Death and pestis secunda epidemics. We show a novel method of calculating Bayesian credible intervals for a ratio of beta distributed random variables and use this to quantify uncertainty of relative risk estimates for these two epidemics which we consider in a 2 × 2 contingency table framework.

Modelling the global spread of diseases: A review of current practice and capability.

Mathematical models can aid in the understanding of the risks associated with the global spread of infectious diseases. To assess the current state of mathematical models for the global spread of infectious diseases, we reviewed the literature highlighting common approaches and good practice, and identifying research gaps. We followed a scoping study method and extracted information from 78 records on: modelling approaches; input data (epidemiological, population, and travel) for model parameterization; model validation data. We found that most epidemiological data come from published journal articles, population data come from a wide range of sources, and travel data mainly come from statistics or surveys, or commercial datasets. The use of commercial datasets may benefit the modeller, however makes critical appraisal of their model by other researchers more difficult. We found a minority of records (26) validated their model. We posit that this may be a result of pandemics, or far-reaching epidemics, being relatively rare events compared with other modelled physical phenomena (e.g. climate change). The sparsity of such events, and changes in outbreak recording, may make identifying suitable validation data difficult. We appreciate the challenge of modelling emerging infections given the lack of data for both model parameterisation and validation, and inherent complexity of the approaches used. However, we believe that open access datasets should be used wherever possible to aid model reproducibility and transparency. Further, modellers should validate their models where possible, or explicitly state why validation was not possible.

A review of back-calculation techniques and their potential to inform mitigation strategies with application to non-transmissible acute infectious diseases.

Back-calculation is a process whereby generally unobservable features of an event leading to a disease outbreak can be inferred either in real-time or shortly after the end of the outbreak. These features might include the time when persons were exposed and the source of the outbreak. Such inferences are important as they can help to guide the targeting of mitigation strategies and to evaluate the potential effectiveness of such strategies. This article reviews the process of back-calculation with a particular emphasis on more recent applications concerning deliberate and naturally occurring aerosolized releases. The techniques can be broadly split into two themes: the simpler temporal models and the more sophisticated spatio-temporal models. The former require input data in the form of cases' symptom onset times, whereas the latter require additional spatial information such as the cases' home and work locations. A key aspect in the back-calculation process is the incubation period distribution, which forms the initial topic for consideration. Links between atmospheric dispersion modelling, within-host dynamics and back-calculation are outlined in detail. An example of how back-calculation can inform mitigation strategies completes the review by providing improved estimates of the duration of antibiotic prophylaxis that would be required in the response to an inhalational anthrax outbreak.

Strategies for controlling non-transmissible infection outbreaks using a large human movement data set.

Prediction and control of the spread of infectious disease in human populations benefits greatly from our growing capacity to quantify human movement behavior. Here we develop a mathematical model for non-transmissible infections contracted from a localized environmental source, informed by a detailed description of movement patterns of the population of Great Britain. The model is applied to outbreaks of Legionnaires' disease, a potentially life-threatening form of pneumonia caused by the bacteria Legionella pneumophilia. We use case-report data from three recent outbreaks that have occurred in Great Britain where the source has already been identified by public health agencies. We first demonstrate that the amount of individual-level heterogeneity incorporated in the movement data greatly influences our ability to predict the source location. The most accurate predictions were obtained using reported travel histories to describe movements of infected individuals, but using detailed simulation models to estimate movement patterns offers an effective fast alternative. Secondly, once the source is identified, we show that our model can be used to accurately determine the population likely to have been exposed to the pathogen, and hence predict the residential locations of infected individuals. The results give rise to an effective control strategy that can be implemented rapidly in response to an outbreak.

Transmission dynamics of methicillin-resistant Staphylococcus aureus in a medical intensive care unit.

Intensive care units (ICUs) play an important role in the epidemiology of methicillin-resistant Staphyloccocus aureus (MRSA). Although successful interventions are multi-modal, the relative efficacy of single measures remains unknown. We developed a discrete time, individual-based, stochastic mathematical model calibrated on cross-transmission observed through prospective surveillance to explore the transmission dynamics of MRSA in a medical ICU. Most input parameters were derived from locally acquired data. After fitting the model to the 46 observed cross-transmission events and performing sensitivity analysis, several screening and isolation policies were evaluated by simulating the number of cross-transmissions and isolation-days. The number of all cross-transmission events increased from 54 to 72 if only patients with a past history of MRSA colonization are screened and isolated at admission, to 75 if isolation is put in place only after the results of the admission screening become available, to 82 in the absence of admission screening and with a similar reactive isolation policy, and to 95 when no isolation policy is in place. The method used (culture or polymerase chain reaction) for admission screening had no impact on the number of cross-transmissions. Systematic regular screening during ICU stay provides no added-value, but aggressive admission screening and isolation effectively reduce the number of cross-transmissions. Critically, colonized healthcare workers may play an important role in MRSA transmission and their screening should be reinforced.

Behaviour and control of influenza in institutions and small societies.

A literature review was undertaken to assess the impact of influenza in enclosed societies. The literature spanned 120 years and included both readily accessible material from online keyword searches, as well as more obscure paper documents found through in-depth library research. Enclosed societies have been predominantly found in some type of institution through this period although noticeable similarities exist in communities isolated by distance and geography. We observe that no matter how isolated a community is, it is not necessarily insulated from infection by influenza and that even where there are no complicating factors, such as the age distribution or the presence of individuals with greater susceptibility in the enclosed population, their organization tends to increase influenza transmission and the risk of secondary infection. The collected accounts demonstrate important features of outbreaks in such societies and the necessity of considering them in pandemic planning: in particular, rapid intervention is essential for the control of influenza spread in such circumstances. Recent experience has shown that administration of modern antiviral drugs, such as neuraminidase inhibitors are effective at moderating outbreaks of influenza, but only in combination with other methods of control. In more remote communities where such drugs are not, or less, readily available, and medical care is limited, such outbreaks can still pose particular difficulties. In all cases delay in correct diagnosis, detection of an outbreak or the implementation of control measures can result in the majority of the enclosed population succumbing to the disease.

Modeling inhalational tularemia: deliberate release and public health response.

Two epidemic modeling studies of inhalational tularemia were identified in the published literature, both demonstrating the high number of potential casualties that could result from a deliberate aerosolized release of the causative agent in an urban setting. However, neither study analyzed the natural history of inhalational tularemia nor modeled the relative merits of different mitigation strategies. We first analyzed publicly available human/primate experimental data and reports of naturally acquired inhalational tularemia cases to better understand the epidemiology of the disease. We then simulated an aerosolized release of the causative agent, using airborne dispersion modeling to demonstrate the potential number of casualties and the extent of their spatial distribution. Finally, we developed a public health intervention model that compares 2 mitigation strategies: targeting antibiotics at symptomatic individuals with or without mass distribution of antibiotics to potentially infected individuals. An antibiotic stockpile that is sufficient to capture all areas where symptomatic individuals were infected is likely to save more lives than treating symptomatic individuals alone, providing antibiotics can be distributed rapidly and their uptake is high. However, with smaller stockpiles, a strategy of treating symptomatic individuals alone is likely to save many more lives than additional mass distribution of antibiotics to potentially infected individuals. The spatial distribution of symptomatic individuals is unlikely to coincide exactly with the path of the dispersion cloud if such individuals are infected near their work locations but then seek treatment close to their homes. The optimal mitigation strategy will depend critically on the size of the release relative to the stockpile level and the effectiveness of treatment relative to the speed at which antibiotics can be distributed.

An individual-based simulation of pneumonic plague transmission following an outbreak and the significance of intervention compliance.

The existence of primary pneumonic plague outbreaks raises concerns over the use of the causative bacteria as an aerosol-based bioweapon. We employed an individual-based model, parameterised using published personal contact information, to assess the severity of a deliberate release in a discrete community, under the influence of two proposed intervention strategies. We observed that the severity of the resulting epidemic is determined by the degree of personal compliance with said strategies, implying that prior preparedness activities are essential in order that public awareness and willingness to seek treatment is achieved quickly.

Modeling Legionnaires' disease outbreaks: estimating the timing of an aerosolized release using symptom-onset dates.

BACKGROUND: Over the last 30 years, there have been a number of reported Legionnaires' disease outbreaks resulting from the release of causative organisms from aerosol-producing devices. METHODS: We model a Legionnaires' disease epidemic curve as the convolution of an infection-time distribution (representing the aerosolized release) and an incubation-period distribution. The model is fitted to symptom-onset data from specific outbreaks to estimate the start and end dates of the release. We also develop this retrospective "back-calculation" model into a prospective "real-time" model that can estimate the final size of an ongoing outbreak, in addition to the timing of its release. RESULTS: In the retrospective analysis, the estimated release end dates were generally earlier than reported end dates. This suggests that, in many outbreaks, the release might have already ended by the time the source was reportedly cleaned or closed. Prospective analysis showed that valid estimates of the release start date could be achieved early in the outbreak, the total number of cases could be reasonably determined shortly after the release had ended, and estimates of the release end date could be satisfactorily achieved in the latter stages of the outbreak. CONCLUSIONS: This model could be used in the course of a Legionnaires' disease outbreak to provide early estimates of the total number of cases, thus helping to inform public-health planning. Toward the end of the outbreak, estimates of the release end date could help corroborate standard epidemiologic, environmental, and microbiologic investigations that seek to identify the source.

Stamping out fires! Controlling smallpox with targeted mass vaccination.

BACKGROUND: More than 30 years have now passed since the last naturally occurring case of smallpox; however, the variola virus still exists in at least 2 locations. The possibility that any clandestine stocks could be used for bioterrorism is a continuing concern for the public health community. OBJECTIVE: . Mathematical modeling is used to assess the impact of mass vaccination following a smallpox release when either standard public health controls are failing or political/public opinion is urging more comprehensive methods. Two mass vaccination strategies are considered: a blanket nationwide campaign v. an approach targeted only at those geographic areas that experience smallpox cases. The study evaluates which intervention strategy results in the fewest combined disease and vaccine-related deaths. RESULTS: . Outbreaks that go unnoticed until up to 50 cases have occurred are optimally controlled with targeted mass vaccination of the affected administrative districts in the majority of scenarios considered. The number of people vaccinated is approximately two thirds fewer than when implementing a nationwide campaign. Similar results arise when contact tracing is either highly unsuccessful or reduced in favor of reallocating limited resources for a policy of mass vaccination. CONCLUSIONS: . Reactive nationwide mass vaccination remains a suboptimal strategy for controlling an expanding smallpox outbreak in all but the most extreme circumstances. Rather, targeted mass vaccination of affected areas is likely to result in fewer deaths. The vaccines administered are also likely to be much fewer because they would probably be distributed to a much smaller number of districts, thus relieving pressure on potentially stretched public health systems.

Re-assessment of mitigation strategies for deliberate releases of anthrax using a real-time outbreak characterization tool.

Responding rapidly and appropriately to a covert anthrax release is an important public health challenge. A methodology to assist the geographical targeting of such a response has recently been published; as have a number of independent studies that investigate mitigation strategies. Here, we review and combine some of these published techniques to more realistically assess how key aspects of the public health response might impact on the outcomes of a bioterrorist attack. We combine a within-host mathematical model with our spatial back-calculation method to investigate the effects of a number of important response variables. These include how previously reported levels of adherence with taking antibiotics might affect the total outbreak size compared to assuming full adherence. Post-exposure vaccination is also considered, both with and without the use of antibiotics. Further, we investigate a range of delays (2, 4 and 8 days) before interventions are implemented, following the last day of symptomatic onset of some number of observed initial cases (5, 10 and 15). Our analysis confirms that outbreak size is minimised by implementing prophylactic treatment after having estimated the exposed area based on 5 observed cases; however, imperfect (rather than full) adherence with antibiotics results in approximately 15% additional cases. Moreover, of those infected individuals who only partially adhere with a prophylactic course of antibiotics, 86% remain disease free; a result that holds for scenarios in which infected individuals inhale much higher doses than considered here. Increasing logistical delays have a particularly detrimental effect on lives saved with an optimal strategy of early identification and analysis. Our analysis shows that it is critical to have systems and processes in place to rapidly identify, geospatially analyse and then swiftly respond to a deliberate anthrax release.

Estimating the location and spatial extent of a covert anthrax release.

Rapidly identifying the features of a covert release of an agent such as anthrax could help to inform the planning of public health mitigation strategies. Previous studies have sought to estimate the time and size of a bioterror attack based on the symptomatic onset dates of early cases. We extend the scope of these methods by proposing a method for characterizing the time, strength, and also the location of an aerosolized pathogen release. A back-calculation method is developed allowing the characterization of the release based on the data on the first few observed cases of the subsequent outbreak, meteorological data, population densities, and data on population travel patterns. We evaluate this method on small simulated anthrax outbreaks (about 25-35 cases) and show that it could date and localize a release after a few cases have been observed, although misspecifications of the spore dispersion model, or the within-host dynamics model, on which the method relies can bias the estimates. Our method could also provide an estimate of the outbreak's geographical extent and, as a consequence, could help to identify populations at risk and, therefore, requiring prophylactic treatment. Our analysis demonstrates that while estimates based on the first ten or 15 observed cases were more accurate and less sensitive to model misspecifications than those based on five cases, overall mortality is minimized by targeting prophylactic treatment early on the basis of estimates made using data on the first five cases. The method we propose could provide early estimates of the time, strength, and location of an aerosolized anthrax release and the geographical extent of the subsequent outbreak. In addition, estimates of release features could be used to parameterize more detailed models allowing the simulation of control strategies and intervention logistics.