Modelling Pandemic Influenza in the United States Timothy C. Germann, Kai Kadau, and Catherine A. Macken Los Alamos National Laboratory 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 High (individual, minute-by- minute) Low (homogeneously mixed population) Moderate (individual, with mixing groups) Community City State Nation World Spatial Scale EpiSims Elveback, Longini, Epstein, … EpiCast SIR equations (PDE’s) Oversimplified Perspective of Various Epi-models S'(t) = -rSI I'(t) = rSI -  I R'(t) =  I Computational Cost Supercomputer Workstation/PC

The four key elements of our model n Community-level transmission between people, through various contact groups (household, work group, school, …) n Disease natural history model and parameters n U.S. Census demographics (where people live) and workerflow data (where they work), at tract- level resolution n DOT statistics on long-distance travel

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). I. M. Longini et al, Science 309, 1083 (2005). WG WG: Work group

Stochastic Transmission n Each susceptible individual (blue) has a daily probability of becoming infected, based on all of their potential contacts with infectious individuals (red):

Stochastic Transmission n 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, …

The four key elements of our model n Community-level transmission between people, through various contact groups (household, work group, school, …) n Disease natural history model and parameters n U.S. Census demographics (where people live) and workerflow data (where they work), at tract-level resolution n DOT statistics on long-distance travel

Latency Incubation Asymptomatic (33%) 0 Probability of infecting others days Exposure and infection 1.2d 1.9d 4.1d Natural History for Pandemic Influenza Possibly symptomatic Symptomatic (67%) Persons who become ill may self-isolate to household-only contacts

Case Serial Interval n Time between illness onset times for a case and the person infected u Latent, incubation and infectious period lengths u Distribution of infectiousness u Our model, mean = 3.5 days u Ferguson, et al. mean = 2.6 days n Determines the speed of the epidemic, but not the final size n Current Avian A(H5N1), seems to have longer serial interval than current human strains

Basic Reproductive Number: R 0 n Number of secondary infections due to a single typical infected person in a totally susceptible population R 0 > 1 for sustained transmission n For pandemic influenza: 1< R 0 ≤ 2.4 u A(H3N2) , R 0 ≈ 1.7 u A(H1N1) 1918, second wave, R 0 ≈ 2

Rapid Real Time Evaluation n Important to rapidly estimate key parameters of pandemic strain u Pathogenecity, virulence, natural history parameters u Transmissibility parameters F R 0 F Serial interval F Secondary attack rates F Others

The four key elements of our model n Community-level transmission between people, through various contact groups (household, work group, school, …) n Disease natural history model and parameters n U.S. Census demographics (where people live) and workerflow data (where they work), at tract-level resolution n 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): 65,433 U.S. census tracts Average tract population: 4,300

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

Census worker flow data Home County Work County # Workers 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 ……… Santa Fe, NM 180 Los Alamos, NM District of Columbia 5 ……… 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):

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

The four key elements of our model n Community-level transmission between people, through various contact groups (household, work group, school, …) n Disease natural history model and parameters n U.S. Census demographics (where people live) and workerflow data (where they work), at tract-level resolution n 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 (R 0 = 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 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) * n July 1957, sporadic cases, West Coast and Louisiana n Aug. 1957, local small epidemics begin n Sept – Oct. 1957, peaks occur u Most epidemic activity over this 60 day period * Source: Kilbourne (1975)

Hong Kong Influenza A(H3N2) * n July 1968, sporadic cases, West Coast n Oct. 1968, local epidemics begin n Dec – Jan. 1969, peaks occur u Most epidemic activity over this 60 day period n March. 1968, end of epidemic activity * Source: WHO ( ), Rvachev and Longini (1985)

Day 60 Day 80 Day 100 Day 120 Introduction of 40 infecteds on day 0, either in NY or LA, with and without nationwide travel restrictions

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) Vaccination (with a fixed rate of production and distribution) Targeted antiviral prophylaxis (from a limited national stockpile) Targeted antiviral prophylaxis (from a limited national stockpile) School closure School closure Social distancing, either a voluntary response to an ongoing pandemic, or as the result of an imposed quarantine or travel restrictions Social distancing, either a voluntary response to an ongoing pandemic, or as the result of an imposed quarantine or travel restrictions

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 Zoonoses Pandemic spread Pandemic in U.S. Time Low efficacy Low efficacy - one dose High efficacy - two doses Simulated protection by vaccination 30d 60d -60d Dynamic Vaccination Options

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 Random distribution to the entire (eligible) population Distribute preferentially to children first, then any remaining supply to the adult 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: 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: 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

VaccinationBaseline

Random vaccination, R 0 = 1.6

CONTACTS Household Household cluster Preschool/daycare School Workplace TAP: Targeted antiviral prophylaxis using neuraminidase inhibitors (oseltamivir/relenza) 60% ascertainment 100% household + HH cluster 100% preschool 60% school 60% workplace

Targeted Antiviral Prophylaxis (TAP) Close contacts of symptomatic individuals are treated prophylactically, until the national stockpile is exhausted Close contacts of symptomatic individuals are treated prophylactically, until the national stockpile is exhausted Assume X% of symptomatic cases can be identified, then: 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 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 Antiviral treatment reduces the sick period by 1 day 5% of patients stop taking antiviral after 1 day 5% of patients stop taking antiviral after 1 day Antiviral efficacy for susceptibility AVEs = 0.30 Antiviral efficacy for susceptibility AVEs = 0.30 Antiviral efficacy for infectiousness AVEi = 0.62 Antiviral efficacy for infectiousness AVEi = 0.62 Antiviral efficacy for illness given infection Antiviral efficacy for illness given infection AVEd = 0.60

TAP (20M courses) Baseline

Rapid intervention can preserve the limited antiviral stockpile and reduce the attack rate: Pandemic virus arrives in U.S.Pandemic alert 60% TAP R 0 = 1.9 U.S. Strategic National Stockpile of Tamiflu ® Now: 2.3M courses Planned: 20M courses

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 R 0 and either a 1-day or 2-day diagnosis period: InterventionR 0 = 1.6R 0 = 1.9R 0 = 2.1R 0 = 2.4 Baseline (no intervention) 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)

School closure We assume that once schools are closed, they remain closed for the duration of the epidemic. School closure includes: High schools High schools Middle schools Middle schools Elementary schools Elementary schools Preschools Preschools Regular preschool-age playgroups 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. School, preschool, and playgroup contact rates are cut in half. Workgroup contact rates are cut in half. Workgroup contact rates are cut in half. Household contact rates double. Household contact rates double. Household cluster contact rates remain unchanged. 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.

90% travel cutBaseline

TAP, vaccination, or school closure can contain an outbreak for R 0 ≤ 1.6 (cumulative ill per 100) InterventionR 0 = 1.6R 0 = 1.9R 0 = 2.1R 0 = 2.4 Baseline (no intervention) Targeted Antiviral Prophylaxis 1 (# of courses) 0.06 (2.8 M) 4.3 (182 M) 12.2 (418 M) 19.3 (530 M) Dynamic vaccination 2 (1-dose regimen) Dynamic child-first vaccination Dynamic vaccination 3 (2-dose regimen) Dynamic child-first vaccination School closure Local social distancing Travel restrictions 5 during entire time % 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 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. 4 Intervention starting 7 days after pandemic alert. 5 Reduction in long-distance travel, to 10% of normal frequency.

An aggressive combination of therapeutic and social measures can succeed for R 0 ≤ 2.4 InterventionR 0 = 1.6R 0 = 1.9R 0 = 2.1R 0 = 2.4 Social distancing & travel restictions 4, % TAP 4, school closure 5, and social distancing (0.6 M) 0.07 (1.6 M) 0.14 (3.3 M) 2.8* (20 M) Dynamic vaccination 2, social distancing 4, travel restrictions 4,5, and school closure % TAP 4, dynamic vaccination 2, social distancing 4, travel restrictions 4,5, and school closure (0.3 M) 0.3 (0.7 M) 0.06 (1.4 M) 0.1 (3.0 M) Dynamic child-first vaccination 2, social distancing 4, travel restrictions 4,5, and school closure 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. 4 Intervention starting 7 days after pandemic alert. 5 Reduction in long-distance travel, to 10% of normal frequency. 6 Intervention starting 14 days after pandemic alert. *Exhausted the available supply of 20M antiviral courses.

Epi curves (note log scale)

Recommendations n For R 0 ≥ 1.9, we would need at least 182 million courses of oseltamivir to have an impact on spread n For R 0 ≤ 1.6, spread can be controlled by dynamic vaccination with low efficacy vaccine (10 million doses per week), school closure n For 1.9 ≤ R 0 ≤ 2.4, only combinations of TAP, vaccination, social distancing measures and travel restrictions are effective n Social distancing and travel restrictions are not effective when used alone

Recommendations (cont.) n For limited quantities of vaccine u Rapid vaccination of one-dose low efficacy is more effective than two-dose high efficacy u Vaccination of school children first is much better than random vaccination n Vaccination alone requires high vaccination rates and production total n Rapid use of TAP preserves limited antiviral stockpiles n We can effectively divert antivirals and vaccines to the critical workforce within limits

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