The statistical analysis of truncated data: application to the Sverdlovsk anthrax outbreak

Modeling on the Effects of Deliberate Release of Aerosolized Inhalational Bacillus anthracis (Anthrax) on an Australian Population

This study aimed to determine optimal mitigation strategies in the event of an aerosolized attack with Bacillus anthracis, a category A bioterrorism agent with a case fatality rate of nearly 100% if inhaled and untreated. To simulate the effect of an anthrax attack, we used a plume dispersion model for Sydney, Australia, accounting for weather conditions. We determined the radius of exposure in different sizes of attack scenarios by spore quantity released per second. Estimations of different spore concentrations were then used to calculate the exposed population to inform a Susceptible-Exposed-Infected-Recovered (SEIR) deterministic mathematical model. Results are shown as estimates of the total number of exposed and infected people, along with the burden of disease, to quantify the amount of vaccination and antibiotics doses needed for stockpiles. For the worst-case scenario, over 500,000 people could be exposed and over 300,000 infected. The number of deaths depends closely on timing to start postexposure prophylaxis. Vaccination used as a postexposure prophylaxis in conjunction with antibiotics is the most effective mitigation strategy to reduce deaths after an aerosolized attack and is more effective when the response starts early (2 days after release) and has high adherence, while it makes only a small difference when started late (after 10 days).

Analyzing left-truncated and right-censored infectious disease cohort data with interval-censored infection onset

In an infectious disease cohort study, individuals who have been infected with a pathogen are often recruited for follow up. The period between infection and the onset of symptomatic disease, referred to as the incubation period, is of interest because of its importance on disease surveillance and control. However, the incubation period is often difficult to ascertain due to the uncertainty associated with asymptomatic infection onset time. An additional complication is that the observed infected subjects are likely to have longer incubation periods due to the prevalent sampling. In this article, we demonstrate how to estimate the distribution of the incubation period with the uncertain infection onset, subject to left-truncation and right-censoring. We employ a family of sufficiently general parametric models, the generalized odds-rate class of regression models, for the underlying incubation period and its correlation with covariates. In simulation studies, we assess the finite sample performance of the model fitting and hazard function estimation. The proposed method is illustrated on data from the HIV/AIDS study on injection drug users admitted to a detoxification program in Badalona, Spain.

A Review of Arguments for the Existence of Latent Infections of Bacillus anthracis, and Research Needed to Understand their Role in the Outbreaks of Anthrax

Hugh-Jones and Blackburn and Turnbull’s collective World Health Organization (WHO) report did literature reviews of the theories and the bases for causes of anthrax outbreaks. Both comment on an often-mentioned suspicion that, even though unproven, latent infections are likely involved. Hugh-Jones suggested Gainer do an updated review of our present-day knowledge of latent infections, which was the basis for Gainer’s talk at the Biology of Anthrax Conference in Bari, Italy 2019. At the Conference Gainer met Vergnaud who presented anthrax genome studies that implied that the disease might have spread throughout Asia and from Europe to North America in a short time span of three or four centuries. Vergnaud wondered if latent infections might have played a role in the process. Several other presenters at the Conference also mentioned results that might suggest the existence of latent infections. Vergnaud subsequently looked into some of the old French literature about related observations, results, and discussions of early Pasteur vaccine usage (late 1800′s) and found mentions of suspected latent infections. The first part of the paper is a focused summary and interpretation of Hugh-Jones and Blackburn’s and Turnbull’s reviews specifically looking for suggestions of latent infections, a few additional studies with slightly different approaches, and several mentions made of presentations and posters at the Conference in Italy. In general, many different investigators in different areas and aspects of the anthrax study at the Conference found reasons to suspect the existence of latent infections. The authors conclude that the affected species most studied, including Homo sapiens, provide circumstantial evidence of latent infections and modified host resistance. The last part of the review explores the research needed to prove or disprove the existence of latent infections.

Quantifying the Risk and Cost of Active Monitoring for Infectious Diseases

During outbreaks of deadly emerging pathogens (e.g., Ebola, MERS-CoV) and bioterror threats (e.g., smallpox), actively monitoring potentially infected individuals aims to limit disease transmission and morbidity. Guidance issued by CDC on active monitoring was a cornerstone of its response to the West Africa Ebola outbreak. There are limited data on how to balance the costs and performance of this important public health activity. We present a framework that estimates the risks and costs of specific durations of active monitoring for pathogens of significant public health concern. We analyze data from New York City’s Ebola active monitoring program over a 16-month period in 2014–2016. For monitored individuals, we identified unique durations of active monitoring that minimize expected costs for those at “low (but not zero) risk” and “some or high risk”: 21 and 31 days, respectively. Extending our analysis to smallpox and MERS-CoV, we found that the optimal length of active monitoring relative to the median incubation period was reduced compared to Ebola due to less variable incubation periods. Active monitoring can save lives but is expensive. Resources can be most effectively allocated by using exposure-risk categories to modify the duration or intensity of active monitoring.

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.

Evaluation of Inhaled Versus Deposited Dose Using the Exponential Dose-Response Model for Inhalational Anthrax in Nonhuman Primate, Rabbit, and Guinea Pig

The application of the exponential model is extended by the inclusion of new nonhuman primate (NHP), rabbit, and guinea pig dose-lethality data for inhalation anthrax. Because deposition is a critical step in the initiation of inhalation anthrax, inhaled doses may not provide the most accurate cross-species comparison. For this reason, species-specific deposition factors were derived to translate inhaled dose to deposited dose. Four NHP, three rabbit, and two guinea pig data sets were utilized. Results from species-specific pooling analysis suggested all four NHP data sets could be pooled into a single NHP data set, which was also true for the rabbit and guinea pig data sets. The three species-specific pooled data sets could not be combined into a single generic mammalian data set. For inhaled dose, NHPs were the most sensitive (relative lowest LD50) species and rabbits the least. Improved inhaled LD50 s proposed for use in risk assessment are 50,600, 102,600, and 70,800 inhaled spores for NHP, rabbit, and guinea pig, respectively. Lung deposition factors were estimated for each species using published deposition data from Bacillus spore exposures, particle deposition studies, and computer modeling. Deposition was estimated at 22%, 9%, and 30% of the inhaled dose for NHP, rabbit, and guinea pig, respectively. When the inhaled dose was adjusted to reflect deposited dose, the rabbit animal model appears the most sensitive with the guinea pig the least sensitive species.

Trends in epidemiology in the 21st century: time to adopt Bayesian methods

2013 marked the 250th anniversary of the presentation of Bayes’ theorem by the philosopher Richard Price. Thomas Bayes was a figure little known in his own time, but in the 20th century the theorem that bears his name became widely used in many fields of research. The Bayes theorem is the basis of the so-called Bayesian methods, an approach to statistical inference that allows studies to incorporate prior knowledge about relevant data characteristics into statistical analysis. Nowadays, Bayesian methods are widely used in many different areas such as astronomy, economics, marketing, genetics, bioinformatics and social sciences. This study observed that a number of authors discussed recent advances in techniques and the advantages of Bayesian methods for the analysis of epidemiological data. This article presents an overview of Bayesian methods, their application to epidemiological research and the main areas of epidemiology which should benefit from the use of Bayesian methods in coming years.

Deterministic models of inhalational anthrax in New Zealand white rabbits

Computational models describing bacterial kinetics were developed for inhalational anthrax in New Zealand white (NZW) rabbits following inhalation of Ames strain B. anthracis. The data used to parameterize the models included bacterial numbers in the airways, lung tissue, draining lymph nodes, and blood. Initial bacterial numbers were deposited spore dose. The first model was a single exponential ordinary differential equation (ODE) with 3 rate parameters that described mucociliated (physical) clearance, immune clearance (bacterial killing), and bacterial growth. At 36 hours postexposure, the ODE model predicted 1.7×10⁷ bacteria in the rabbit, which agreed well with data from actual experiments (4.0×10⁷ bacteria at 36 hours). Next, building on the single ODE model, a physiological-based biokinetic (PBBK) compartmentalized model was developed in which 1 physiological compartment was the lumen of the airways and the other was the rabbit body (lung tissue, lymph nodes, blood). The 2 compartments were connected with a parameter describing transport of bacteria from the airways into the body. The PBBK model predicted 4.9×10⁷ bacteria in the body at 36 hours, and by 45 hours the model showed all clearance mechanisms were saturated, suggesting the rabbit would quickly succumb to the infection. As with the ODE model, the PBBK model results agreed well with laboratory observations. These data are discussed along with the need for and potential application of the models in risk assessment, drug development, and as a general aid to the experimentalist studying inhalational anthrax.

Quantitative models of the dose-response and time course of inhalational anthrax in humans

Anthrax poses a community health risk due to accidental or intentional aerosol release. Reliable quantitative dose-response analyses are required to estimate the magnitude and timeline of potential consequences and the effect of public health intervention strategies under specific scenarios. Analyses of available data from exposures and infections of humans and non-human primates are often contradictory. We review existing quantitative inhalational anthrax dose-response models in light of criteria we propose for a model to be useful and defensible. To satisfy these criteria, we extend an existing mechanistic competing-risks model to create a novel Exposure–Infection–Symptomatic illness–Death (EISD) model and use experimental non-human primate data and human epidemiological data to optimize parameter values. The best fit to these data leads to estimates of a dose leading to infection in 50% of susceptible humans (ID₅₀) of 11,000 spores (95% confidence interval 7,200–17,000), ID₁₀ of 1,700 (1,100–2,600), and ID₁ of 160 (100–250). These estimates suggest that use of a threshold to human infection of 600 spores (as suggested in the literature) underestimates the infectivity of low doses, while an existing estimate of a 1% infection rate for a single spore overestimates low dose infectivity. We estimate the median time from exposure to onset of symptoms (incubation period) among untreated cases to be 9.9 days (7.7–13.1) for exposure to ID₅₀, 11.8 days (9.5–15.0) for ID₁₀, and 12.1 days (9.9–15.3) for ID₁. Our model is the first to provide incubation period estimates that are independently consistent with data from the largest known human outbreak. This model refines previous estimates of the distribution of early onset cases after a release and provides support for the recommended 60-day course of prophylactic antibiotic treatment for individuals exposed to low doses.

Anthrax poses a potential community health risk due to accidental or intentional aerosol release. We address the need for a transparent and defensible quantitative dose-response model for inhalational anthrax that is useful for risk assessors in estimating the magnitude and timeline of potential public health consequences should a release occur. Our synthesis of relevant data and previous modeling efforts identifies areas of improvement among many commonly cited dose-response models and estimates. To address those deficiencies, we provide a new model that is based on clear, transparent assumptions and published data from human and non-human primate exposures. Our resulting estimates provide important insight into the infectivity to humans of low inhaled doses of anthrax spores and the timeline of infections after an exposure event. These insights are critical to assessment of the impacts of delays in responding to a large scale aerosol release, as well as the recommended course of antibiotic administration to those potentially exposed.

The sepsis model: an emerging hypothesis for the lethality of inhalation anthrax

Inhalation anthrax is often described as a toxin-mediated disease. However, the toxaemia model does not account for the high mortality of inhalation anthrax relative to other forms of the disease or for the pathology present in inhalation anthrax. Patients with inhalation anthrax consistently show extreme bacteraemia and, in contrast to animals challenged with toxin, signs of sepsis. Rather than toxaemia, we propose that death in inhalation anthrax results from an overwhelming bacteraemia that leads to severe sepsis. According to our model, the central role of anthrax toxin is to permit the vegetative bacteria to escape immune detection. Other forms of B. anthracis infection have lower mortality because their overt symptoms early in the course of disease cause patients to seek medical care at a time when the infection and its sequelae can still be reversed by antibiotics. Thus, the sepsis model explains key features of inhalation anthrax and may offer a more complete understanding of disease pathology for researchers as well as those involved in the care of patients.

Modeling low-dose mortality and disease incubation period of inhalational anthrax in the rabbit

There is a need to advance our ability to conduct credible human risk assessments for inhalational anthrax associated with exposure to a low number of bacteria. Combining animal data with computational models of disease will be central in the low-dose and cross-species extrapolations required in achieving this goal. The objective of the current work was to apply and advance the competing risks (CR) computational model of inhalational anthrax where data was collected from NZW rabbits exposed to aerosols of Ames strain Bacillus anthracis. An initial aim was to parameterize the CR model using high-dose rabbit data and then conduct a low-dose extrapolation. The CR low-dose attack rate was then compared against known low-dose rabbit data as well as the low-dose curve obtained when the entire rabbit dose-response data set was fitted to an exponential dose-response (EDR) model. The CR model predictions demonstrated excellent agreement with actual low-dose rabbit data. We next used a modified CR model (MCR) to examine disease incubation period (the time to reach a fever >40 °C). The MCR model predicted a germination period of 14.5h following exposure to a low spore dose, which was confirmed by monitoring spore germination in the rabbit lung using PCR, and predicted a low-dose disease incubation period in the rabbit between 14.7 and 16.8 days. Overall, the CR and MCR model appeared to describe rabbit inhalational anthrax well. These results are discussed in the context of conducting laboratory studies in other relevant animal models, combining the CR/MCR model with other computation models of inhalational anthrax, and using the resulting information towards extrapolating a low-dose response prediction for man.

A Bayesian approach for estimating bioterror attacks from patient data

Terrorist attacks using an aerosolized pathogen have gained credibility as a national security concern after the anthrax attacks of 2001. Inferring some important details of the attack quickly, for example, the number of people infected, the time of infection, and a representative dose received can be crucial to planning a medical response. We use a Bayesian approach, based on a short time series of diagnosed patients, to estimate a joint probability density for these parameters. We first test the formulation with idealized cases and then apply it to realistic scenarios, including the Sverdlovsk anthrax outbreak of 1979. We also use simulated outbreaks to explore the impact of model error, as when the model used for generating simulated epidemic curves does not match the model subsequently used to characterize the attack. We find that in all cases except for the smallest attacks (fewer than 100 infected people), 3-5 days of data are sufficient to characterize the outbreak to a specificity that is useful for directing an emergency response.

Predicting Hospital Surge after a Large-Scale Anthrax Attack: A Model-Based Analysis of CDC's Cities Readiness Initiative Prophylaxis Recommendations

Background . After a major bioterrorism attack, the US Centers for Disease Control and Prevention (CDC) Cities Readiness Initiative (CRI) calls for dispensing of medical countermeasures to targeted populations within 48 hours. The authors explore how meeting or missing this 48-hour goal after a hypothetical aerosol anthrax attack would affect hospital surge, in light of the multiple uncertainties surrounding anthrax-related illness and response. Design . The authors created a discrete-time state transition computer model representing the dynamic interaction between disease progression of inhalational anthrax and the rate of dispensing of prophylactic antibiotics in an exposed population. Results . A CRI-compliant prophylaxis campaign starting 2 days after exposure would protect from 86% to 87% of exposed individuals from illness (assuming, in the base case, 90% antibiotic effectiveness and a 95% attack rate). Each additional day needed to complete the campaign would result in, on average, 2.4% to 2.9% more hospitalizations in the exposed population; each additional day's delay to initiating prophylaxis beyond 2 days would result in 5.2% to 6.5% additional hospitalizations. These population protection estimates vary roughly proportionally to antibiotic effectiveness but are relatively insensitive to variations in anthrax incubation period. Conclusion . Delays in detecting and initiating response to large-scale, covert aerosol anthrax releases in a major city would render even highly effective CRI-compliant mass prophylaxis campaigns unable to prevent unsustainable levels of surge hospitalizations. Although outcomes may improve with more rapid epidemiological identification of affected subpopulations and increased collaboration across regional public health and hospital systems, these findings support an increased focus on prevention of this public health threat.

Bioterrorism for the respiratory physician

Terrorist attacks by definition are designed to cause fear and panic. There is no question that a terrorist attack using biological agents would present a grave threat to stability of the society in which they were released. Early recognition of such a bioterrorist attack is crucial to containing the damage they could cause. As many of the most likely bioterrorism agents present with pulmonary disease, respiratory physicians may be crucial in the initial recognition and diagnosis phase, and certainly would be drawn into treatment of affected individuals. This review focuses on the biological agents thought most likely to be used by terrorists that have predominantly respiratory presentations. The primary focus of this review is on anthrax, plague, tularaemia, ricin, and Staphylococcal enterotoxin B. The pathogenesis, clinical manifestations and treatment of these agents will be discussed as well as historical examples of their use. Other potential bioterrorism agents with respiratory manifestations will also be discussed briefly.

Modeling the incubation period of inhalational anthrax

Ever since the pioneering work of Philip Sartwell, the incubation period distribution for infectious diseases is most often modeled using a lognormal distribution. Theoretical models based on underlying disease mechanisms in the host are less well developed. This article modifies a theoretical model originally developed by Brookmeyer and others for the inhalational anthrax incubation period distribution in humans by using a more accurate distribution to represent the in vivo bacterial growth phase and by extending the model to represent the time from exposure to death, thereby allowing the model to be fit to nonhuman primate time-to-death data. The resulting incubation period distribution and the dose dependence of the median incubation period are in good agreement with human data from the 1979 accidental atmospheric anthrax release in Sverdlovsk, Russia, and limited nonhuman primate data. The median incubation period for the Sverdlovsk victims is 9.05 (95% confidence interval = 8.0-10.3) days, shorter than previous estimates, and it is predicted to drop to less than 2.5 days at doses above 10(6) spores. The incubation period distribution is important because the left tail determines the time at which clinical diagnosis or syndromic surveillance systems might first detect an anthrax outbreak based on early symptomatic cases, the entire distribution determines the efficacy of medical intervention-which is determined by the speed of the prophylaxis campaign relative to the incubation period-and the right tail of the distribution influences the recommended duration for antibiotic treatment.

Modeling the logistics of response to anthrax bioterrorism

BACKGROUND

A bioterrorism attack with an agent such as anthrax will require rapid deployment of medical and pharmaceutical supplies to exposed individuals. How should such a logistical system be organized? How much capacity should be built into each element of the bioterrorism response supply chain?

METHODS

The authors developed a compartmental model to evaluate the costs and benefits of various strategies for preattack stockpiling and postattack distribution and dispensing of medical and pharmaceutical supplies, as well as the benefits of rapid attack detection.

RESULTS

The authors show how the model can be used to address a broad range of logistical questions as well as related, nonlogistical questions (e.g., the cost-effectiveness of strategies to improve patient adherence to antibiotic regimens). They generate several key insights about appropriate strategies for local communities. First, stockpiling large local inventories of medical and pharmaceutical supplies is unlikely to be the most effective means of reducing mortality from an attack, given the availability of national and regional supplies. Instead, communities should create sufficient capacity for dispensing prophylactic antibiotics in the event of a large-scale bioterror attack. Second, improved surveillance systems can significantly reduce deaths from such an attack but only if the local community has sufficient antibiotic-dispensing capacity. Third, mortality from such an attack is significantly affected by the number of unexposed individuals seeking prophylaxis and treatment. Fourth, full adherence to treatment regimens is critical for reducing expected mortality.

CONCLUSIONS

Effective preparation for response to potential bioterror attacks can avert deaths in the event of an attack. Models such as this one can help communities more effectively prepare for response to potential bioterror attacks.

Bacillus anthracis: interactions with the host and establishment of inhalational anthrax

Due to its potential as a bioweapon, Bacillus anthracis has received a great deal of attention in recent years, and a significant effort has been devoted to understanding how this organism causes anthrax. There has been a particular focus on the inhalational form of the disease, and studies over the past several years have painted an increasingly complex picture of how B. anthracis enters the mammalian host, survives the host's defense mechanisms, disseminates throughout the body and causes death. This article reviews recent advances in these areas, with a focus on how the bacterium interacts with its host in establishing infection and causing anthrax.

Public health response to an anthrax attack: an evaluation of vaccination policy options

A discrete-time, deterministic, compartmental model was developed and analyzed to provide insight into how the use of anthrax vaccine before or after a large-scale attack can reduce casualties. The model accounts for important response and protection factors such as antibiotic and vaccine efficacy, the protective effects of buildings, the timing of emergency response, and antibiotic adherence and vaccine coverage in the population prior to the attack. The relative benefit of pre- versus post-exposure vaccination is influenced by the timing of the post-exposure antibiotic distribution campaign as well as assumptions of antibiotic adherence. The results indicate that, regardless of which vaccination policy is adopted, a rapid and effective post-attack medical response has a large impact on the number of lives that can be saved by a post-exposure prophylaxis (PEP) campaign. A sensitivity analysis of the model indicates that uncertainty in medical efficacy and the time to initiate a PEP campaign are the model parameters that have the greatest impact on the number of predicted deaths. It is shown that for each day that a mass prophylaxis campaign is delayed, more casualties and deaths result than for each day that the completion of the campaign is delayed.

Early efforts in modeling the incubation period of infectious diseases with an acute course of illness

The incubation period of infectious diseases, the time from infection with a microorganism to onset of disease, is directly relevant to prevention and control. Since explicit models of the incubation period enhance our understanding of the spread of disease, previous classic studies were revisited, focusing on the modeling methods employed and paying particular attention to relatively unknown historical efforts. The earliest study on the incubation period of pandemic influenza was published in 1919, providing estimates of the incubation period of Spanish flu using the daily incidence on ships departing from several ports in Australia. Although the study explicitly dealt with an unknown time of exposure, the assumed periods of exposure, which had an equal probability of infection, were too long, and thus, likely resulted in slight underestimates of the incubation period. After the suggestion that the incubation period follows lognormal distribution, Japanese epidemiologists extended this assumption to estimates of the time of exposure during a point source outbreak. Although the reason why the incubation period of acute infectious diseases tends to reveal a right-skewed distribution has been explored several times, the validity of the lognormal assumption is yet to be fully clarified. At present, various different distributions are assumed, and the lack of validity in assuming lognormal distribution is particularly apparent in the case of slowly progressing diseases. The present paper indicates that (1) analysis using well-defined short periods of exposure with appropriate statistical methods is critical when the exact time of exposure is unknown, and (2) when assuming a specific distribution for the incubation period, comparisons using different distributions are needed in addition to estimations using different datasets, analyses of the determinants of incubation period, and an understanding of the underlying disease mechanisms.

Evaluating detection of an inhalational anthrax outbreak

Timely detection of an inhalational anthrax outbreak is critical for clinical and public health management. Syndromic surveillance has received considerable investment, but little is known about how it will perform relative to routine clinical case finding for detection of an inhalational anthrax outbreak. We conducted a simulation study to compare clinical case finding with syndromic surveillance for detection of an outbreak of inhalational anthrax. After simulated release of 1 kg of anthrax spores, the proportion of outbreaks detected first by syndromic surveillance was 0.59 at a specificity of 0.9 and 0.28 at a specificity of 0.975. The mean detection benefit of syndromic surveillance was 1.0 day at a specificity of 0.9 and 0.32 days at a specificity of 0.975. When syndromic surveillance was sufficiently sensitive to detect a substantial proportion of outbreaks before clinical case finding, it generated frequent false alarms.

The weapon potential of human pathogenic fungi

With the exception of Coccidioides spp., human pathogenic fungi are not found among lists of microbes with potential for biological warfare and bioterrorism against humans. However, many human pathogenic fungi are easily obtainable from the environment, are highly dispersible and can cause significant disease after inhalation with relatively low inocula. When the biological and pathogenic attributes of certain human pathogenic fungi are considered using a formula for calculating the relative weapon potential of a microbe it is as apparent that some organisms such as Coccidioides spp. are comparable to other microbes for which there is significant concern. Our analysis suggests that the current indifference to fungi as potential biological weapons against human populations is probably a perception engendered by their non-communicability, lack of history of use or development as biological weapons, and a relatively low incidence of symptomatic disease following natural infection. Awareness of the weapon potential of human pathogenic fungi is an important consideration for greater preparedness against the threat posed by biowarfare and bioterrorism.

Discernment between deliberate and natural infectious disease outbreaks

Public health authorities should be vigilant to the potential for outbreaks deliberately caused by biological agents (bioterrorism). Such events require a rapid response and incorporation of non-traditional partners for disease investigation and outbreak control. The astute application of infectious disease epidemiological principles can promote an enhanced index of suspicion for such events. We discuss epidemiological indicators that should be considered during outbreak investigations, and also examine their application during bioterrorism incidents, an accidental release of an agent, outbreaks of infections that were alleged to have been deliberately initiated, and a model scenario. The Grunow & Finke epidemiological assessment tool is used to examine these historical events and the model scenario. The results received from this analysis, coupled with an understanding of epidemiological clues to unnatural events, and knowledge of how to manage such events, can aid in the improved response and resolution of epidemics.

Reducing mortality from anthrax bioterrorism: strategies for stockpiling and dispensing medical and pharmaceutical supplies

A critical question in planning a response to bioterrorism is how antibiotics and medical supplies should be stockpiled and dispensed. The objective of this work was to evaluate the costs and benefits of alternative strategies for maintaining and dispensing local and regional inventories of antibiotics and medical supplies for responses to anthrax bioterrorism. We modeled the regional and local supply chain for antibiotics and medical supplies as well as local dispensing capacity. We found that mortality was highly dependent on the local dispensing capacity, the number of individuals requiring prophylaxis, adherence to prophylactic antibiotics, and delays in attack detection. For an attack exposing 250,000 people and requiring the prophylaxis of 5 million people, expected mortality fell from 243,000 to 145,000 as the dispensing capacity increased from 14,000 to 420,000 individuals per day. At low dispensing capacities (<14,000 individuals per day), nearly all exposed individuals died, regardless of the rate of adherence to prophylaxis, delays in attack detection, or availability of local inventories. No benefit was achieved by doubling local inventories at low dispensing capacities; however, at higher dispensing capacities, the cost-effectiveness of doubling local inventories fell from 100,000 US dollars to 20,000 US dollars/life year gained as the annual probability of an attack increased from 0.0002 to 0.001. We conclude that because of the reportedly rapid availability of regional inventories, the critical determinant of mortality following anthrax bioterrorism is local dispensing capacity. Bioterrorism preparedness efforts directed at improving local dispensing capacity are required before benefits can be reaped from enhancing local inventories.

A hypothesis test for the end of a common source outbreak

The objective of this article is to develop a hypothesis-testing procedure to determine whether a common source outbreak has ended. We consider the case when neither the calendar date of exposure to the pathogen nor the exact incubation period distribution is known. The hypothesis-testing procedure is based on the spacings between ordered calendar dates of disease onset of the cases. A simulation study was performed to evaluate the robustness of the methods to various models for the incubation period of infectious diseases. We investigated the impact of multiple testing on the overall outbreak-wise type I error probability. We derive expressions for the outbreak-wise type I error probability and show that multiple testing has minimal effect on inflating that error probability. The results are discussed in the context of the 2001 U.S. anthrax outbreak.

Sverdlovsk revisited: modeling human inhalation anthrax

Several models have been proposed for the dose-response function and the incubation period distribution for human inhalation anthrax. These models give very different predictions for the severity of a hypothetical bioterror attack, when an attack might be detected from clinical cases, the efficacy of medical intervention and the requirements for decontamination. Using data from the 1979 accidental atmospheric release of anthrax in Sverdlovsk, Russia, and limited nonhuman primate data, this paper eliminates two of the contending models and derives parameters for the other two, thereby narrowing the range of models that accurately predict the effects of human inhalation anthrax. Dose-response functions that exhibit a threshold for infectivity are contraindicated by the Sverdlovsk data. Dose-dependent incubation period distributions explain the 10-day median incubation period observed at Sverdlovsk and the 1- to 5-day incubation period observed in nonhuman primate experiments.

Evaluation of public health interventions for Anthrax: a report to the secretary's council on Public Health Preparedness

To aid in understanding how best to respond to a bioterror anthrax attack, we analyze a system of differential equations that includes a disease progression model, a set of spatially distributed queues for distributing antibiotics, and vaccination (pre-event and/or post-event). We derive approximate expressions for the number of casualties as a function of key parameters and management levers, including the time at which the attack is detected, the number of days to distribute antibiotics, the adherence to prophylactic antibiotics, and the fraction of the population that is preimmunized. We compare a variety of public health intervention policies in the event of a hypothetical anthrax attack in a large metropolitan area. Modeling assumptions were decided by the Anthrax Modeling Working Group of the Secretary's Council on Public Health Preparedness. Our results highlight the primary importance of rapid antibiotic distribution and lead us to argue for ensuring post-attack surge capacity to rapidly produce enough anthrax vaccine for an additional 100 million people.

Anthrax Countermeasures: Current Status and Future Needs

The U.S. government does not yet have the range of medical countermeasures needed to protect its citizens from anthrax and other potential bioweapons. In the event of an anthrax attack, treatment interventions in addition to antibiotics would be needed so that very ill patients can be treated and clean-up crews can be better protected, especially if an engineered strain is used. This article describes specific anthrax countermeasures that are in development, barriers to development, and potential mechanisms the government could use to accelerate the movement of these countermeasures through the pipeline. A key challenge will be to encourage the transition of promising leads from basic research to the product development stage, when they may qualify for BioShield funds.

The weapon potential of a microbe

The designation of a microbe as a potential biological weapon poses the vexing question of how such a decision is made given the many pathogenic microbes that cause disease. Analysis of the properties of microbes that are currently considered biological weapons against humans revealed no obvious relationship to virulence, except that all are pathogenic for humans. Notably, the weapon potential of a microbe rather than its pathogenic properties or virulence appeared to be the major consideration when categorizing certain agents as biological weapons. In an effort to standardize the assessment of the risk that is posed by microbes as biological warfare agents using the basic principles of microbial communicability (defined here as a parameter of transmission) and virulence, a simple formula is proposed for estimating the weapon potential of a microbe.

Modelling the incubation period of anthrax

Models of the incubation period of anthrax are important to public health planners because they can be used to predict the delay before outbreaks are detected, the size of an outbreak and the duration of time that persons should remain on antibiotics to prevent disease. The difficulty is that there is little direct data about the incubation period in humans. The objective of this paper is to develop and apply models for the incubation period of anthrax. Mechanistic models that account for the biology of spore clearance and germination are developed based on a competing risks formulation. The models predict that the incubation period distribution depends critically on the rate that spores are cleared from the lung and to a lesser extent on the dose of inhaled spores. The models are used in a statistical analysis of data from an anthrax outbreak that occurred in Sverdlovsk, Russia. The analysis suggests that spores are cleared from the lung at a rate between 8 per cent per day and 14 per cent per day, which is in good agreement with experimental studies of animals. The analysis suggests that at low doses, the overall median incubation period time is about 10 days, which includes a median lag of about 2 days between spore germination and onset of symptoms. Male gender and younger ages were associated with longer incubation periods as was lower dose of inhaled spores.

Estimating time and size of bioterror attack

Time and size of possible bioterror event estimated in real time.

In the event of a bioterror attack, rapidly estimating the size and time of attack enables short-run forecasts of the number of persons who will be symptomatic and require medical care. We present a Bayesian approach to this problem for use in real time and illustrate it with data from a simulated anthrax attack. The method is simple enough to be implemented in a spreadsheet.

Modeling the optimum duration of antibiotic prophylaxis in an anthrax outbreak

A critical consideration in effective and measured public health responses to an outbreak of inhalational anthrax is the optimum duration of antibiotic prophylaxis. We develop a competing-risks model to address the duration of antibiotic prophylaxis and the incubation period that accounts for the risks of spore germination and spore clearance. The model predicts the incubation period distribution, which is confirmed by empirical data. The optimum duration of antibiotic prophylaxis depends critically on the dose of inhaled spores. At high doses, we show that exposed persons would need to remain on antibiotic prophylaxis for at least 4 months, and considerable morbidity would likely occur before antibiotic prophylaxis could even be initiated. At very low doses, 60 days of antibiotic prophylaxis is adequate. Exposure doses can be estimated from the cumulative attack rate up to the point antibiotic prophylaxis begins. The model explains that whereas < or =60 days of antibiotics were enough to protect persons in the 2001 U.S. outbreak, because doses were very low, at moderate or high doses considerably longer durations would be necessary to adequately protect exposed populations.

Evaluating factors associated with STD infection in a study with interval-censored event times and an unknown proportion of participants not at risk for disease

Sexually transmitted diseases (STD) are a major cause of morbidity and mortality world-wide. Because of their association with an increased risk of infection with human immunodeficiency virus, the prevention and control of STD are particularly important. Studies designed to evaluate factors associated with the transmission of STD can pose a number of statistical challenges, however. Two such concerns are the interval-censored event times that result from spacing between follow-up test visits, and an unknown proportion of study participants who are not at risk for infection. Researchers in various fields of study have used parametric mixture models to account for individuals not at risk. Owing to non-identifiability concerns within the mixture model framework, however, it is not always possible to distinguish between effects of explanatory variables on the distribution of event times for at-risk individuals and their effects on the probability of being at risk. We address these issues using data from a clinical trial designed to investigate the effectiveness of an intravaginal microbicide in preventing male-to-female transmission of STD. Factors associated with time to infection among at-risk women are initially identified by fitting right-truncated models to the interval-censored event times of participants who tested positive for STD, and hence are known to have been at risk. Subsequently, factors associated with the probability of being at risk are evaluated using mixture models that incorporate information contributed by the right-censored event-free times of uninfected study participants.

Emergency response to an anthrax attack

We developed a mathematical model to compare various emergency responses in the event of an airborne anthrax attack. The system consists of an atmospheric dispersion model, an age-dependent dose-response model, a disease progression model, and a set of spatially distributed two-stage queueing systems consisting of antibiotic distribution and hospital care. Our results underscore the need for the extremely aggressive and timely use of oral antibiotics by all asymptomatics in the exposure region, distributed either preattack or by nonprofessionals postattack, and the creation of surge capacity for supportive hospital care via expanded training of nonemergency care workers at the local level and the use of federal and military resources and nationwide medical volunteers. The use of prioritization (based on disease stage andor age) at both queues, and the development and deployment of modestly rapid and sensitive biosensors, while helpful, produce only second-order improvements.

Protection against anthrax toxin by recombinant antibody fragments correlates with antigen affinity

The tripartite toxin produced by Bacillus anthracis is the key determinant in the etiology of anthrax. We have engineered a panel of toxin-neutralizing antibodies, including single-chain variable fragments (scFvs) and scFvs fused to a human constant kappa domain (scAbs), that bind to the protective antigen subunit of the toxin with equilibrium dissociation constants (K(d)) between 63 nM and 0.25 nM. The entire antibody panel showed high serum, thermal, and denaturant stability. In vitro, post-challenge protection of macrophages from the action of the holotoxin correlated with the K(d) of the scFv variants. Strong correlations among antibody construct affinity, serum half-life, and protection were also observed in a rat model of toxin challenge. High-affinity toxin-neutralizing antibodies may be of therapeutic value for alleviating the symptoms of anthrax toxin in infected individuals and for medium-term prophylaxis to infection.