Research Article Spatial Spread of Tuberculosis through Neighborhoods Segregated by Socioeconomic Position: A Stochastic Automata Model David Rehkopf, 1 Alice Furumoto-Dawson, 2 Anthony Kiszewski, 3 and Tamara Awerbuch-Friedlander 4 1 Department of Medicine, School of Medicine, Stanford University, Medical School Ofce Building, 251 Campus Drive, Room X3c46, MC5411, Stanford, CA 94305, USA 2 Program on the Global Environment, Te University of Chicago, 5828 S. University Avenue, Pick 101, Chicago, IL 60637, USA 3 Department of Natural and Applied Sciences, Bentley University, 175 Forest Street, Waltham, MA 02452, USA 4 Department of Global Health and Population, Harvard School of Public Health, 665 Huntington Avenue, Room 1219, Boston, MA 02115, USA Correspondence should be addressed to Tamara Awerbuch-Friedlander; tamara@hsph.harvard.edu Received 25 March 2015; Revised 20 June 2015; Accepted 25 June 2015 Academic Editor: Aleksei A. Koronovskii Copyright © 2015 David Rehkopf et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Transmission of the agent of tuberculosis, Mycobacterium tuberculosis, is dependent on social context. A discrete spatial model representing neighborhoods segregated by levels of crowding and immunocompetence is constructed and used to evaluate prevention strategies, based on a number of assumptions about the spatial dynamics of tuberculosis. A cellular automata model is used to (a) construct neighborhoods of diferent densities, (b) model stochastically local interactions among individuals, and (c) model the spread of tuberculosis within and across neighborhoods over time. Since infected people may become progressively sick but also heal through treatment, the transition among stages was modeled with transition probabilities. A moderate level of successful treatment (40%) dramatically reduced the number of infections across all neighborhoods. Increasing the treatment in neighborhoods of a lower socioeconomic level from 40% to 90% results in an additional decrease of approximately 25% in the number of infected individuals overall. In conclusion, we fnd that a combination of a moderate level of successful treatment across all areas with more focused treatment eforts in lower socioeconomic areas resulted in the least number of infections over time. 1. Introduction and Background Cellular automata (if a deterministic model) and stochastic automata (if implemented with varying probabilities of trans- mission) are methods that allow us to study the dynamics of the population at large, based on local interactions among neighbors, as shown in models of physical systems [1]. Cellular automata consist of a lattice of cells and proceed through discrete time steps where each cell is characterized by a state and where its future states are determined stochas- tically in relation to a fnite number of neighboring cells. Its applicability in biology was validated by implementing it in a study of a homogeneous population where individuals interact locally, resulting in the same dynamics as the one obtained with diference equations [2]. Tus it is possible with this method to follow the spread of disease in a population at large by looking at interactions among individuals [3–8]. Te method is being applied here, to study the spread of tuberculosis and identify sites for treatment. Tuberculosis is both an ancient, familiar infectious dis- ease (the White Plague, “consumption”) and a dangerous, resurgent threat to the lives and health of millions worldwide [9, 10]. Rising rates of comorbidities that undermine the immunocompetence of populations; the migration of popu- lations dislocated by confict, market failures, and economic transitions [11–13]; incarceration, homelessness, and crowd- ing in inadequate housing for disadvantaged groups living in high income inequity countries [14]; defunding of barely adequate screening and treatment programs; the emergence of drug-resistant strains out of inadequately treated prison, Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2015, Article ID 583819, 8 pages http://dx.doi.org/10.1155/2015/583819