Biological Attack Model (BAM) 11 May 2007

1. Biological Attack Model(BAM)11 May 2007 Sponsor: Dr. Yifan Liu Team: Richard Bornhorst Robert Grillo Deepak Janardhanan Shubh Krishna Kathryn Poole

2. Agenda • Introduction • Project Objective & Scope • Technical Approach • Biological Risk Assessment • Existing Policies and Modeling Methods • Biological Attack Model (BAM) Details • Conclusions/Recommendations • Future Work

3. Introduction • The United States has a number of large cities that are potential targets for a biological terrorist attack • For example, Washington Metro Area (WMA) is especially susceptible to terrorist attacks • Home to the federal government • Tourist destination • High concentration of people in a relatively small area • The threat of a biological attack is a major concern • Example: the October 2001 incident where two envelops containing Anthrax were mailed to offices on Capitol Hill • 5-10 identified or suspected chemical or biological releases a month • Preparation is key to the successful response to a biological attack • Any assistance that could be provided to emergency responders would be potentially invaluable

4. Project Objective • Develop a Biological Attack Model (BAM) to assist emergency responders and emergency planners with the following: • Containment strategy selection in the event of a biological attack • Maximizing the effectiveness of limited resources such as hospital beds and vaccines (if available) • Improving the time required to respond to and contain a potential epidemic

5. Project Scope Existing Models & Tools Biological Attack BAM • Disease Behavior Modeling Recommendations for Emergency Response First Responders National & District Response Plans

6. Technical Approach • Part 1: Evaluate potential biological warfare agents to determine the threat potential • Evaluate and rank each disease based on spread, diagnosis, incubation, vaccination, and deadliness • Part 2: Assess the depth and applicability of current models and processes to the bio-terror problem • Survey the internet for available information • Analyze the current models and procedures • Part 3: Develop a disease behavior model • Evaluate existing models and determine applicability to a biological attack • Develop or modify existing models to address identified gaps • Part 4: Evaluate the effectiveness of various containment strategies • Conduct sensitivity analyses and parametric studies to provide guidance on various containment strategies to emergency responders and emergency planners in the event of a biological attack

7. Biological Risk Assessment • 43 biological agents are considered potential bio-terror weapons • Of these agents, six are considered “Category A” based on the following criteria: • Ability to spread person to person • High mortality rate • Public panic • Require special actions for containment • A risk analysis was conducted to determine which “Category A” biological agent has a high threat potential • Threat = (weight x parameter value) • The biological agent identified was smallpox • Smallpox will be used to evaluate the model and analyze the effectiveness of various containment strategies

8. Existing Policies Containment Strategies • The BAM can be used to analyze the following six control strategies: • Quarantine/isolation of confirmed and suspected cases • Reduces transmissions from those that are or may be infected • Voluntary confinement and movement restrictions • Includes closure of public gatherings and transportation systems • Ring vaccination • Tracing/vaccinating contacts of confirmed and suspected cases • Targeted vaccination • Vaccination of the whole population in a specific area • Mass vaccination • Vaccination of the whole population of a threatened country • Prophylactic vaccination • Vaccination before an outbreak is detected

9. Existing Policies CDC Post-Event Guidance • Public health personnel and other public service personnel needed for controlling the outbreak should be vaccinated as soon as possible • The ring vaccination and quarantine policy should be adhered to as the initial response • Diagnosis of cases needs to be executed rapidly and efficiently for the ring policy to work effectively • Epidemiological investigations need to be conducted to identify potential linkages between patients • Travel histories of a 2-3 week period prior to the onset of symptoms • The decision to offer the vaccine to everyone within a city, state, or the country would be made by public health officials • Detailed, real-time data is required to keep policy makers, health officials, clinic managers, and the public informed about the status of the response activities

10. Existing Modeling Methods • Many epidemic models build upon the simple SIR model (Susceptible – Infected – Recovered) • Represents the number of people in each state as a function of time • Each member of the population typically progresses from susceptible to infectious to recovered, based on disease transition rates • With differential equations these states can be used to analyze outbreaks and methods to bring them under control • A common extension of the SIR model is the basic SEIR model (Susceptible – Exposed – Infected – Recovered) • Further refines the status of each member of the population • Takes into account that individuals in the susceptible population first become exposed and then become infectious • However, the basic SEIR model does not provide the level of detail, in terms of population status, that is desired for the BAM

11. BAM Assumptions • Attack Assumptions • Single source where a given number of people are initially exposed • Input may come from existing dispersion models • Diseases will be transmitted person to person • Rather than air, water, or food borne transmission • Population Assumptions • Constant population with no immigration/emigration, births, or deaths that are not related to the disease • People in the incubation stage (non-symptomatic) are handled the same way susceptible people are, since they are not yet known to be infected

12. BAM Assumptions • Quarantine Assumptions • Confirmed and suspected cases are quarantined, per CDC guidance • A percentage of the population cannot be quarantined • Vaccination and Treatment Assumptions • Vaccinations and treatments are available and have no side effects • Available quantity can be added as a constraint and is not addressed in this study • When applicable, part of the population has prophylactic vaccination • Emergency response and medical staff are already vaccinated • Susceptible population does not include those already vaccinated • Those in quarantine without symptoms and all traced contacts receive vaccination • Those showing symptoms do not receive vaccination • These patients only receive treatment

13. BAM Model Overview • BAM expands upon the basic SEIR (Susceptible-Exposed-Infectious-Recovered) model to incorporate additional parameters relevant to response planning • Quarantine • Percentage of infected population quarantined per day • Number of contacts of infected population quarantined per day • Treatment (vaccination, antibiotics, etc.) • Number of people in the susceptible population treated per day • Deaths related to the bio-attack • Mortality rate of the disease • BAM is comprised of 8 states and 8 differential equations • Runge-Kutta (fourth-order) numerical method used to solve the ODEs • Matlab solver: ODE45

14. Input Parameters • “Known” input parameters – determined via research • Incubation period (generally given as a range) • Deterministic model will use the mean • Infectious period (generally given as a range) • Deterministic model will use the mean • Mortality rate (generally given as an average percentage) • Disability rate • Not readily available • Transmission rate • “Controllable” input parameters – modified as part of the containment analysis • Close contacts identification rate • Quarantine rate • Treatment rate

15. Input ParametersBaseline Values Known Parameters Controllable Parameters

16. E (exposed) S (susceptible) Q1 (quarantined non-symptomatic) I (infectious) Q2 (quarantined symptomatic) D (dead) M (maimed) R (recovered) Model Diagram

17. ES(t) RS(t) QE(t) QS(t) IE(t) QI(t) QQ(t) DQ(t) DI(t) MI(t) MQ(t) RQ(t) RI(t) Model ODEs Transition Naming Convention: AB(t) where A = Destination State B = Origination State

18. Model ODEs ExampleExposed State ES(t) RS(t) QE(t) QS(t) IE(t) QI(t) QQ(t) DQ(t) DI(t) MI(t) MQ(t) RQ(t) RI(t) α = close contact identification rate β = disease transmission rate γ = quarantine rate μ1 = incubation period Transition Naming Convention: AB(t) where A = Destination State B = Origination State

19. Results – Baseline Values Initial Population = 1,000,000 (Initial Number of Infected People = 300) Max in Quarantine-1 ≈ 190,000 Max in Quarantine-2 ≈ 270,000 Total Dead ≈ 200,000 Ramp-up in # dead starts the same time the # infected reaches a maximum  between days 30-40  reasonable timing considering the lengthy incubation & infectious periods for smallpox

20. Sensitivity Analysis • BAM is a deterministic model that uses the average value for the known input parameters • Evaluate the sensitivity of the model to variations in each of the “known” input parameters • Change one parameter at a time (keep all other parameters fixed) • Primarily interested in the impact of the known parameters on: • Total number of deaths and disabilities as a result of the outbreak • Maximum number of people in quarantine during the outbreak

21. Sensitivity AnalysisDeaths • Objective: Minimize the number of people who are killed or seriously disabled as a result of the outbreak incubation period infectious period β and d have a significant impact on the total number of deaths transmission rate mortality rate disability rate

22. Sensitivity AnalysisQuarantine • Objective: Monitor the number of people who are sent to quarantine (available resources for quarantine are not unlimited) • Changes in the mortality rate (d) and disability rate (m) do not alter the max number of people in quarantine incubation period infectious period transmission rate * β has a significant impact on the number of people sent to quarantine (both symptomatic and non-symptomatic) * μ1 and μ2 have a significant impact on the number of people sent to quarantine (symptomatic only)

23. Parametric Analysis • Baseline values were selected for each of the controllable input parameters to represent a reasonable response to an outbreak • Additional runs were executed to assess the impact of variations in these parameters on the end result • Provides insight into which containment strategies are most effective in controlling an outbreak • Increasing any of the rates for the controllable parameters reduces the total number of deaths • The challenge for emergency planners is selecting reasonable values without overstepping availability constraints

24. Model Evaluation • The effective reproductive number, Reff(t), was used to compare the BAM to other models • Reff(t), measures the average number of secondary cases per infectious case at time t • When Reff(t) ≤ 1, the epidemic can be considered under control • This is a rough comparison since inputs, outputs, and assumptions for each model vary Policies: QI = Quarantine/Isolation, RV = Ring Vaccination, MV = Mass Vaccination, PV = Prophylactic Vaccination

25. Conclusions/Recommendations • BAM can be used to provide comparative results for use in disaster planning • Results obtained using different input values can be used to assess the relative impact of the various input parameters that define the response strategy • Quarantine rate (γ), mass vaccination rate (φ), close contact identification rate (α) • Results are inline with intuition • Increasing γ, φ and α reduces mortality • Early detection of the attack/release of the pathogen is key • BAM is deterministic whereas the real world is not • Converting BAM to a stochastic model will improve the accuracy (and increase the complexity) • The results of the sensitivity analysis indicate that the deterministic model provides reasonable guidelines for disaster planning purposes

26. Future Work • Incorporate constraints and optimization into the model • Account for resource constraints : vaccine dosage, ER personnel, quarantine facilities.. etc. • Incorporate multiple control strategies into the model • Allow choice of strategy as a parameter • Modify the model to use a transmission rate that decays over time • Simulate the reduction in person to person contacts as a result of voluntary quarantine, public service announcements.. etc. • Convert BAM to a stochastic model • More accurately account for parameters with significant uncertainty • Allow for dynamic changes in population • Incorporate additional states, transitions • Reflect the differences between : quarantine facilities, points of treatment • Allow transition from Recovered to Susceptible • Expand to accommodate other pathogens/transmission methods • Animal to human, waterborne, airborne, food borne • Generate a user friendly interface • Dash board view for ease of use • Evaluate usage of this model for other classes of problems • Computer virus containment on the Internet

27. Acknowledgements Thanks to Dr. Liu for sponsoring our project and providing technical guidance. Also, thanks to Dr. Laskey for constructive feedback and project guidance throughout the semester.

28. Questions ?

29. Back-Up

30. Project Schedule

31. Project Team Assignments

32. Project Tracking

33. Biological Risk Assesment Parameter Values for Risk Matrix • Spread– A terrorist is most likely to initiate a biological attack using air or water dispersion techniques. However, beyond the initial attack, a biological agent that can spread from human to human has the potential to affect more people. • Diagnosis – A disease that is easier to detect is ideal for a disease behavioral modal and containment model. A disease that is harder to detect will likely effect the entire population before containment strategies can be initiated. • Incubation – A short incubation period is ideal in a biological attack. The sooner people begin to get sick the sooner mass hysteria will break which is the main objective of a terrorist. • Vaccination/Antibiotic – A biological agent that does not have a vaccination or an effective antibiotic treatment has a greater potential to cause mass hysteria. • Deadliness – A terrorist is more likely to use the deadliest or most toxic agents in an attack.

34. Biological Risk Assessment

35. Existing Models • M.I. Meltzer, I. Damon, J.W. LeDuc, D. Millar, Modeling potential responses to smallpox as a bioterrorist weapon, Emerging Infectious Diseases, 7 (2001) 959. • Utilized a Markov chain model to evaluate the rates of mass vaccination and infected isolation after a deliberate release of smallpox • E.H. Kaplan, D.L. Craft, L.M. Wein, Emergency response to a smallpox attack: the case for mass vaccination, Proceedings of the National Academy of Sciences of the United States of America, 99 (2002) 10935. • Used simulations of a deterministic model to compare the effectiveness of mass and ring vaccination in reducing the consequences of a smallpox release • M. Eichner, Case isolation and contact tracing can prevent the spread of smallpox, American Journal of Epidemiology, 158 (2) (2003) 118. • With stochastic simulations, showed that contact tracing and case isolation could control smallpox outbreaks • S. Del Valle, H. Hethcote, J.M. Hyman, C. Castillo-Chavez, Effects of behavioral changes in a smallpox attack model, Mathematical Biosciences, 195 (2005) 228-251. • Incorporated the effects of population behavioral changes into a smallpox release model

36. Functional Requirements • F-100 - The BAM shall be applicable to a class of phenomena (diseases, bio hazard) and shall not be restricted to a single event. • F-200 - The BAM shall allow for at least 8 variables that can be used to perform sensitivity analyses of the various parameters and attributes that are inputs to the model. For example: Implicit attributes may be behavior of various pathogens (smallpox, bird flu…). Explicit input parameters may be: the efficacy of a vaccine, concentration of the pathogen, quantity of antidote available etc. • F-300 - The BAM shall comprise of multiple states including: susceptible, exposed, infectious, dead, maimed, recovered, quarantined (non-symptomatic), and quarantined (symptomatic).

37. Functional Requirements – Cont. • F-301 - The BAM shall provide the total number of people in each state at time (t). • F-400 - The mathematical formulation for BAM shall use ordinary differential equations to represent each state given time (t). • F-401 - The mathematical formulation for BAM shall be solved using a common numerical method such as Forward Euler or Runge-Kutta. • F-600 - The BAM shall leverage existing emergency response policies, procedures, and models to develop recommendations.

38. Functional Requirements – Cont. • F-700 - The BAM shall provide a disease behavioral model based on a single or multiple point of attack. • F-800 - The BAM shall provide recommendations on the containment and control of a biological release based on the dispersion and disease behavioral models. • F-900 - The BAM shall provide recommendations on vaccination, if necessary, in the event of a biological release.

39. Non- Functional Requirements • N-200 - The BAM shall be usable by subject experts as end users and shall not mandate Operational Research skills for usage and interpretation of the results. • N-300 - The components of the BAM shall be modular which will allow for the study to be extendable with the addition of additional modules or stages if necessary. • N-400 - The outputs obtained from a simulation using BAM shall be traceable and repeatable for a given set of input parameters (precision). • N-500 - The outputs of the BAM shall be logically consistent (i.e. there shall be no contradictions inherent in the model). • N-600 - The mathematical formulation of the BAM shall be independently verifiable and recorded as part of the final report.

40. Performance Requirements • P-100 - The BAM shall be implemented as a light solution solver versus being computer intensive. In short, it shall be possible to implement the model using standard personal computing hardware and software resources. • P-200 - It shall be possible for the computerized implementation of the BAM to generate outputs for any valid input scenarios in less than 5 minutes. Valid input scenarios are those identified in the problem scope. • P-300 - It shall be possible to obtain an assessment of the accuracy and consistency of the outputs from multiple simulation runs in terms of confidence intervals, variances etc.

41. Interface Requirements • I-100 - The BAM shall accept input parameters for the transmission rate, close contact identification rate, mortality rate, disability rate, treatment rate, quarantine rate, the incubation period, and the infection period. • I-200 - The BAM shall accept input parameters for the initial size of the susceptible population and the initial size of the exposed populations. • I-201 - The BAM shall accept emergency response capability information. • I-202 - The BAM shall accept input parameters for the total amount of vaccine or hospital beds available to treat exposed and infectious patients. • I-300 - The BAM shall output the number of people in each state at time (t). This can be accomplished by means of a graphical representation of the entire population over time. • I-400 - The BAM shall be designed to work with existing dispersion models.