Modeling the incubation period of inhalational anthrax

Backtracking: Improved methods for identifying the source of a deliberate release of Bacillus anthracis from the temporal and spatial distribution of cases

Reverse epidemiology is a mathematical modelling tool used to ascertain information about the source of a pathogen, given the spatial and temporal distribution of cases, hospitalisations and deaths. In the context of a deliberately released pathogen, such as Bacillus anthracis (the disease-causing organism of anthrax), this can allow responders to quickly identify the location and timing of the release, as well as other factors such as the strength of the release, and the realized wind speed and direction at release. These estimates can then be used to parameterise a predictive mechanistic model, allowing for estimation of the potential scale of the release, and to optimise the distribution of prophylaxis. In this paper we present two novel approaches to reverse epidemiology, and demonstrate their utility in responding to a simulated deliberate release of B. anthracis in ten locations in the UK and compare these to the standard grid-search approach. The two methods-a modified MCMC and a Recurrent Convolutional Neural Network-are able to identify the source location and timing of the release with significantly better accuracy compared to the grid-search approach. Further, the neural network method is able to do inference on new data significantly quicker than either the grid-search or novel MCMC methods, allowing for rapid deployment in time-sensitive outbreaks.

Animal-to-Human Dose Translation of ANTHRASIL for Treatment of Inhalational Anthrax in Healthy Adults, Obese Adults, and Pediatric Subjects

Anthrax Immune Globulin Intravenous (AIGIV [ANTHRASIL]), was developed for the treatment of toxemia associated with inhalational anthrax. It is a plasma product collected from individuals vaccinated with anthrax vaccine and contains antitoxin IgG antibodies against Bacillus anthracis protective antigen. A pharmacokinetic (PK) and exposure-response model was constructed to assess the PKs of AIGIV in anthrax-free and anthrax-exposed rabbits, non-human primates and anthrax-free humans, as well as the relationship between AIGIV exposure and survival from anthrax, based on available preclinical/clinical studies. The potential effect of anthrax on the PKs of AIGIV was evaluated and estimates of survival odds following administration of AIGIV protective doses with and without antibiotic co-treatment were established. As the developed PK model can simulate exposure of AIGIV in any species for any dosing scenario, the relationship between the predicted area under the concentration curve of AIGIV in humans and the probability of survival observed in preclinical studies was explored. Based on the simulation results, the intravenous administration of 420 U (units of potency as measured by validated Toxin Neutralization Assay) of AIGIV is expected to result in a > 80% probability of survival in more than 90% of the human population. Additional simulations suggest that exposure levels were similar in healthy and obese humans, and exposure in pediatrics is expected to be up to approximately seven-fold higher than in healthy adults, allowing for doses in pediatric populations that ranged from one to seven vials. Overall, the optimal human dose was justified based on the PK/pharmacodynamic (PD) properties of AIGIV in animals and model-based translation of PK/PD to predict human exposure and efficacy.

Efficacy of ANTHRASIL (Anthrax Immune Globulin Intravenous (Human)) in rabbit and nonhuman primate models of inhalational anthrax: Data supporting approval under animal rule

To meet the requirements of the Animal Rule, the efficacy of monotherapy with ANTHRASIL® (Anthrax Immune Globulin Intravenous (Human)) for inhalational anthrax was evaluated in blinded studies using rabbit and nonhuman primate models. Animals in both studies were randomized to treatment groups exposed to ~ 200 LD50 Bacillus anthracis (Ames strain) spores by the aerosol route to induce inhalational anthrax. Rabbits (N = 50/group) were treated with either 15 U/kg ANTHRASIL or a volume-matching dose of IGIV after disease onset as determined by the detection of bacterial toxin in the blood. At the end of the study, survival rates were 2% (1 of 48) in the IGIV control group, and 26% (13 of 50) in the ANTHRASIL-treated group (p = 0.0009). Similarly, ANTHRASIL was effective in cynomolgus monkeys (N = 16/group) when administered therapeutically after the onset of toxemia, with 6% survival in the IGIV control and a dose-related increase in survival of 36%, 43%, and 70% with 7.5, 15 or 30 U/kg doses of ANTHRASIL, respectively. These studies formed the basis for approval of ANTHRASIL by FDA under the Animal Rule.

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).

Clinical Features of Patients Hospitalized for All Routes of Anthrax, 1880-2018: A Systematic Review

BACKGROUND

Anthrax is a toxin-mediated zoonotic disease caused by Bacillus anthracis, with a worldwide distribution recognized for millennia. Bacillus anthracis is considered a potential biowarfare agent.

METHODS

We completed a systematic review for clinical and demographic characteristics of adults and children hospitalized with anthrax (cutaneous, inhalation, ingestion, injection [from contaminated heroin], primary meningitis) abstracted from published case reports, case series, and line lists in English from 1880 through 2018, assessing treatment impact by type and severity of disease. We analyzed geographic distribution, route of infection, exposure to anthrax, and incubation period.

RESULTS

Data on 764 adults and 167 children were reviewed. Most cases reported for 1880 through 1915 were from Europe; those for 1916 through 1950 were from North America; and from 1951 on, cases were from Asia. Cutaneous was the most common form of anthrax for all populations. Since 1960, adult anthrax mortality has ranged from 31% for cutaneous to 90% for primary meningitis. Median incubation periods ranged from 1 day (interquartile range [IQR], 0-4) for injection to 7 days (IQR, 4-9) for inhalation anthrax. Most patients with inhalation anthrax developed pleural effusions and more than half with ingestion anthrax developed ascites. Treatment and critical care advances have improved survival for those with systemic symptoms, from approximately 30% in those untreated to approximately 70% in those receiving antimicrobials or antiserum/antitoxin.

CONCLUSIONS

This review provides an improved evidence base for both clinical care of individual anthrax patients and public health planning for wide-area aerosol releases of B. anthracis spores.

Modeling the effect of age on quantiles of the incubation period distribution of COVID-19

BACKGROUND

The novel coronavirus SARS-CoV-2 (coronavirus disease 2019, COVID-19) has caused serious consequences on many aspects of social life throughout the world since the first case of pneumonia with unknown etiology was identified in Wuhan, Hubei province in China in December 2019. Note that the incubation period distribution is key to the prevention and control efforts of COVID-19. This study aimed to investigate the conditional distribution of the incubation period of COVID-19 given the age of infected cases and estimate its corresponding quantiles from the information of 2172 confirmed cases from 29 provinces outside Hubei in China.

METHODS

We collected data on the infection dates, onset dates, and ages of the confirmed cases through February 16th, 2020. All the data were downloaded from the official websites of the health commission. As the epidemic was still ongoing at the time we collected data, the observations subject to biased sampling. To address this issue, we developed a new maximum likelihood method, which enables us to comprehensively study the effect of age on the incubation period.

RESULTS

Based on the collected data, we found that the conditional quantiles of the incubation period distribution of COVID-19 vary by age. In detail, the high conditional quantiles of people in the middle age group are shorter than those of others while the low quantiles did not show the same differences. We estimated that the 0.95-th quantile related to people in the age group 23 ∼55 is less than 15 days.

CONCLUSIONS

Observing that the conditional quantiles vary across age, we may take more precise measures for people of different ages. For example, we may consider carrying out an age-dependent quarantine duration in practice, rather than a uniform 14-days quarantine period. Remarkably, we may need to extend the current quarantine duration for people aged 0 ∼22 and over 55 because the related 0.95-th quantiles are much greater than 14 days.

A Stochastic Intracellular Model of Anthrax Infection With Spore Germination Heterogeneity

We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis. The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis. The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.

Modeling Tool for Decision Support during Early Days of an Anthrax Event

Health officials lack field-implementable tools for forecasting the effects that a large-scale release of Bacillus anthracis spores would have on public health and hospitals. We created a modeling tool (combining inhalational anthrax caseload projections based on initial case reports, effects of variable postexposure prophylaxis campaigns, and healthcare facility surge capacity requirements) to project hospitalizations and casualties from a newly detected inhalation anthrax event, and we examined the consequences of intervention choices. With only 3 days of case counts, the model can predict final attack sizes for simulated Sverdlovsk-like events (1979 USSR) with sufficient accuracy for decision making and confirms the value of early postexposure prophylaxis initiation. According to a baseline scenario, hospital treatment volume peaks 15 days after exposure, deaths peak earlier (day 5), and recovery peaks later (day 23). This tool gives public health, hospital, and emergency planners scenario-specific information for developing quantitative response plans for this threat.

Modeling Rabbit Responses to Single and Multiple Aerosol Exposures of Bacillus anthracis Spores

Survival models are developed to predict response and time-to-response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple-dose data set to predict the probability of death through specifying functions of dose response and the time between exposure and the time-to-death (TTD). Among the models developed, the best-fitting survival model (baseline model) is an exponential dose-response model with a Weibull TTD distribution. Alternative models assessed use different underlying dose-response functions and use the assumption that, in a multiple-dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this article. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high-dose rabbit data sets. More accurate survival models depend upon future development of dose-response data sets specifically designed to assess potential multiple-dose effects on response and time-to-response. The process used in this article to develop the best-fitting survival model for exposure of rabbits to multiple aerosol doses of B. anthracis spores should have broad applicability to other host-pathogen systems and dosing schedules because the empirical modeling approach is based upon pathogen-specific empirically-derived parameters.

Medical Allocations to Persons with Special Needs during a Bioterrorism Event

After the bioterrorism-anthrax attacks of 2001, public health officials were tasked with planning population-wide medicine dispensing. This planning started with assumptions and then evaluations of seasonal immunization clinics. Research on the 2009 H1N1 pandemic-vaccination campaign showed that an adequately prepared public health system could have prevented over 16% of flu-associated hospitalizations. The 2011 ice storms revealed difficulties with sheltering medically fragile persons with disabilities. Later research showed that training and preparedness levels increased responders' willingness to serve. When triaging disaster survivors to community-mass-care-services of general shelters, medical shelters, or mental health services; sorting improved up to 15% when past traumatic effects, personal care assistance, or service methodology were accounted for. The number of persons who are disabled and dependent on electric medical equipment are increasing. This current study compared the time it takes to dispense medication to two different cohorts: a general-population cohort (n=31) and a special-needs cohort (n=30). The cohort comprised entirely of persons with special needs took 4.1 compared to 2.48 minutes per person in a general population cohort (p=.057). A person with any special needs took 3.73 versus 2.43 minutes for a person with no special needs (p=.082). Modeling of service times per station and cohort type found significant delays at the medical station among persons in the general population who are pregnant (14 minutes or 840 seconds, p=.002) and persons in the special needs cohort with a language barrier (12.5 minutes or 750 seconds, p=.001). Recommendations include planning for closed Points of Dispensing Sites (PODS) to those with special needs, ensuring a sufficient number of medical dispenser in open PODS, and assigning extra capacity at the medical station area for special needs involving children, language, or pregnancy issues.

Computational fluid dynamics modeling of Bacillus anthracis spore deposition in rabbit and human respiratory airways

Three-dimensional computational fluid dynamics and Lagrangian particle deposition models were developed to compare the deposition of aerosolized Bacillus anthracis spores in the respiratory airways of a human with that of the rabbit, a species commonly used in the study of anthrax disease. The respiratory airway geometries for each species were derived respectively from computed tomography (CT) and μCT images. Both models encompassed airways that extended from the external nose to the lung with a total of 272 outlets in the human model and 2878 outlets in the rabbit model. All simulations of spore deposition were conducted under transient, inhalation-exhalation breathing conditions using average species-specific minute volumes. Two different exposure scenarios were modeled in the rabbit based upon experimental inhalation studies. For comparison, human simulations were conducted at the highest exposure concentration used during the rabbit experimental exposures. Results demonstrated that regional spore deposition patterns were sensitive to airway geometry and ventilation profiles. Due to the complex airway geometries in the rabbit nose, higher spore deposition efficiency was predicted in the nasal sinus compared to the human at the same air concentration of anthrax spores. In contrast, higher spore deposition was predicted in the lower conducting airways of the human compared to the rabbit lung due to differences in airway branching pattern. This information can be used to refine published and ongoing biokinetic models of inhalation anthrax spore exposures, which currently estimate deposited spore concentrations based solely upon exposure concentrations and inhaled doses that do not factor in species-specific anatomy and physiology for deposition.

Humoral and Cell-Mediated Immune Responses to Alternate Booster Schedules of Anthrax Vaccine Adsorbed in Humans

Protective antigen (PA)-specific antibody and cell-mediated immune (CMI) responses to annual and alternate booster schedules of anthrax vaccine adsorbed (AVA; BioThrax) were characterized in humans over 43 months. Study participants received 1 of 6 vaccination schedules: a 3-dose intramuscular (IM) priming series (0, 1, and 6 months) with a single booster at 42 months (4-IM); 3-dose IM priming with boosters at 18 and 42 months (5-IM); 3-dose IM priming with boosters at 12, 18, 30, and 42 months (7-IM); the 1970 licensed priming series of 6 doses (0, 0.5, 1, 6, 12, and 18 months) and two annual boosters (30 and 42 months) administered either subcutaneously (SQ) (8-SQ) or IM (8-IM); or saline placebo control at all eight time points. Antibody response profiles included serum anti-PA IgG levels, subclass distributions, avidity, and lethal toxin neutralization activity (TNA). CMI profiles included frequencies of gamma interferon (IFN-γ)- and interleukin 4 (IL-4)-secreting cells and memory B cells (MBCs), lymphocyte stimulation indices (SI), and induction of IFN-γ, IL-2, IL-4, IL-6, IL-1β, and tumor necrosis factor alpha (TNF-α) mRNA. All active schedules elicited high-avidity PA-specific IgG, TNA, MBCs, and T cell responses with a mixed Th1-Th2 profile and Th2 dominance. Anti-PA IgG and TNA were highly correlated (e.g., month 7,r(2)= 0.86,P< 0.0001, log10 transformed) and declined in the absence of boosters. Boosters administered IM generated the highest antibody responses. Increasing time intervals between boosters generated antibody responses that were faster than and superior to those obtained with the final month 42 vaccination. CMI responses to the 3-dose IM priming remained elevated up to 43 months. (This study has been registered at ClinicalTrials.gov under registration no. NCT00119067.).

Animal Models for the Pathogenesis, Treatment, and Prevention of Infection by Bacillus anthracis

This article reviews the characteristics of the major animal models utilized for studies on Bacillus anthracis and highlights their contributions to understanding the pathogenesis and host responses to anthrax and its treatment and prevention. Advantages and drawbacks associated with each model, to include the major models (murine, guinea pig, rabbit, nonhuman primate, and rat), and other less frequently utilized models, are discussed. Although the three principal forms of anthrax are addressed, the main focus of this review is on models for inhalational anthrax. The selection of an animal model for study is often not straightforward and is dependent on the specific aims of the research or test. No single animal species provides complete equivalence to humans; however, each species, when used appropriately, can contribute to a more complete understanding of anthrax and its etiologic agent.

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.

Microbial dose response modeling: past, present, and future

The understanding of the risk to humans from exposure to pathogens has been firmly put into a risk assessment framework. A key element of applying this approach is the understanding of the relationship between dose and response for particular pathogens. This understanding has progressed from early use of threshold concepts ("minimal infectious dose") thru multiple generations of models. Generation 1 models describe probability of response to exposed dose. Generation 2 models incorporate host factors (e.g., age) and/or pathogen factors (e.g., particle size of inhaled agents). Generation 3 models describe the rate at which effects develop, i.e. the epidemic curve. These (generation 1 through three models) have been developed and used in multiple contexts. Beyond Generation 3 lies an opportunity for the deep incorporation of in vivo physiological responses and the coupling of the individual host dynamics to the dynamics of spread of contagious diseases in the population. This would enable more direct extrapolation from controlled dosing studies to estimate population level effects. There remain also needs to understand broader categories of infectious agents, including pathogenic amoebae and fungi. More advanced models need to be validated against well-characterized human outbreak data.

Responding to biological incidents--what are the current issues in remediation of the contaminated environment?

Since 2000 there have been a number of biological incidents resulting in environmental contamination with Bacillus anthracis, the causative agent of anthrax. These incidents include the US anthrax attacks in 2001, the US and UK drumming incidents in 2006-2008 and more recently, anthrax contamination of heroin in 2009/2010 and 2012/2013. Remediation techniques used to return environments to normal have varied between incidents, with different decontamination technologies being employed. Many factors need to be considered before a remediation strategy or recovery option can be implemented, including; cost, time (length of application), public perception of risk, and sampling strategies (and results) to name a few. These incidents have demonstrated that consolidated guidance for remediating biologically contaminated environments in the aftermath of a biological incident was required. The UK Recovery Handbook for Biological Incidents (UKRHBI) is a project led by Public Health England (PHE), formerly the Health Protection Agency (HPA) to provide guidance and advice on how to remediate the environment following a biological incident or outbreak of infection, and is expected to be published in 2015.

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.

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.

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.

Pathology and pathophysiology of inhalational anthrax in a guinea pig model

Nonhuman primates (NHPs) and rabbits are the animal models most commonly used to evaluate the efficacy of medical countermeasures against anthrax in support of licensure under the FDA's "Animal Rule." However, a need for an alternative animal model may arise in certain cases. The development of such an alternative model requires a thorough understanding of the course and manifestation of experimental anthrax disease induced under controlled conditions in the proposed animal species. The guinea pig, which has been used extensively for anthrax pathogenesis studies and anthrax vaccine potency testing, is a good candidate for such an alternative model. This study was aimed at determining the median lethal dose (LD50) of the Bacillus anthracis Ames strain in guinea pigs and investigating the natural history, pathophysiology, and pathology of inhalational anthrax in this animal model following nose-only aerosol exposure. The inhaled LD50 of aerosolized Ames strain spores in guinea pigs was determined to be 5.0 × 10(4) spores. Aerosol challenge of guinea pigs resulted in inhalational anthrax with death occurring between 46 and 71 h postchallenge. The first clinical signs appeared as early as 36 h postchallenge. Cardiovascular function declined starting at 20 h postexposure. Hematogenous dissemination of bacteria was observed microscopically in multiple organs and tissues as early as 24 h postchallenge. Other histopathologic findings typical of disseminated anthrax included suppurative (heterophilic) inflammation, edema, fibrin, necrosis, and/or hemorrhage in the spleen, lungs, and regional lymph nodes and lymphocyte depletion and/or lymphocytolysis in the spleen and lymph nodes. This study demonstrated that the course of inhalational anthrax disease and the resulting pathology in guinea pigs are similar to those seen in rabbits and NHPs, as well as in humans.

Inhalational anthrax (Ames aerosol) in naïve and vaccinated New Zealand rabbits: characterizing the spread of bacteria from lung deposition to bacteremia

There is a need to better understand inhalational anthrax in relevant animal models. This understanding could aid risk assessment, help define therapeutic windows, and provide a better understanding of disease. The aim here was to characterize and quantify bacterial deposition and dissemination in rabbits following exposure to single high aerosol dose (> 100 LD₅₀) of Bacillus anthracis (Ames) spores immediately following exposure through 36 h. The primary goal of collecting the data was to support investigators in developing computational models of inhalational anthrax disease. Rabbits were vaccinated prior to exposure with the human vaccine (Anthrax Vaccine Adsorbed, AVA) or were sham-vaccinated, and were then exposed in pairs (one sham and one AVA) so disease kinetics could be characterized in equally-dosed hosts where one group is fully protected and is able to clear the infection (AVA-vaccinated), while the other is susceptible to disease, in which case the bacteria are able to escape containment and replicate uncontrolled (sham-vaccinated rabbits). Between 4–5% of the presented aerosol dose was retained in the lung of sham- and AVA-vaccinated rabbits as measured by dilution plate analysis of homogenized lung tissue or bronchoalveolar lavage (BAL) fluid. After 6 and 36 h, >80% and >96%, respectively, of the deposited spores were no longer detected in BAL, with no detectable difference between sham- or AVA-vaccinated rabbits. Thereafter, differences between the two groups became noticeable. In sham-vaccinated rabbits the bacteria were detected in the tracheobronchial lymph nodes (TBLN) 12 h post-exposure and in the circulation at 24 h, a time point which was also associated with dramatic increases in vegetative CFU in the lung tissue of some animals. In all sham-vaccinated rabbits, bacteria increased in both TBLN and blood through 36 h at which point in time some rabbits succumbed to disease. In contrast, AVA-vaccinated rabbits showed small numbers of CFU in TBLN between 24 and 36 h post-exposure with small numbers of bacteria in the circulation only at 24 h post-exposure. These results characterize and quantify disease progression in naïve rabbits following aerosol administration of Ames spores which may be useful in a number of different research applications, including developing quantitative models of infection for use in human inhalational anthrax risk assessment.

The age of necrotizing enterocolitis onset: an application of Sartwell's incubation period model

OBJECTIVE

Model age of necrotizing enterocolitis (NEC) onset applying Sartwell's model of incubation periods, and examine its relationship to gestational age (GA).

STUDY DESIGN

Retrospective chart review of St Louis Children's Hospital neonates diagnosed with NEC (≥Bell's stage II) from 2004 to 2008, inclusive.

RESULT

The relationship between age of NEC (N=84 cases) onset and GA best fits a non-linear model, with infants ≤28 weeks having a disproportionately longer time to onset than older GA groups and explained 50.3% of the variability in age of NEC onset. Additional clinical variables provided no improvement in explaining age of NEC onset. Application of Sartwell's model to age of NEC onset proved a good fit, when birth is used as the common exposure episode, and age is equivalent of the incubation period.

CONCLUSION

The relationship between day of NEC diagnosis and GA is non-linear, with lower GA infants having disproportionately longer time to onset. Despite these GA differences, the fit to Sartwell's model for incubation periods model is consistent with NEC being a consequence of an event that occurs at or soon after birth.

Modeling the host response to inhalation anthrax

Inhalation anthrax, an often fatal infection, is initiated by endospores of the bacterium Bacillus anthracis, which are introduced into the lung. To better understand the pathogenesis of an inhalation anthrax infection, we propose a two-compartment mathematical model that takes into account the documented early events of such an infection. Anthrax spores, once inhaled, are readily taken up by alveolar phagocytes, which then migrate rather quickly out of the lung and into the thoracic/mediastinal lymph nodes. En route, these spores germinate to become vegetative bacteria. In the lymph nodes, the bacteria kill the host cells and are released into the extracellular environment where they can be disseminated into the blood stream and grow to a very high level, often resulting in the death of the infected person. Using this framework as the basis of our model, we explore the probability of survival of an infected individual. This is dependent on several factors, such as the rate of migration and germination events and treatment with antibiotics.

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.

Uncertainty and operational considerations in mass prophylaxis workforce planning

BACKGROUND

The public health response to an influenza pandemic or other large-scale health emergency may include mass prophylaxis using multiple points of dispensing (PODs) to deliver countermeasures rapidly to affected populations. Computer models created to date to determine "optimal" staffing levels at PODs typically assume stable patient demand for service. The authors investigated POD function under dynamic and uncertain operational environments.

METHODS

The authors constructed a Monte Carlo simulation model of mass prophylaxis (the Dynamic POD Simulator, or D-PODS) to assess the consequences of nonstationary patient arrival patterns on POD function under a variety of POD layouts and staffing plans. Compared are the performance of a standard POD layout under steady-state and variable patient arrival rates that may mimic real-life variation in patient demand.

RESULTS

To achieve similar performance, PODs functioning under nonstationary patient arrival rates require higher staffing levels than would be predicted using the assumption of stationary arrival rates. Furthermore, PODs may develop severe bottlenecks unless staffing levels vary over time to meet changing patient arrival patterns. Efficient POD networks therefore require command and control systems capable of dynamically adjusting intra- and inter-POD staff levels to meet demand. In addition, under real-world operating conditions of heightened uncertainty, fewer large PODs will require a smaller total staff than many small PODs to achieve comparable performance.

CONCLUSIONS

Modeling environments that capture the effects of fundamental uncertainties in public health disasters are essential for the realistic evaluation of response mechanisms and policies. D-PODS quantifies POD operational efficiency under more realistic conditions than have been modeled previously. The authors' experiments demonstrate that effective POD staffing plans must be responsive to variation and uncertainty in POD arrival patterns. These experiments highlight the need for command and control systems to be created to manage emergency response successfully.

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.

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.