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UW STAT 517 - Mitigation Strategies for Pandemic Influenza

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Germann, Kadau, Longini, and Macken Supporting Info: Page 1 of 37 2/26/06 Mitigation Strategies for Pandemic Influenza in the United States: Supporting Information Timothy C. Germann,1 Kai Kadau,1 Ira M. Longini Jr.,2 and Catherine A. Macken1 1Los Alamos National Laboratory, Los Alamos, NM 87545 2Program of Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center and Department of Biostatistics, School of Public Health and Community Medicine, University of Washington, Seattle, WA 98109 A. Simulation Model Details The three basic elements of our national-level simulation model are (1) a previously developed stochastic agent-based model for disease spread at the community level; (2) detailed U.S. Census demographics and worker flow data for daily commuter traffic at short distances, and Bureau of Transportation Statistics data for the less frequent long-range travel behavior; and (3) high-performance parallel computing expertise in modeling millions to billions of particles on hundreds to thousands of processors. These three components, each of which we describe next in some detail, are brought together to provide a unique capability for a detailed modeling of disease spread in the United States population. (1) Community-Level Stochastic Simulation Model Population Structure As the starting point for constructing our national simulation model, we employ a discrete-time, stochastic simulation model of disease spread within a structured 2,000-Germann, Kadau, Longini, and Macken Supporting Info: Page 2 of 37 2/26/06 person community. Similar models have been developed and applied previously to both influenza (1-4) and smallpox (5). The model population is stochastically generated to match census-based nationwide distributions of age, household size, and employment status. Each person in the population belongs to one of five age groups: preschool-age children (0-4 years), school-age children (5-18 years), young adults (19-29 years), adults (30-64 years), and older adults (64+ years). Households consist of one to seven persons, with either one or two adults, and are grouped randomly into clusters of four households each, and further grouped into one of four non-overlapping neighborhoods, each containing approximately 500 people. Every person also belongs to a set of close and casual contact (also referred to as “mixing”) groups, ranging from their household and household cluster (highest contact rates), to schools and workplaces, down to their neighborhood and the entire community (with the lowest contact rates, representing occasional interactions in malls, supermarkets, and churches, for instance). All preschool-age children are assigned to either a neighborhood daycare center, with 14 children on average, or to one of several smaller neighborhood playgroups, each with 4 children. Depending on their age, school-age children may belong to one of two elementary school groups (each shared between two neighborhoods, with 79 students each on average), to a community-wide middle school group (128 students on average), or to a community-wide high school group (average 155 students). These school contact groups are in general not actual schools, but rather representative of the typical daily interactions a student may have with classmates and other peers. According to US census data, 93% of children 5 – 18 years old attend school, so we allow the remaining 7% to mix in the household, household cluster, neighborhood and community during the daytime. Working adults (restricted to those who are 19 – 64 years old) belong to a work group of approximately 20 people. Although in reality many workplaces are larger than 20 people, we assume that workers make a contact of sufficient duration and/or closeness to transmit influenza virus with a subset of the entire workforce at that location. Disease transmission model Transmission within each contact group is described by a contact probability ci (Table 3), which may depend on the age of both the infectious and susceptible persons. This contact probability represents the likelihood (within each 12-hour period) of having a contact of sufficient duration and closeness for transmission of an infectious dose ofGermann, Kadau, Longini, and Macken Supporting Info: Page 3 of 37 2/26/06 influenza virus to be possible between these two individuals in this social setting. The probability of transmission given such contact, Ptrans, is a single scalar number which multiplies each contact probability, allowing for a simple variation in contagiousness (typically represented by the basic reproductive number, R0) without modifying the underlying social interaction network parameters. We do not allow for any seasonal or weekly variation in contact rates or transmission probability, and no births or non-flu-related deaths are included in our model. Each day, the probability of infection for each susceptible individual is computed based on the transmission probabilities for each potential infectious contact, pi = Ptrans × ci. If the infectious contact is receiving antiviral treatment, this transmission probability is further multiplied by (1 – AVEi), where AVEi is the antiviral efficacy for infectiousness. Similarly, if they have been vaccinated, the vaccine efficacy for infectiousness VEi reduces the transmission probability by (1 – VEi). The transmission probability pi can be further reduced for asymptomatic (yet infectious) contacts, as described in the next section. The probability of a susceptible person becoming infected is then computed as a product of all of the possible infectious contacts each day. Figure 3 illustrates this calculation for a susceptible adult (shown in blue) with one infectious child in the household (HH), one infectious workgroup (WG) contact, and three other infectious people in the wider community (Comm). The probability that this susceptible adult becomes infected is ! P = 1" (1" pHHc #a) $ (1" pWGa #a) $ (1" pComma #a) $ (1" pCommc #a)2, where c and a denote child and adult, respectively.

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