Biological Attack Model
(BAM)
Progress Report
March 8
Sponsor: Dr. Yifan Liu
Richard Bornhorst
Robert Grillo
Deepak Janardhanan
Shubh Krishna
Kathryn Poole
Agenda
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2
Project Plan
Work Breakdown
Biological Agent Parameters
Assumptions Revisited
Preliminary Model Overview
Current Modeling Issues
Project Plan
Description
Detailed Design and Model
Development
Progress Presentation
Status Report # 2
Progress Discussion
Testing, Evaluation, and
Recommendations
Formal Progress Presentation
Final Report Drafting
Final Report Due
Presentation Preparation
Final Presentation
3
WEEK 7 WEEK 8 WEEK 9 WEEK WEEK WEEK WEEK WEEK WEEK
10
11
12
13
14
15
Work Breakdown
Project Task
Week 7
Week 8
Units---->
Project Management
Configuration Mangement
Group Meetings
RB RG
DJ
1
1
1.5 1.5 1.5
1.5
Online Discussions
Status/Progress Brief Preparation
Develop a disease behavioral model
0.5
0.5
3.75
Develop containment model
TOTALS
5
10
10
10
10
5
10 10
10
10
12.8 19.5 15.75 19.5 19.5 12.8 21 19.5 19.5 20.5
0.5
3.75 7.5
SK
KP
1.5
RB RG DJ
1
1
1.5 1.5 1.5
1.5
1.5
0.5
0.5
0.5
0.5
0.5
7.5
7.5
7.5
7.5
0.5
1
7.5
0.5
1
3.75 7.5
SK
KP
• 320 of 875 man-hours completed.
• Ahead of schedule on modeling
– End modeling phase by next brief to give an extra week to testing,
evaluation, analysis, and recommendations (4 weeks)
– Develop early skeleton for final report
4
Biological Agent Parameters
• Smallpox (β = 3) (d = 30%)
– Incubation Period: 7-17 days
– Prodrome Period: 2-4 days
– Symptomatic Period: 20 days
• Ebola (β = 1-2) (d = 40%-90%)
– Incubation Period: 2-20 days
– Prodrome Period: 2-4 days
– Symptomatic Period: 6-9 days
• Viral Encephalitis (β = 3-4) (d = 3%-60%)
– Incubation Period: 5-15 days
– Prodrome Period: 2-4 days
– Symptomatic Period: 7-14 days
5
Assumptions Revisited
• Attack Assumptions
– Single source where a certain number of people are initially
exposed
– Diseases will be transmitted person to person rather than
airborne or food borne
– Detected 24 hours after incident (may adjust for future analysis)
• Population Assumptions
– Constant population with no immigration/emigration, births, or
deaths that aren’t related to the disease
– People in the incubation stage (non-contagious) are considered
susceptible in terms of quarantine and treatment since they are
not yet known to be infected
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Assumptions Revisited
• Quarantine Assumptions
– Various percentages of the population are quarantined to analyze
effectiveness
• Isolation of confirmed and suspected cases with vaccination and
quarantine of contacts traced to these cases
• All other quarantine is voluntary confinement
– A percentage of the population cannot be quarantined
• Vaccination and Treatment Assumptions
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A percentage of population is already vaccinated (when applicable)
Emergency response and medical staff already vaccinated (if available)
Treatments are available for recovering those that receive it
Vaccination and treatment have no significant side effects
Those in quarantine without symptoms receive available vaccination
Those showing symptoms do not receive vaccination (treatment only)
Two Phases
• First Phase
– The spread of the pathogen before detection
• Initial assumption is detection occurs after 24 hours, but this will be
adjusted to analyze the importance of early detection
– Only three states during this phase: Susceptible, Infected,
Infectious
• Second Phase
– Occurs after outbreak has been identified
• The status of states at end of first phase provide initial conditions
for second phase
• Containment strategies employed
8
Preliminary Model Diagram
Track 10 different populations
S+Qi1+Qi2+Qs+I1+I2+RN+RT+RD+D = N
Recovered
With
Treatment
RT
Susceptible
S
Quarantined
Infected
Qi1
Infected
I1
Dead
D
Quarantined
Susceptible
QS
9
Quarantined
Infectious
Qi2
Infectious
I2
Recovered
Without
Treatment
RN
Disabled
RD
Preliminary Model Parameters
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Transmission Rate (b)
Average Incubation Length (m1)
Average Infectious Length (m2)
Disease Mortality Rate (d)
Quarantine Rate (q)
Tracing Close Contacts of Infectious (a)
Number of Treated Per Day (f)
Treatment Efficacy Period (b)
Disability Ratio (g)
Total Population (N)
Preliminary Model Parameters (Excel
snapshot)
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Example Plot:
10,000 treated per day, 30% Quarantine Rate
Populations
120.00%
Susceptible
Infected
Infectious
Quarantined Infected
Quarantined Infectious
Quarantined Susceptible
Recovered by Treatment
Recovered Without Treatment
Disabled
Dead
Percentage of Population
100.00%
80.00%
60.00%
40.00%
20.00%
Day Number
12
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
1
0.00%
Example Plot:
10,000 treated per day, No Quarantine
Populations
120.00%
Susceptible
Infected
Infectious
Quarantined Infected
Quarantined Infectious
Quarantined Susceptible
Recovered by Treatment
Recovered Without Treatment
Disabled
Dead
Percentage of Population
100.00%
80.00%
60.00%
40.00%
20.00%
Day Number
13
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
1
0.00%
Example Plot:
20,000 treated per day, 30% Quarantine Rate
Populations
120.00%
Susceptible
Infected
Infectious
Quarantined Infected
Quarantined Infectious
Quarantined Susceptible
Recovered by Treatment
Recovered Without Treatment
Disabled
Dead
Percentage of Population
100.00%
80.00%
60.00%
40.00%
20.00%
Day Number
14
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
1
0.00%
Current Modeling Issues
• Modeling a Coherent Detection Scheme
• Disease incubation periods vs. appearance of symptoms
• Arriving at a Balance between Number of States & Reality
• Risk of Inaccuracy vs. simplification
• Recovery without treatment, Side effects….
• Integrity checks to be built in
• Containment as a combination of Reducing Contacts and
Treatment Resource Allocation
• Effective Treatment allocation issue
• Availability of Emergency Responders
• Effect of varying β due to Intervention efforts
• Diverse Containment strategies emerging for different
diseases
• More data available on Smallpox than the others
• Translating results into Information for a Decision Maker
• Use of percentages of population vs. absolute numbers
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Questions
16