A Network Control Theory Approach to Modeling and Optimal Control of Zoonoses: Case Study of Brucellosis Transmission in Sub-Saharan Africa Sandip Roy 1,2 *, Terry F. McElwain 2 , Yan Wan 3 1 School of Electrical Engineering and Computer Science, Washington State University, Pullman, Washington, United States of America, 2 School for Global Animal Health, Washington State University, Pullman, Washington, United States of America, 3 Department of Electrical Engineering, University of North Texas, Denton, Texas, United States of America Abstract Background: Developing control policies for zoonotic diseases is challenging, both because of the complex spread dynamics exhibited by these diseases, and because of the need for implementing complex multi-species surveillance and control efforts using limited resources. Mathematical models, and in particular network models, of disease spread are promising as tools for control-policy design, because they can provide comprehensive quantitative representations of disease transmission. Methodology/Principal Findings: A layered dynamical network model for the transmission and control of zoonotic diseases is introduced as a tool for analyzing disease spread and designing cost-effective surveillance and control. The model development is achieved using brucellosis transmission among wildlife, cattle herds, and human sub-populations in an agricultural system as a case study. Precisely, a model that tracks infection counts in interacting animal herds of multiple species (e.g., cattle herds and groups of wildlife for brucellosis) and in human subpopulations is introduced. The model is then abstracted to a form that permits comprehensive targeted design of multiple control capabilities as well as model identification from data. Next, techniques are developed for such quantitative design of control policies (that are directed to both the animal and human populations), and for model identification from snapshot and time-course data, by drawing on recent results in the network control community. Conclusions/Significance: The modeling approach is shown to provide quantitative insight into comprehensive control policies for zoonotic diseases, and in turn to permit policy design for mitigation of these diseases. For the brucellosis- transmission example in particular, numerous insights are obtained regarding the optimal distribution of resources among available control capabilities (e.g., vaccination, surveillance and culling, pasteurization of milk) and points in the spread network (e.g., transhumance vs. sedentary herds). In addition, a preliminary identification of the network model for brucellosis is achieved using historical data, and the robustness of the obtained model is demonstrated. As a whole, our results indicate that network modeling can aid in designing control policies for zoonotic diseases. Citation: Roy S, McElwain TF, Wan Y (2011) A Network Control Theory Approach to Modeling and Optimal Control of Zoonoses: Case Study of Brucellosis Transmission in Sub-Saharan Africa. PLoS Negl Trop Dis 5(10): e1259. doi:10.1371/journal.pntd.0001259 Editor: Ricardo E. Gu ¨ rtler, Universidad de Buenos Aires, Argentina Received June 22, 2010; Accepted June 14, 2011; Published October 11, 2011 Copyright: ß 2011 Roy et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work has been generously supported by the National Science Foundation under grant ECS-0901137 (www.nsf.gov), the School of Global Animal Health at Washington State University (globalhealth.wsu.edu), and the School of Electrical Engineering and Computer Science at Washington State University (www.eecs.wsu.edu). 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. * E-mail: sroy@eecs.wsu.edu Introduction Zoonoses–infectious diseases that can be transmitted to humans from other animals–incur significant cost though their impact on both agricultural production and human communities. Zoonoses have particular prevalence and impact in the developing world, where low-cost yet effective strategies for their control and eventual eradication are badly needed (e.g., [1,2]). Control of these zoonoses can be quite challenging, requiring 1) understand- ing (and sometimes new development) of the surveillance, vaccination, and treatment capabilities of a particular zoonotic agent in human and/or animal populations; 2) recognition/ modeling of the mechanisms and rates of spread in each species and between species; 3) cooperation across animal- and public health sectors; and 4) the ability to build the infrastructures needed for control within the limitations imposed by the financial and societal circumstances of the community. Historically, infectious disease specialists in collaboration with governmental organiza- tions have attempted to develop effective control and eradication strategies gradually, using field experience that is unique to the region and disease. A particular challenge in controlling zoonotic infections in this way is to appropriately characterize the animal- human interface that leads to spread, and in turn to appropriately allocate resources in the multi-species system. Recently, several studies have demonstrated that mathematical modeling can aid practitioners in developing control strategies, by www.plosntds.org 1 October 2011 | Volume 5 | Issue 10 | e1259