Synopsis of Epidemic Modeling Studies* March 20, 2001 John N. Bombardt, Jr. Institute for Defense Analyses Telephone: 703-845-2204 E Mail:
[email protected]
*Work Sponsored by: (a) Defense Threat Reduction Agency and (b) Joint Program Office for Biological Defense with U.S. Army Office of The Surgeon General
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Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18
Topics • INTRODUCTION • Epidemic Modeling Overview • Epidemic Modeling Example – Background Information On Smallpox – Smallpox Casualty Estimates For Scenario B
• Concluding Comments
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2
Objectives
• Acquire Actual and, as Appropriate, “Surrogate” Epidemiological Data Sets for Smallpox, Pneumonic Plague and Hemorrhagic Fever Outbreaks • On the Basis of Available Epidemiological Data, – Analytically Reconstruct Historical Outbreaks – Then Make Estimates of Potential Outbreak Casualties for New Initial Conditions and Modern Outbreak Controls
• Relate These Outbreak Casualty Estimates to Biological Attacks on In-Theater Military Forces
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Analytical Scope
ANALYSES
BRIGADE, DIVISION OR CORPS DEFENSIVE MEASURES Pre-Attack Prophylaxis
Early Warning (Standoff Detection)
Trans-Attack Respiratory Protection
Prompt Identification Of BW Agent
Post-Attack Prophylaxis And/Or Therapy
Quarantine
Scenario A
NO
NO
NO
YES
YES (Early)
YES
Scenario B
NO
NO
NO
NO
YES (Late)
YES
Scenario C
NO
YES
YES
NO
YES (Late)
YES
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Status of Modeling Efforts • Basic Semi-Empirical Approach & Ebola Hemorrhagic Fever Epidemics – Sponsor: JPO-BD with Army OTSG (LTC Carl Curling) – Technical Effort: Completed in December 1999 – Published Report: “Contagious Disease Dynamics for Biological Warfare and Bioterrorism Casualty Assessments”, Institute for Defense Analyses, IDA Paper P-3488, February 2000, Unclassified
• Smallpox Epidemics – Sponsor: DTRA/ASCO (Dr. Peter Merkle) – Technical Effort: Completed in October 2000 – Draft Final Report: “Smallpox Transmission and BW Casualty Assessments,” Institute for Defense Analyses, IDA Paper P-3550, October 2000, Unclassified
• Pneumonic Plague Epidemics – Sponsor: JPO-BD with Army OTSG (LTC Debra Schnelle) – Technical Effort: Nearing Completion – Draft Final Report: Scheduled for Delivery in May 2001
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5
Topics • Introduction • EPIDEMIC MODELING OVERVIEW • Epidemic Modeling Example – Background Information On Smallpox – Smallpox Casualty Estimates For Scenario B
• Concluding Comments
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6
Epidemic Modeling Possibilities & Choices
POSSIBILITIES
MY CHOICES
•
“First Principles”
•
Semi-Empiricism
•
Stochastic Framework
•
Deterministic (“MeanField”) Framework
•
Spatiotemporal Spread •
Outbreak Dynamics
•
“Ball-Park” Estimates
•
“AccuWeather-Like” Predictions
Increasing Complexity & Computational Requirements
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Semi-Empirical Mean-Field Approach HISTORICAL OUTBREAK DATA
EPIDEMIC MODEL •Monte Carlo Method For New Infections Per Unit Time •Difference Equations For Disease Dynamics
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•Population Size •Initial Infections
•Symptom Onset Cases •Fatalities •Hospitalizations
Underlying Epidemiological Circumstances DISEASE TRANSMISSION RATE •Outbreak-Specific Time-Varying Function •Determinant of Outbreak Time History
FUTURE BW OR BT EVENT
MODEL ALTERATIONS
•Based On Derived Rate Of Disease Transmission •Modern Outbreak Controls
CASUALTY ESTIMATES
8
Basic Elements of Casualty Estimation Review Historical Outbreaks, Select the Most Pertinent Ones & Format Epidemiological Data
Historical Outbreak
Brigade (4,000)
Division (18,000)
Corps (80,000)
Scenario A
Scenario A
Scenario A
Scenario B
Scenario B
Scenario B
Scenario C
Scenario C
Scenario C
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FOR EACH SELECTED HISTORICAL OUTBREAK, Derive a Transmission Rate That Reproduces the Dynamics of This Outbreak in the Population of Interest FOR EACH POPULATION & SCENARIO, • Account for Future Epidemiological Circumstances by Changing Initial Conditions, by Truncating the Historically Derived Rate of Disease Transmission, and/or by Modifying the Mean-Field Algorithm • Calculate the Total Number of Removals (Deaths and Recoveries) as a Function of the Number of Initial Exposures (Infections)
9
Key Methodological Constraints •
Geographical Aspects of Epidemics – –
IDA Modeling Efforts Do Not Involve Explicit Quantitative Analyses of Where Individuals Become Infected. However, the Semi-Empirical Mean-Field Approach Does Have Geographical Implications × Population Density × Spatial Aspects of Historical Input.
•
Mass Action Law – –
•
The Mass Action Law Calls for the Homogeneous Mixing of Contagious and Susceptible Individuals and It Invokes a Constant Rate of Disease Transmission. However, Outbreak-Specific Time-Varying Rates of Disease Transmission Extend the Reach of Mean-Field Models by Accounting for Epidemiological Circumstances Like the Growth of Disease Awareness in the Populace, the Gradual Imposition of Systematic Outbreak Controls, Etc.
Disease-Causing Contacts in Military Units Versus Civilian Populations – –
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Historical Disease Transmission Rates for Civilian Populations May or May Not Capture Critical Features of Outbreaks in Forward-Deployed Military Units. The Concept of Epidemiological Surrogates for Diseases Like Pneumonic Plague and Smallpox Is Currently under Investigation. This Is to Suggest That Analyses of Common Respiratory Disease Outbreaks in Military Populations Could Yield Meaningful Surrogate Transmission Rates. 10
Topics • Introduction • Epidemic Modeling Overview • EPIDEMIC MODELING EXAMPLE – Background Information On Smallpox – Smallpox Casualty Estimates For Scenario B
• Concluding Comments
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11
General Concerns about Smallpox
• From Antiquity Until Its Worldwide Eradication, Smallpox Was Regarded as a Severe Contagious Disease with a Substantial Fatality Rate (Many Millions of Deaths in the 20th Century) • The FSU Reportedly Weaponized the Smallpox (Variola Major) Virus and Maintained a Large Stockpile • Today’s Young Adults Haven’t Been Vaccinated Against Smallpox, and Few of Today’s Physicians Have Ever Treated a Smallpox Case • The Live Vaccinia Virus Vaccine Can Provide Effective Protection If Administered Before or Soon After Exposure, But the Timely InTheater Utilization of Vaccine Stocks Could Be Problematic
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Clinical Features of “Ordinary” Smallpox
41
Average Asymptomatic Period of 12 Days
Sequelae: Blindness and Limb Deformities 1.0
Average Infectious Period of 12 Days (Rash Onset Until Scab Formation)
40
Pustules
Relative Extent of Skin Lesions
Temperature in Degrees Centigrade
Prodromal Period (Fever, Malaise, Enanthem) of 3 Days
Scab Formation
Vesicles
39
Scab Separation
38
Papules
Macules
37
0.0 10
20
30
Time After Infection in Days 3/20/01
13
Relevance of the Last European Smallpox Outbreaks • By 1953, Smallpox Was Not an Endemic Disease in European Countries Because of Comprehensive Vaccination Programs • European Smallpox Outbreaks Still Occurred in the 1950s, 1960s, and the Early 1970s, But These Outbreaks Were Often Linked to: (a) Travelers Who Were Infected Elsewhere (Pakistan, Indonesia, etc.), and (b) Fewer Vaccinations of European Adults • Epidemiological Circumstances that Surrounded the Last European Smallpox Outbreaks May Be Qualitatively Similar to Those Surrounding a Future BW or Bioterrorism Event – – – – 3/20/01
Disease Awareness & Medical Response Time Disease Transmission Factors Medical Treatment Capabilities & Patient Isolation Procedures Outbreak Controls (E.G., “Ring” or Other Vaccination Strategies) 14
Selected European Smallpox Outbreaks
Available Epidemiological Modes Of Outbreak Geographical Epidemiological Circumstances Disease Foci Area Of Data Transmission Containment Stockholm, Sweden 1963
Excellent
Meschede, Germany 1970
Good
Yugoslavia 1972
Good
Vaccination Program, No Early Diagnosis Of Index Case Vaccination Program, Index Case Diagnosis In Five Days Vaccination Program, No Early Diagnosis Of Index Case
Moderate (About 30 Square Kilometers)
Mixed
Four Hospitals
Airborne*
Single Hospital
Small
Several Medical Facilities
Very Large (About 50,000 Square Kilometers)
Mixed
* Infectious Aerosol & Disease Transmission At Distances Of 10 Meters Or More
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1963 Smallpox Outbreak in Stockholm & Input for Lower-Bound Analyses OBSERVED RASH ONSET DISTRIBUTION 3
•
2.5
Cases
Per
Day
•
2 1.5
New
1 0.5 0 0
10 20 30 40 50 60 70 80 90 100 First Case On 4Z7Z63 And Last Case On 7Z8Z 63
110
Note: The Above Rash Onset Data Does Not Account for 1 Case of Abortive Variola, 3 Cases of Variola Sine Eruptione, and 1 Case of Variola Asymptomatica.
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•
Last Swedish Case of Smallpox Was in 1932 Circumstances Surrounding 1963 Stockholm Outbreak – Susceptible Population – Delayed Diagnosis – Infections Among Health Care Workers (27% of All Secondary Infections) – Infections Among Hospital Patients (27% of All Secondary Infections) – Long Vaccination Program
Case-Fatality Rate for 1963 Stockholm Outbreak – –
Overall Rate of 15% 2 of the 3 Previously Unvaccinated Cases Resulted in Death 16
1972 Smallpox Outbreak in Yugoslavia & Input for Upper-Bound Analyses • • OBSERVED SYMPTOM ONSET DISTRIBUTION
New Cases
Per
Day
25 20 15 10 5
•
0 0
10 20 30 40 50 60 First Case On 2Z16Z 72 And Last Case On 4Z11Z72
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Last Yugoslavian Case of Smallpox Was in 1927 Circumstances Surrounding 1972 Yugoslavian Outbreak – Susceptible Population – Delayed diagnosis – Nosocomial Transmission (48% of All Infections) – Unsuccessful Revaccination (Liquid Vaccine Problems) – Communication Problems in Tracing Exposed People – Unusually High Proportion of Hemorrhagic Cases (10% Vice the Typical 1%) Case-Fatality Rate for 1972 Yugoslavian Outbreak – Overall Rate of 20% – Rate for the Unvaccinated Twice That for the Previously Vaccinated 17
Topics • Introduction • Epidemic Modeling Overview • EPIDEMIC MODELING EXAMPLE – Background Information On Smallpox – Smallpox Casualty Estimates For Scenario B
• Concluding Comments
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18
Smallpox & Scenario B
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•
No Pre-Attack Smallpox Vaccinations
•
No Trans-Attack Respiratory Protection
•
No Prompt Post-Attack Identification of Aerosolized Variola Virus
•
Upon Lab Confirmation of First Smallpox Diagnosis, One-Day Smallpox Vaccination Program Covers Entire Brigade, Division or Corps
•
Isolation/Quarantine Prevents Smallpox Transmission Beyond Vaccinated Military Population
19
Time Frame from Day of Infection to First Lab Confirmation of Smallpox Infection? END OF SMALLPOX PRODROME & ONSET OF RASH 0.999 0.994 0.977 0.933 0.841
Days After Infection
20 18 16
0.691 0.5
14 12 10
0.309 0.159 0.067 0.023 0.006 0.001 0
0.2
0.4 0.6 Probability
0.8
1
Note: The Above Graph Is Based upon a Combined Incubation Period and Prodrome that Is Characterized by a Normal PDF with a Mean of 15 Days and a Standard Deviation of 2 Days. For 1000 Initial Infections, this Graph Indicates there Would Be 1 Infected Person with a Rash After 9 Days, 6 People with Rashes After 10 Days, 23 People After 11 Days, Etc. 3/20/01
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Smallpox Casualty Contour Plots: An Illustration Of Usage BRIGADE CASUALTY CONTOURS H SWEDEN,1963L 1000
Number Of Initial H D+0L Infections
1000
800
3500
3750
750
• The X-Axis in Smallpox Casualty Contour Plots Defines the Day Number (D+T) when Disease Transmission Ends (E.G., Because of Vaccinations).
500
• The Y-Axis Defines the Number of D+0 Infections Due to a Smallpox Attack on an Initially Isolated Military Unit (E.G., Brigade).
600
400
1250 250 200
• Suppose Both the Number of D+0 Infections (E.G., 600) and the Duration of Smallpox Transmission (E.G., 16 Days) Are Known. Then the Casualty Contour Plot Provides A “Point” Casualty Estimate (E.G., 1250). • Casualty Contour Plots Can Also Be Used in Other Ways.
250
0 10 20 30 Duration Of Smallpox Transmission In Days
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40
21
Smallpox Casualty Calculations for the Brigade in Scenario B BRIGADE CASUALTY CONTOURS H SWEDEN,1963L
BRIGADE CASUALTY CONTOURS HYUGOSLAVIA ,1972L
1000
1000
800
3750
Number Of Initial HD+0L Infections
Number Of Initial H D+0L Infections
3750
600
400
200
800
600
400
200
250
0
250
0 10 20 30 Duration Of Smallpox Transmission In Days
40
10 20 30 Duration Of Smallpox Transmission In Days
40
Note: Since a Completely Successful Vaccination Program Occurs on D+τ, +τ, the Duration of Smallpox Transmission Cannot Exceed τ. For this Reason, Values Along the X Axis in the Above Graphs Are Values of τ. 3/20/01
22
Smallpox Casualty Calculations for the Corps in Scenario B CORPS CASUALTY CONTOURS HYUGOSLAVIA,1972L
CORPS CASUALTY CONTOURS HSWEDEN,1963L
1000
10250
Number Of Initial HD+0L Infections
Number Of Initial HD+0L Infections
1000
800
600
400
200
250
0 10 20 30 Duration Of Smallpox Transmission In Days
40
68000
800
600
400
200
0
1000
10 20 30 Duration Of Smallpox Transmission In Days
40
Note: Since a Completely Successful Vaccination Program Occurs on D+τ, +τ, the Duration of Smallpox Transmission Cannot Exceed τ. For this Reason, Values Along the X Axis in the Above Graphs Are Values of τ. 3/20/01
23
Topics • Introduction • Epidemic Modeling Overview • Epidemic Modeling Example – Background Information On Smallpox – Smallpox Casualty Estimates For Scenario B
• CONCLUDING COMMENTS
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Concluding Comments
•
Semi-Empirical Casualty Estimates for Scenarios A, B and C Elucidate Both Benefits of Major Defensive Capabilities and Consequences of Critical Defensive Deficiencies. These Estimates Should Also Help Health Care Planners Put Proposed or Existent BW/BT Medical Requirements in the Context of Historical Outbreaks.
•
To Be Sure, Scenarios A, B and C Are Not the Only Interesting or Analyzable Situations. For Instance, Quarantine Relaxation Effects (in the Midst of a Pneumonic Plague Outbreak) Are Presently under Investigation.
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Backups
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Smallpox Casualty Contour Plots: An Illustration Of Usage BRIGADE CASUALTY CONTOURS H SWEDEN,1963L 1000
Number Of Initial H D+0L Infections
1000
800
3500
3750
• The X-Axis in Smallpox Casualty Contour Plots Defines the Day Number (D+T) when Disease Transmission Ends (E.G., Because of Vaccinations). • The Y-Axis Defines the Number of D+0 Infections Due to a Smallpox Attack on an Initially Isolated Military Unit (E.G., Brigade).
750
600
• If the Number of D+0 Infections Is Known (E.G., 100), Then the Casualty Contour Plot Provides Casualty Estimates (E.G., 250, 500 and 750) for Various Periods of Disease Transmission (16, 29 and about 34 Days, Respectively).
500 400
250 200
250
0 10 20 30 Duration Of Smallpox Transmission In Days
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40
• On the Other Hand, If D+0 Infections Are Unknown and There Is a Planned Vaccination Day (E.G., D+20), Then the Casualty Contour Plot Provides Casualty Estimates (E.G., 1000 and 2000) for Various D+0 Infections (350 and about 800, Respectively).
27
