Efficient Simulation of the Spatial Transmission Dynamics of Influenza

et al. (2010) Efficient Simulation of the Spatial Transmission Dynamics of Influenza. PLoS ONE 5(11): e13292. doi:10.1371/journal.pone.0013292 Efficient Simulation of the Spatial Transmission Dynamics of Influenza Meng-Tsung Tsai 0 Tsurng-Chen Chern 0 Jen-Hsiang Chuang 0 Chih-Wen Hsueh 0 Hsu-Sung Kuo 0 Churn- Jung Liau 0 Steven Riley 0 Bing-Jie Shen 0 Chih-Hao Shen 0 Da-Wei Wang 0 Tsan-Sheng Hsu 0 Vladimir Brusic, Dana-Farber Cancer Institute, United States of America 0 1 Institute of Information Science , Academia Sinica, Taipei, Taiwan , 2 Epidemic Intelligence Center, Centers for Disease Control , Taipei, Taiwan , 3 Department of Computer Science and Information Engineering, National Taiwan University , Taipei, Taiwan , 4 Centers for Disease Control , Taipei, Taiwan , 5 Department of Infectious Disease Epidemiology, University of Hong Kong, Hong Kong, 6 Department of Radiation Oncology, Far Eastern Memorial Hospital , Taipei, Taiwan , 7 Department of Computer Science, University of Virginia , Charlottesville, Virginia , United States of America Early data from the 2009 H1N1 pandemic (H1N1pdm) suggest that previous studies over-estimated the within-country rate of spatial spread of pandemic influenza. As large spatially resolved data sets are constructed, the need for efficient simulation code with which to investigate the spatial patterns of the pandemic becomes clear. Here, we present a significant improvement to the efficiency of an individual-based stochastic disease simulation framework commonly used in multiple previous studies. We quantify the efficiency of the revised algorithm and present an alternative parameterization of the model in terms of the basic reproductive number. We apply the model to the population of Taiwan and demonstrate how the location of the initial seed can influence spatial incidence profiles and the overall spread of the epidemic. Differences in incidence are driven by the relative connectivity of alternate seed locations. The ability to perform efficient simulation allows us to run a batch of simulations and take account of their average in real time. The averaged data are stable and can be used to differentiate spreading patterns that are not readily seen by only conducting a few runs. - Funding: This work was supported in part by the following grants: Jen-Hsiang Chuang is supported in part by DOH98-DC-2036 from the Centers for Disease Control, Department of Health, Taiwan, R.O.C.; Tsan-sheng Hsu and Bing-Jie Shen are supported in part by 97-2221-E-001-011-MY3 from National Science Council, Taiwan, R.O.C.; Churn-Jung Liau is supported in part by 98-2221-E-001-013-MY3 from National Science Council, Taiwan, R.O.C.; Steven Riley is supported in part by R01 TW008246-01 from Fogarty International Centre, RAPIDD program from Fogarty International Centre with the Science and Technology Directorate Department of Homeland Security, and Research Fund for the Control of Infectious Disease of the Government of the Hong Kong SAR. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. The current global spread of a novel influenza strain [1] highlights gaps in our understanding of the spatial component of disease transmission at national and regional scales. For example, the early summer 2009 wave in the United States affected some populations much more so than others (Centers for Disease Control, USA), even at similar latitudes. In addition, there was substantial transmission in parts of southern England throughout the summer of 2009, but very little in most of northern mainland Europe (European Centre for Disease Prevention and Control). This slow progression between national and regional level synchrony is not obviously consistent with previous theoretical studies of the withincountry dynamics of pandemic influenza [24], in which censusreported commuting patterns and airline flight data were used to characterize very rapid spatial spread. Explaining these early patterns of spatial spread for the 2009 pandemic will likely be an active area of epidemiological research in the coming years. Stochastic spatial transmission models, in which individuals or small communities are represented explicitly in space, are an extension of more traditional approaches and have been a valuable tool in the study of infectious diseases in humans and animals [5]. Traditionally, mathematical models of epidemics often take the form of deterministic differential equations in which the variables represent the expected number of individuals in broad disease classes (e.g., susceptible, infected, or recovered) [6]. Although such models can be extended to model the geographic spread of infectious diseases on patches [7], when it is not clear which spatial scales are most important, it is difficult to use compartmental approaches with confidence. Here, we describe an algorithmic refinement of a spatial stochastic model of individuals and their communities. This framework was originally designed to investigate community interventions against influenza in a generic sense [8]. It was later extended to examine the optimal response to a bio-terrorist smallpox attack [9] and to examine the potential for the containment of influenza pandemic in large wellmixed populations [10]. A spatial component was added to the model to study the feasibility of containing an emergent influenza pandemic in a rural setting in Southeast Asia [11]. In its last major development, the underlying algorithm was parallelized to allow it to run with a population of 300 million, and used to predict the likely impact of mitigation measures on an influenza pandemic in the United States [2]. More recently, the same framework has been used to describe the likely fall wave transmission dynamics for H1N1pdm in Los Angeles County [12], and to study the effects of school closure strategies in Allegheny County, Pennsylvania [13]. We have implemented a more efficient algorithm for this popular disease transmission model. We demonstrate increased computational efficiency compared with previous implementations and we describe a parameterization scheme for the model using the basic reproductive number, rather than the per contact transmission potential. We illustrate the utility of the refined model with simulation studies of seeding dynamics for a pandemic of influenza in Taiwan. Materials and Methods Our model incorporates epidemiological attributes of viral infection with computer generated mock population to simulate the spatio-temporal spreading of pandemic influenza viruses. The mock population is constructed according to national demographics and daily commuter (worker flow) statistics from Taiwan Census 2000 Data (http://www.stat.gov.tw/) in order to retain some population characteristics. The model is, effectively, a highly connected network mode (...truncated)