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.

the first eight days of the Sverdlovsk event (due to Toth's use of just confirmed cases) (6). After the eighth day of case reports, it appears that the 2008 Wilkening distribution fits the Sverdlovsk data better. In Wilkening's 2008 analysis, he also compares the fit of his 2006 log-normal model to his 2008 exponential model and claims the following: "a log-normal model fits the data just as well as the [exponential mechanistic model]…Therefore, aside from inferring the value of several parameters associated with disease progression in the host (i.e. lung clearance rate, the spore germination rate, and the bacterial generation time), there would not be much value added". He also goes on to state, that while his exponential mechanistic model was the more accurate model it is also more analytically intractable. Given the apparent equal empiric fit of both model types to the available data and our desire to implement this work in a spreadsheet model using the best, least mathematically intensive method (so that they are more readily understood and accepted by public health officials), we had a preference for Wilkening's 2006 log-normal model.
Influence of capping the event at 60 days: We capped the length of the event at 60 days in order to simplify tool construction and focus graphical output on the event period with most cases. In doing so we prevent 0.02% of infected individuals from contributing to our median projections based on solving the cumulative incubation distribution function at time equals 60 days [result is 99.98]. Capping the event length was irrelevant for our low FCC estimate (all cases occur before then), but in our high FCC estimates (resulting from the lowest calculable exposure assumption of 1 spore) this caused the exclusion of 1.4% of cases (98.6% become symptomatic on or before day 60).

Additional Analyses and Results:
To determine the maximal projection accuracy, we also ran the model using the entire 40-day Sverdlovsk-like case series as input. We then compared these results with the actual "Sverdlovsk-like" case count. When the entire Sverdlovsk-like case series is used, the tools projects 701 symptomatic patients (1 more than the actual case count, plausible range: 700-736 cases), mortality of 38% (264 deaths), and a peak hospital caseload of 366 patients on day 19.
Interpreting Accuracy in an Outbreak Situation: Users of Anthrax Assist are cautioned that there may be notable differences between actual case counts and the median estimated cases counts curves. Such differences can be anticipated in the course of model use during an outbreak (such as when updating the model daily with new case information from the field) as a result of the under-reporting of cases and different sub-populations within the impacted area being exposed to different levels of inhaled spores. A mismatch between the Epidemic Curve projections and the event's line list data may provide a hint that the exposure is not the result of a single point-source one-time release (for which Anthrax Assist is designed). Such issues are not likely to be noted until four or more days of data are used as input, but can be dealt with by altering the values of the average inhaled spore counts, and utilizing different case series as input (Anthrax Assist permits up to 3 case series of data as input) to account for various degrees of potential under-reporting. In such a way a user can "fit" the projections to their case data or their case data to the projections. Such user-controlled adjustments accomplish the type of curvefitting that can be performed automatically by more sophisticated statistical methods (e.g., the "back-calculation" software of Egan et al [2]).

PEP-Impact Model
Adherence Decay: The proportion of individuals adhering to the prescribed twice daily antibiotic PEP regimen was based on an assumption that adherence degrades linearly between the campaign initiation, where it is 100%, and the user-specified adherence value on the final event day. This structure directly contributed to adherence exhibiting the least influence on averted cases and deaths (shown in the sensitivity analyses results). This was due to most infected already having become symptomatic in the event days before a decrease in adherence (even the most precipitous one) exerted its influence on PEP effectiveness. Even when we lengthened the incubation period to the greatest extent possible (based on an exposure using the minimum possible infectious dose [1 spore]), adherence was still the least influential PEP-related parameter on averted cases/deaths, although the span between the percent of averted cases at 15% and 90% adherence widened from 5% (Table 5) to 8% (the difference between 48% and 56%, respectively for a 1 spore exposure profile). We could not find any evidence to support a different method for modeling the change in adherence over time. One consideration (based on the findings of Egan et al. showing a dynamic relationship between the importance of the length of adherence and an event size) was to use the severity and size of the event as positive feedback for adherence (i.e. more deaths = better adherence), but we would be speculating in actually defining such a relationship (2).
Additionally, for the sake of simplicity, we assumed that 1) the proportion of individuals not fully compliant with the regimen on their calculated day of becoming symptomatic were 0% protected by PEP, and 2) individuals were 100% protected by PEP if it was taken on their calculated date of becoming symptomatic, even if they stopped taking antibiotics altogether anytime during the next 60 days. The first "simplifying" assumption ignores the potential for partial protection among individuals who have not stopped taking their antibiotics altogether, but who are ingesting less than the prescribed dose over the course of the entire event. During the 2001 Amerithrax event in the US, 42% of postal workers who began taking PEP were classified in this adherence category (7). However, estimating the efficacy of a partial dose would have been difficult as we could find no evidence of this in the literature. As such, we felt keeping PEP protection at "all or none" was justifiable. The second "simplifying" assumption disregards the potential for some proportion of the individuals who are initially compliant with the regimen, and who then stop the regimen, to experience a delay in symptomatic illness (i.e. lengthening of the calculated incubation period). This proportion is determined by the inhaled spore count (a higher count requires longer adherence to be protective, as shown by Egan et al. [2]) and the shape of our adherence decay curve over time. For example, in an experiment where non-human primates were exposed to ~400,000 spores (1,000 times the median dose in our baseline scenario), Friedlander et al. found that 10% of non-human primates still developed IA after a 30day doxycycline regimen was completed (8). We suspect that in a large inhalation anthrax event (i.e. where the public witnesses illness and death in the community similar to our "Sverdlovsklike" scenario), that our linear decay in PEP adherence overestimates adherence decay in the initial weeks of the event. Taking Friedlander's results together with our conservative adherence decay rate, we theorize that any diminished impact of PEP resulting from our second "simplifying" assumption is small. Finally, since the influence of each "simplifying" assumption on our projected PEP impact offsets the other, we felt that accounting for the realities they address would unnecessarily complicate the value of the PEP Impact model outputs for decisionmakers.
Relationship between the prophylaxis goal and PEP Uptake: In our model, the proportion of infected persons receiving PEP on each day of the campaign decreases as the number of unexposed individuals requiring prophylaxis increases and when the daily campaign throughput capacity cannot accommodate the increase. This occurs because we assume there is no way of distinguishing infected, asymptomatic individuals from unexposed individuals at the point of dispensation, causing infected individuals to be diluted among the population seeking PEP. As a result, a portion of infected persons will experience a delay in obtaining and starting PEP. In our base case scenario, we assumed public health responders target 500,000 to receive PEP (have enough antibiotics to do so), and can dispense 250,000 regimens daily over 2 days, resulting in 52% of cases averted. For every additional campaign day required to provide PEP to a larger population (using our baseline scenario), responders sacrifice saving 2% to 4% of cases (Technical Appendix Table 1).
Relationship between adherence and PEP Uptake: In our evaluation of the PEP Impact model we compared scenarios with assumptions of both improved uptake and adherence (Scenario 2), or a decrease in both uptake and adherence (Scenario 4), to the baseline PEP scenario (Table 3). It should be noted, however, that in a real IA event, good uptake could be paired with poor adherence and vice versa.

Healthcare-Impact Model
In instances where multiple transition routes out of a single disease/treatment state are possible, our calculations were completed in the following order (each event day): Averted cases were removed from the incubating population each day before determining how many incubating infected transitioned to symptomatic illness; Untreated Prodromals transitioning to fulminant illness were removed before determining the number of prodromals entering treatment; Prodromals in treatment transitioning to fulminant were removed before determining the number recovering; and Fulminants transitioning to death were removed before determining the number of fulminants entering treatment.
Transition rates were selected to approximate the Weibull distribution modeled by Holty overestimating the need for resources to treat advanced IA illness at the expense of underestimating the resources needs for treating early IA illness. As the latter set of resources are likely more abundant or more easily obtained, we felt this the more conservative approach. Users of our model who prefer a different approach, however, may specify a "percent of prodromal patients which recover through fulminant illness" to match the definition of their choice ( Table   2).
Public health messaging impact: The timing of public health messaging also impacted CFR, but its influence was limited to an event without a PEP campaign or an ineffective one, due to a logic constraint we imposed on a user's PHM date input: PHM must occur on or before the date of a PEP campaign's initiation because we assume PHM to occur as part of a PEP campaign's "rollout". When the first 3 days of case data were utilized for projections in an unmitigated scenario, and public health messaging was disseminated on the second event day [the base case without a PEP campaign], the Healthcare Impact model projected 51 fewer deaths (a 5% lower CFR) than when messaging occurred 1 week later. CFR improved (decreased) with earlier PHM by improving the ratio of symptomatic individuals seeking treatment in the prodromal illness stage to those seeking treatment in the fulminant illness stage.

Attack Scenario: Sverdlovsk Adaptation:
Our choice of attack scenario stemmed from a desire to illustrate the model with a plausible event that was also large enough to necessitate a wide-scale public health response. As such, we created an attack scenario case series patterned after the 1979 Sverdlovsk (USSR) event and inflated it into a larger event. We created this "Sverdlovsk-like" case series by multiplying each day's case count from the Sverdlovsk event by a factor of 10 (Technical Appendix Figure).
Using an historical event, vs. one manufactured mathematically, also avoids the issue of "fractional patients". The resultant scenario was a 40-day, 700-patient case series that matched the daily proportional caseload of the 1979 event. have similarly intensive treatment requirements as the inhalational form (11), and up to 40% could require a hospital bed (based on the percent of cutaneous cases expected to develop "malignant edema", which would require administration of IV steroids and antibiotics) (12,13).
Uniform exposure dosage: In a real population-wide anthrax event, different populations would likely be exposed to different amounts of aerosolized spores (e.g. based on proximity to a release source or time spent in an exposure zone), and even respond differently to the same exposure amounts, resulting in many different incubation distributions among the populations exposed. We chose to rein in these issues by assuming a singular incubation distribution based on an average exposure dosage (a median value of 360 spores/person [range 1-8,000]), and a consistent relationship between exposure dosage and patient types. These assumptions result in our projections both overestimating and underestimating the rapidity with which some groups of individuals in the impacted population would become symptomatic. Although there is not enough data to quantify the bias introduced from assuming a consistent relationship between dose and incubation across patient type, one could potentially express the direction of the bias on the model's estimate based on any known differences between the demographics in the first cases and the general populace of the impacted region. We chose to use one spore as the minimum possible, average infectious dose, to generate a maximal possible upper bound on the Final Case Count projections We chose 360 spores as the median dosage because it was the dosage estimated to have occurred during the 1979 aerosol release of B. anthracis spores in Sverdlovsk, USSR; and 8,000 spores is a plausible high-dose (and therefore lower case-count) estimate (1,3). Toth et al. notes that among 13 anthrax modeling papers reviewed, the ID1 (that is, the number of inhaled spores necessary to cause infection in 1% of exposed individuals) ranged from 1 to 9,900 (3).Such an exposure profile in an event seems extremely unrealistic (and it can be changed to user's liking), but its use greatly improves the likelihood that this model will overestimate the actual event size. And this is our intention, as it is the authors' opinion, that in a population-wide event, public health practitioners would rather deal with the repercussions of an 'over-response' than the loss of life from being under-prepared.