Modelling Pandemic Influenza in the United States

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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

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Outline

• EpiCast (Epidemiological Forecasting) model
  design and parameterization
• Simulated pandemics in a fully susceptible
  population
• Assessment of various mitigation strategies

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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.
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Oversimplified Perspective of Various Epi-models
High (individual, minute-by-minute)
EpiSims
Moderate (individual, with mixing groups)
Fidelity or Resolution
Elveback, Longini, Epstein,
EpiCast
Low (homogeneously mixed population)
SIR equations (PDEs)
S'(t) -rSI I'(t) rSI - ?I R'(t) ?I
Community City State Nation
World
Spatial Scale
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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

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Person-to-person transmission is described by
contact groups within a 2000-person model
community

• M. E. Halloran et al, Science 298, 1428 (2002)
• I. M. Longini et al, Science 309, 1083 (2005).

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Stochastic Transmission

• Each susceptible individual (blue) has a daily
  probability of becoming infected,

based on all of their potential contacts with
infectious individuals (red)
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Stochastic Transmission

• For the susceptible individual shown in blue, the
  probability of becoming infected is

These may be further modified if the infectious
and/or susceptible individuals have been
vaccinated, are taking antivirals,
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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

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Natural History for Pandemic Influenza
Probability of infecting others
Symptomatic (67)
Asymptomatic (33)
0
days
Latency
Exposure and infection
1.2d
Incubation
Possibly symptomatic
1.9d
4.1d
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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

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Basic Reproductive Number R0

• Number of secondary infections due to a single
  typical infected person in a totally susceptible
  population
• R0 gt 1 for sustained transmission
• For pandemic influenza 1lt R0 2.4
• A(H3N2) 1968-69, R0 1.7
• A(H1N1) 1918, second wave, R0 2

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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

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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

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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
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Constructing the model U.S. population
We use U.S. Census Bureau data on tract-level
demographics and worker-flow, 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
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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 Workers
Los Alamos, NM Los Alamos, NM 9,133
Santa Fe, NM Los Alamos, NM 4,029
Rio Arriba, NM Los Alamos, NM 3,206
Sandoval, NM Los Alamos, NM 606
Bernalillo, NM Los Alamos, NM 474
Taos, NM Los Alamos, NM 242

Essex, MA Los Alamos, NM 9

Los Alamos, NM Santa Fe, NM 180
Los Alamos, NM District of Columbia 5

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People go to work according to the distance to
work survey data
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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

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Long Distance Travel Model

• 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.
• 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.
• 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.
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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)
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Influenza in the US Simulated and Historical
Pandemics
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Baseline (R0 1.9)
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.
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Baselinesimulatedpandemics
Most of the epidemic activity is in a 2-3 month
period, starting 1-2 months after introduction
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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 epidemic activity over this 60 day period

Source Kilbourne (1975)
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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)
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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
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Assessment of Mitigation Strategies
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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

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Dynamic Vaccination Options
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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

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Vaccination Baseline
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Random vaccination, R0 1.6
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TAP Targeted antiviral prophylaxis using
neuraminidase inhibitors (oseltamivir/relenza)
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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

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TAP (20M courses) Baseline
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Rapid intervention can preserve the limited
antiviral stockpile and reduce the attack rate
60 TAP R0 1.9
U.S. Strategic National Stockpile of Tamiflu
Now 2.3M courses Planned 20M courses
Pandemic virus arrives in U.S.
Pandemic alert
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Rapid diagnosis can preserve the limited
antiviral stockpile

• Simulated mean number of cases (cumulative
  incidence per 1000), and antiviral courses
  required, for 80 TAP with an unlimited supply
  initiated 10 days after detection, for different
  values of R0 and either a 1-day or 2-day
  diagnosis period

Intervention R0 1.6 R0 1.9 R0 2.1 R0 2.4
Baseline (no intervention) 326 435 485 537
TAP with 1-day delay (number of courses used) 0.4 (2.0 M) 6 (39 M) 51 (300 M) 135 (600 M)
TAP with 2-day delay (number of courses used) 0.7 (4.0 M) 37 (212 M) 106 (496 M) 174 (641 M)
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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

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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.

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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.

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90 travel cut Baseline
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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
Baseline (no intervention) 32.6 43.5 48.5 53.7
Targeted Antiviral Prophylaxis1 ( of courses) 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
160 TAP, 7 days after pandemic alert, unlimited
antiviral supply. 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. 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.
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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.
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Epi curves (note log scale)
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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

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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

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The End
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