Modelling Pandemic Influenza in
the United States
Timothy C. Germann, Kai Kadau,
and Catherine A. Macken
Los Alamos National Laboratory
Ira M. Longini, Jr.
Fred Hutchinson Cancer Center and
University of Washington, Seattle
Outline
• EpiCast (“Epidemiological Forecasting”)
model design and parameterization
• Simulated pandemics in a fully susceptible
population
• Assessment of various mitigation strategies
What is EpiCast?
A stochastic agent-based simulation model
of the United States population of 281
million individuals (implemented on
modern parallel supercomputers), to predict
the nationwide spread of infectious diseases
and to assess various mitigation strategies.
T. C. Germann, K. Kadau, I. M. Longini, and C. A. Macken,
“Mitigation Strategies for Pandemic Influenza in the United States,”
submitted to Proceedings of the National Academy of Sciences.
Fidelity or Resolution
Oversimplified Perspective of Various
Epi-models
High
(individual,
minute-byminute)
Moderate
(individual,
with mixing
groups)
Low
(homogeneously
mixed population)
S'(t) = -rSI
I'(t) = rSI - I
R'(t) = I
EpiSims
Elveback,
Longini,
Epstein, …
Computational
Cost
EpiCast
Supercomputer
SIR equations (PDE’s)
Community
City
State
Workstation/PC
Nation
Spatial Scale
World
The four key elements of our model

Community-level transmission between people,
through various contact groups (household, work
group, school, …)

Disease natural history model and parameters

U.S. Census demographics (where people live)
and workerflow data (where they work), at tractlevel resolution

DOT statistics on long-distance travel
Person-to-person transmission is
described by contact groups within a
~2000-person model community*
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG
WG: Work group
*M. E. Halloran et al,
Science 298, 1428
(2002);
I. M. Longini et al,
Science 309, 1083
(2005).
Stochastic Transmission

Each susceptible individual (blue) has a
daily probability of becoming infected,
based on all of
their potential
contacts with
infectious
individuals
(red):
Stochastic Transmission

For the susceptible individual shown in blue, the
probability of becoming infected is:
a
a a
c a 2
P  1 (1 p cHH
)  (1 pWa a
)

(1
p
)

(1
p
G
Comm
Comm )
These may be further
 modified if the
infectious and/or
susceptible individuals
have been vaccinated,
are taking antivirals, …
The four key elements of our model

Community-level transmission between people, through
various contact groups (household, work group, school,
…)

Disease natural history model and parameters

U.S. Census demographics (where people live) and
workerflow data (where they work), at tract-level
resolution

DOT statistics on long-distance travel
Natural History for Pandemic Influenza
Persons who become ill
may self-isolate to
household-only contacts
Probability of
infecting others
Symptomatic (67%)
Asymptomatic (33%)
0
Exposure
and infection
days
Latency
1.2d
Incubation
1.9d
Possibly symptomatic
4.1d
Case Serial Interval

Time between illness onset times for a case and
the person infected
 Latent,
incubation and infectious period lengths
 Distribution of infectiousness
 Our model, mean = 3.5 days
 Ferguson, et al. mean = 2.6 days


Determines the speed of the epidemic, but not the
final size
Current Avian A(H5N1), seems to have longer
serial interval than current human strains
Basic Reproductive Number: R0
Number of secondary infections due to a
single typical infected person in a totally
susceptible population
R0 > 1 for sustained transmission
 For pandemic influenza: 1< R0 ≤ 2.4

1968-69, R0 ≈ 1.7
 A(H1N1) 1918, second wave, R0 ≈ 2
 A(H3N2)
Rapid Real Time Evaluation

Important to rapidly estimate key
parameters of pandemic strain
 Pathogenecity,
virulence, natural history
parameters
 Transmissibility parameters
 R0
 Serial
interval
 Secondary attack rates
 Others
The four key elements of our model

Community-level transmission between people, through
various contact groups (household, work group, school,
…)

Disease natural history model and parameters

U.S. Census demographics (where people live) and
workerflow data (where they work), at tract-level
resolution

DOT statistics on long-distance travel
Census tract-level resolution
The US census tract level provides a finer-scale resolution than counties, with
more uniform population sizes that correspond to the 2,000-person community
granularity (so that on average, each tract is modeled by two communities):
Average tract population: 4,300
65,433 U.S. census tracts
Constructing the model U.S.
population
We use U.S. Census Bureau data on
tract-level demographics and workerflow, and Dept. of Transportation data on
irregular long-range travel to assign fixed
residential and workplace communities
to each individual, in addition to
infrequent visits to more distant
communities.
1,344 Cook County (IL) census tracts
Census worker flow data
Raw data represents a snapshot at
the particular week the survey was
carried out; restrict daily commuter
traffic to a “reasonable” distance
(e.g., 100 miles):
Home County
Work County
Los Alamos, NM
Santa Fe, NM
Rio Arriba, NM
Sandoval, NM
Bernalillo, NM
Taos, NM
…
Essex, MA
…
Los Alamos, NM
Los Alamos, NM
…
Los Alamos, NM
Los Alamos, NM
Los Alamos, NM
Los Alamos, NM
Los Alamos, NM
Los Alamos, NM
…
Los Alamos, NM
…
Santa Fe, NM
District of Columbia
…
# Workers
9,133
4,029
3,206
606
474
242
…
9
…
180
5
…
People go to work according to the distance to work survey data
The four key elements of our model

Community-level transmission between people, through
various contact groups (household, work group, school,
…)

Disease natural history model and parameters

U.S. Census demographics (where people live) and
workerflow data (where they work), at tract-level
resolution

DOT statistics on long-distance travel
Long Distance Travel Model*
1.
Trip Generation: Which individuals/households make a
long distance trip?
Use age-dependent average number of trips per year to determine the daily probability of
making a long-distance trip, then roll the dice for each person every day.
2.
Destination Choice: Where do they go?
Simplistic gravity model: choose a random community within the simulation (either a
2,000-person residential or a 1,000-person workgroup-only community), without
any distance dependence.
3.
Trip Duration: How long do they stay there?
Use the national statistics on trip duration to choose a duration from 0-13 nights.
*An advanced model, including household income in step 1, distance
and median destination income in step 2, and trip purpose and distance
in step 3, has been developed and is currently being implemented.
Capturing long-range (irregular)
travel behavior
Use Bureau of Transportation
Statistics data on travel frequency
and duration (in lieu of detailed
city-to-city transportation data):
Influenza in the US: Simulated
and Historical Pandemics
Baseline (R0 = 1.9)
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Each Census tract is represented by a dot colored according to its
prevalence (number of symptomatic cases at any point in time) on
a logarithmic color scale, from 0.3-30 cases per 1,000 residents.
Baseline
simulated
pandemics
Most of the
epidemic activity
is in a 2-3 month
period, starting
1-2 months after
introduction
Asian Influenza A(H2N2) 1957-1958*
July 1957, sporadic cases, West Coast and
Louisiana
 Aug. 1957, local small epidemics begin
 Sept. 1957 – Oct. 1957, peaks occur

 Most
*Source:
epidemic activity over this 60 day period
Kilbourne (1975)
Hong Kong Influenza A(H3N2)
1968-1969*
July 1968, sporadic cases, West Coast
 Oct. 1968, local epidemics begin
 Dec. 1968 – Jan. 1969, peaks occur

 Most

epidemic activity over this 60 day period
March. 1968, end of epidemic activity
*Source:
WHO (1968-1970), Rvachev and Longini (1985)
Introduction of 40
infecteds on day 0,
either in NY or LA,
with and without
nationwide travel
restrictions
Day 60
Day 80
Day 100
Day 120
Assessment of Mitigation
Strategies
Assessment of Mitigation Strategies
(single or in combination)
In the following, we assume (and simulation results confirm)
that disease spread is so rapid that all interventions are
done on a nationwide basis simultaneously; however, a
state-by-state (or more local, down to tract-by-tract) staged
response can also be studied with our model.
•
Vaccination (with a fixed rate of production and distribution)
•
Targeted antiviral prophylaxis (from a limited national stockpile)
•
School closure
•
Social distancing, either a voluntary response to an ongoing
pandemic, or as the result of an imposed quarantine or travel
restrictions
Dynamic Vaccination Options
•Production capacity 4/10/20M doses per week
•Dose (and efficacy) of vaccine - 1 vs. 2 doses
•Timing of vaccination - relative to start of pandemic
Simulated protection by vaccination
-60d
Zoonoses
Pandemic spread
30d
60d
Pandemic in U.S.
Time
Low efficacy
Low efficacy - one dose
High efficacy - two doses
Dynamic Vaccination
Distribute the available supply of vaccine (with a specified starting date,
rate, and limit for production and distribution) to the eligible population
(neither sick nor previously vaccinated) using two strategies:
•
Random distribution to the entire (eligible) population
•
Distribute preferentially to children first, then any remaining supply
to the adult population
Also consider two different scenarios:
• The early production of a low-efficacy, single-dose vaccine, with:
 Vaccine efficacy for susceptibility VEs = 0.30
 Vaccine efficacy for infectiousness VEi = 0.50
• The delayed production of a higher-effficacy, 2-dose vaccine, with:
 Vaccine efficacy for susceptibility VEs = 0.70
(VEs = 0.50 for elderly)
 Vaccine efficacy for infectiousness VEi = 0.80
Baseline
Vaccination
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Random vaccination, R0 = 1.6
TAP: Targeted antiviral prophylaxis
using neuraminidase inhibitors (oseltamivir/relenza)
60% school
60% ascertainment
CONTACTS
Household
Household cluster
Preschool/daycare
School
Workplace
100% household + HH cluster
100% preschool
60% workplace
Targeted Antiviral Prophylaxis (TAP)
•
•
Close contacts of symptomatic individuals are treated
prophylactically, until the national stockpile is exhausted
Assume X% of symptomatic cases can be identified, then:
100% of household, household cluster, and preschool / playgroup
contacts are treated
 Y% of workgroup and school contacts are treated
 We will focus on two cases: X = Y = 60% or 80%

•
•
•
•
•
•
Each course consists of 10 tablets, 2/day for treatment of
symptomatic cases and 1/day for prophylaxis
Antiviral treatment reduces the sick period by 1 day
5% of patients stop taking antiviral after 1 day
Antiviral efficacy for susceptibility AVEs = 0.30
Antiviral efficacy for infectiousness AVEi = 0.62
Antiviral efficacy for illness given infection
AVEd = 0.60
Baseline
TAP (20M courses)
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Rapid intervention can preserve the limited
antiviral stockpile and reduce the attack rate:
60% TAP
R0 = 1.9
Pandemic virus arrives in U.S.
Pandemic alert
U.S. Strategic
National Stockpile of
Tamiflu®
Now: 2.3M courses
Planned: 20M courses
School closure
We assume that once schools are closed, they remain closed
for the duration of the epidemic. School closure includes:
•
High schools
•
Middle schools
•
Elementary schools
•
Preschools
•
Regular preschool-age playgroups
Social distancing / quarantine
As a result of either a formal quarantine program, or
voluntary changes in social and hygienic behavior in the
event of a widespread pandemic, we assume that:
•
School, preschool, and playgroup contact rates are cut
in half.
•
Workgroup contact rates are cut in half.
•
Household contact rates double.
•
Household cluster contact rates remain unchanged.
Once initiated, this alteration in normal behavior is assumed
to last throughout the remainder of the epidemic.
Travel restrictions
The random long-range travel frequency can be reduced at
any time, either due to imposed travel restrictions or
behavioral changes (as occurred during the SARS scare).
While by itself this can only slow the spread, it can
potentially be useful to buy time for other interventions.
Baseline
90% travel cut
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
TAP, vaccination, or school closure can contain an
outbreak for R0 ≤ 1.6 (cumulative ill per 100)
Intervention
R0 = 1.6
R0 = 1.9
R0 = 2.1
R0 = 2.4
32.6
43.5
48.5
53.7
0.06
(2.8 M)
4.3
(182 M)
12.2
(418 M)
19.3
(530 M)
Dynamic vaccination2 (1-dose regimen)
0.7
17.7
30.1
41.1
Dynamic child-first vaccination2
0.04
2.8
16.3
35.3
Dynamic vaccination3 (2-dose regimen)
12.3
32.3
40.1
48.0
Dynamic child-first vaccination3
1.9
24.7
36.1
46.4
School closure4
1.0
29.3
37.9
46.4
Local social distancing4
25.1
39.2
44.6
50.3
Travel restrictions5 during entire time
32.8
44.0
48.9
54.1
Baseline (no intervention)
Targeted Antiviral Prophylaxis1
(# of courses)
160%
TAP, 7 days after pandemic alert, unlimited antiviral supply.
million doses of a low-efficacy vaccine (single-dose regimen) per week for 25 weeks, beginning such that the first
persons treated develop an immune response on the date of the first U.S. introduction.
310 million doses of a high-efficacy vaccine (2-dose regimen) per week for 25 weeks, beginning such that the first
persons treated develop a full immune response 30 days after the first U.S. introduction.
4Intervention starting 7 days after pandemic alert.
5Reduction in long-distance travel, to 10% of normal frequency.
210
An aggressive combination of therapeutic and social
measures can succeed for R0 ≤ 2.4
Intervention
R0 = 1.6
R0 = 1.9
R0 = 2.1
R0 = 2.4
Social distancing & travel restictions4,5
19.6
39.3
44.7
50.5
60% TAP4, school closure5, and social
distancing5
0.02
(0.6 M)
0.07
(1.6 M)
0.14
(3.3 M)
2.8*
(20 M)
Dynamic vaccination2, social
distancing4, travel restrictions4,5, and
school closure6
0.04
0.2
0.6
4.5
60% TAP4, dynamic vaccination2, social
distancing4, travel restrictions4,5, and
school closure6
0.02
(0.3 M)
0.3
(0.7 M)
0.06
(1.4 M)
0.1
(3.0 M)
Dynamic child-first vaccination2, social
distancing4, travel restrictions4,5, and
school closure6
0.02
0.2
0.9
7.7
210
million doses of a low-efficacy vaccine (single-dose regimen) per week for 25 weeks, beginning such that the
first persons treated develop an immune response on the date of the first U.S. introduction.
4Intervention starting 7 days after pandemic alert.
5Reduction in long-distance travel, to 10% of normal frequency.
6Intervention starting 14 days after pandemic alert.
*Exhausted the available supply of 20M antiviral courses.
Epi curves (note log scale)
Recommendations




For R0 ≥ 1.9, we would need at least 182 million
courses of oseltamivir to have an impact on spread
For R0 ≤ 1.6, spread can be controlled by dynamic
vaccination with low efficacy vaccine (10 million
doses per week), school closure
For 1.9 ≤ R0 ≤ 2.4, only combinations of TAP,
vaccination, social distancing measures and travel
restrictions are effective
Social distancing and travel restrictions are not
effective when used alone
Recommendations (cont.)

For limited quantities of vaccine
 Rapid
vaccination of one-dose low efficacy is more
effective than two-dose high efficacy
 Vaccination of school children first is much better than
random vaccination



Vaccination alone requires high vaccination rates
and production total
Rapid use of TAP preserves limited antiviral
stockpiles
We can effectively divert antivirals and vaccines
to the critical workforce within limits
The End
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