Biological Attack Model
(BAM)
11 May 2007
Sponsor:
Dr. Yifan Liu
Team:
Richard Bornhorst
Robert Grillo
Deepak Janardhanan
Shubh Krishna
Kathryn Poole
Agenda
•
•
•
•
•
•
•
•
2
Introduction
Project Objective & Scope
Technical Approach
Biological Risk Assessment
Existing Policies and Modeling Methods
Biological Attack Model (BAM) Details
Conclusions/Recommendations
Future Work
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
3
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
4
Project Scope
Biological
Attack
BAM
Existing
Models &
Tools
•Disease Behavior Modeling
Recommendations for
Emergency Response
First
Responders
National & District
Response Plans
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
BAM Model Overview
• BAM expands upon the basic SEIR (Susceptible-ExposedInfectious-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
13
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
14
Input Parameters
Baseline Values
Known
Parameters
Controllable
Parameters
15
Parameter
Definition
Smallpox
Baseline
Value
β
transmission rate (#/day)
3
d
mortality rate of the disease (%)
0.30
m
disability rate of the disease (%)
0.05
μ1
incubation period (days)
13
μ2
infectious period (days)
20
α
close contacts identification rate (#/day)
5
φ
mass treatment of susceptible population (#/day)
5000
γ
quarantine rate (%)
0.30
Model Diagram
E (exposed)
S (susceptible)
Q1 (quarantined
non-symptomatic)
I (infectious)
Q2 (quarantined
symptomatic)
D (dead)
16
M (maimed)
R (recovered)
Model ODEs
dS
 QS (t )  ES (t )  RS (t )
dt
dE
 ES (t )  I E (t )  QE (t )
dt
dI
 I E (t )  DI (t )  M I (t )  RI (t )  QI (t )
dt
dQ1
 QS (t )  QE (t )  RQ1 (t )  QQ (t )
dt
dQ2
 QI (t )  DQ (t )  M Q (t )  RQ 2 (t )  QQ (t )
dt
dD
 DI (t )  DQ (t )
dt
dM
 M I (t )  M Q(t )
dt
dR
 RI (t )  RQ1 (t )  R Q 2 (t )  RS (t )
dt
17
ES(t)
E (exposed)
S (susceptible)
QE(t)
RS(t)
QS(t)
IE(t)
Q1 (quarantined
non-symptomatic)
QI(t)
I (infectious)
DI(t)
D (dead)
MI(t)
M (maimed)
QQ(t)
Q2 (quarantined
symptomatic)
DQ(t)
MQ(t)
RQ(t)
RI(t)
Transition Naming Convention:
AB(t) where
A = Destination State
B = Origination State
R (recovered)
Model ODEs Example
Exposed State
dE
 ES (t )  I E (t )  QE (t )
dt
ES (t )    i(t )  s(t )
I E (t ) 
1
1
 e(t )
QE (t )      i(t )  e(t )
α = close contact identification rate
β = disease transmission rate
γ = quarantine rate
μ1 = incubation period
18
ES(t)
RS(t)
E (exposed)
S (susceptible)
QE(t)
QS(t)
IE(t)
Q1 (quarantined
non-symptomatic)
QI(t)
I (infectious)
DI(t)
D (dead)
MI(t)
M (maimed)
QQ(t)
DQ(t)
Q2 (quarantined
symptomatic)
MQ(t)
RQ(t)
RI(t)
Transition Naming Convention:
AB(t) where
A = Destination State
B = Origination State
R (recovered)
Results – Baseline Values
Results Using Baseline Parameter Values
1,000,000
Initial Population = 1,000,000
Susceptible
900,000
Exposed
(Initial Number of Infected People = 300)
Infected
800,000
Quarantine-1
Quarantine-2
Number of People
700,000
Dead
Maimed
600,000
Recovered
500,000
Max in Quarantine-1 ≈ 190,000
400,000
Max in Quarantine-2 ≈ 270,000
300,000
Total Dead ≈ 200,000
200,000
100,000
0
0
10
20
30
40
50
60
70
80
90
100 110 120 130
140 150 160 170
Time (days)
19
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
180 190 200
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
Known Parameters (smallpox)
20
Parameter
Min Value
Baseline
Max Value
μ1 – incubation period (days)
7
13
17
μ2 – infectious period (days)
16
20
24
d – mortality rate
0.2
0.3
0.4
m – disability/maimed rate
0.01
0.05
0.2
β – transmission rate (#/day)
1
3
5
Sensitivity Analysis
Deaths
• Objective: Minimize the number of people who are killed or
seriously disabled as a result of the outbreak
incubation period
infectious period
transmission rate
mortality rate
disability rate
21
Parameter
# of Deaths
(compared to baseline)
μ1 – min
+ 11,300
μ1 – max
- 8,500
μ2 – min
- 1,700
μ2 – max
+ 1,000
β – min
- 162,000
β – max
+ 40,000
d – min
- 69,000
d – max
+ 69,000
m – min
0
m – max
0
β and d have a
significant impact
on the total
number of deaths
Sensitivity Analysis
Quarantine
•
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
Parameter
Max # in Q1 (quarantine
non-symptomatic)
(compared to baseline)
Max # in Q2 (quarantine
symptomatic)
(compared to baseline)
μ1 – min
- 7,400
+ 91,000
μ1 – max
- 3,500
- 42,000
μ2 – min
- 4,400
-37,000
μ2 – max
+ 3,000
+ 31,000
β – min
- 148,000
- 235,000
β – max
+ 31,000
+ 65,000
* β has a significant impact on the number of people sent to quarantine (both
symptomatic and non-symptomatic)
22
* μ1 and μ2 have a significant impact on the number of people sent to
quarantine (symptomatic only)
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
Controllable Parameters (smallpox)
23
Parameter
Min
Value
Baseline
Max
Value
α – close contact identification rate (#/day)
1
5
10
γ – quarantine rate
0.1
0.3
0.5
φ – mass vaccination rate (#/day)
0
5,000
25,000
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
Research
Control Policies
Estimated # of Days
Until Controlled
Baseline BAM
QI, RV
42
Historic (Kosovo, 1972)
QI, MV, PV
40
Meltzer et al.
QI, MV
55
Eichner
QI, RV
40
Policies: QI = Quarantine/Isolation, RV = Ring Vaccination,
MV = Mass Vaccination, PV = Prophylactic Vaccination
24
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
25
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
•
26
Evaluate usage of this model for other classes of problems
– Computer virus containment on the Internet
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.
27
Questions
28
Back-Up
29
Project Schedule
30
Event
Description
Completion
Time
(wks)
Start Date
Completion Date
Task
Project Evaluation
1
01/25/2007
02/01/2007
Milestone
Team Formulation
-
02/01/2007
02/01/2007
Task
Project Proposal Drafting
2
02/01/2007
02/15/2007
Milestone
Project Proposal Due
-
02/15/2007
02/15/2007
Task
Research Biological Agents
3
02/15/2007
03/29/2007
Task
Research Existing Models
3
02/15/2007
03/29/2007
Task
Finalize Project Plan and Schedule
1
02/15/2007
02/22/2007
Task
Risk Assessment
1
02/15/2007
02/22/2007
Milestone
Status Report # 1
-
02/22/2007
02/22/2007
Task
Detailed Design and Model Development
5
02/22/2007
03/29/2007
Milestone
Progress Presentation
-
03/08/2007
03/08/2007
Milestone
Status Report # 2
-
03/22/2007
03/22/2007
Milestone
Progress Discussion
-
03/29/2007
03/29/2007
Task
Testing, Evaluation, and Recommendations
2
03/29/2007
04/12/2007
Milestone
Formal Progress Presentation
-
04/05/2007
04/05/2007
Task
Final Report Drafting
3
04/12/2007
05/03/2007
Milestone
Final Report Due
-
05/03/2007
05/03/2007
Task
Presentation Preparation
1
05/03/2007
05/11/2007
Milestone
Final Presentation
-
05/11/2007
05/11/2007
Project Team Assignments
31
Project Task
Responsible Engineer
Project Manger
Richard Bornhorst
Technical Lead
Kathryn Poole
Research/Scribe
Robert Grillo
Modeling and Simulation Design
Deepak Janardhanan, Shubh Krishna
Project Proposal
Richard Bornhorst (LEAD) developed by All
Project Assessment
Robert Grillo, Richard Bornhorst
Biological Risk Assessment
Richard Bornhorst, Robert Grillo
The Model
Kathryn Poole, Deepak Janardhanan, Shubh Krishna
Model Implementation
Deepak Janardhanan
Evaluation Plan
Richard Bornhorst, Robert Grillo, Deepak Janardhanan
Analysis Plan
Richard Bornhorst, Kathryn Poole
Prototype Evaluation
Robert Grillo
Parametric Analysis
Kathryn Poole, Shubh Krishna
Final Report Development
Richard Bornhorst (LEAD) reviewed by All
Final Presentation Development
Kathryn Poole (LEAD) reviewed by All
Project Tracking
Planned Hours
Planned
Actual
EV
Week1
10
10
5
5
Week2
36
33.5
20
10
Week3
40
36
20
10
Week4
40.5
38
40
15
Week5
157.5
80
60
80
Week6
161.5
70
80
200
Week7
149.5
87
70
120
Week8
151.5
90
60
120
Week9
153.5
90
75
50
Week10
66.5
44
60
40
Week11
62.5
40
70
20
Week12
52
38.5
60
50
Week13
52
36
60
50
Week14
52
37.5
60
30
Week15
52
39.5
10
20
1237
770
750
820
51.33
50.00
54.67
Total
Average
32
Project Tracking
Total Manhours
Breakdown
Planned Hours
(Adjusted)
Actual Hours
EV
800
700
600
500
400
300
200
100
0
0
1
2
3
4
5
6
7
8
Weeks
9 10 11 12 13 14 15
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.
33
Biological Risk Assessment
AGENT
Spread
Diagnosis
Incubation
Vaccination
Antibiotic
Deadliness
Threat
Air
(3)
MEDIUM
(3)
1-7 days
(4)
Yes
(1)
5
3.1
Botulism (Clostridium botulinum
toxin)
Water
(2)
MEDIUM
(3)
12-36 hours
(5)
No
(5)
5
3.2
Plague (Yersinia pestis)
Human
Animal
(4)
MEDIUM
(3)
2-6 days
(4)
Yes (pre-exposure)
(3)
5
3.7
Smallpox (variola major)
Human
(5)
EASY
(5)
12 days
(3)
Yes (limited)
(4)
5
4.7
Tularemia (Francisella tularensis)
Air
(3)
HARD
(1)
1-21 days
(2)
No
(5)
4
2.6
Viral hemorrhagic fevers
(filoviruses [e.g., Ebola,
Marburg] and arenaviruses
[e.g., Lassa, Machupo])
Human
(4)
EASY
(5)
2-20 days
(2)
No
(5)
5
4.3
.40
.30
.10
.10
.10
1.00
Anthrax (Bacillus anthracis)
WEIGHTS
34
Existing Models
35
•
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) 228251.
– Incorporated the effects of population behavioral changes into a smallpox
release model
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).
36
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.
37
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.
38
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.
39
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.
40
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.
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