A Network Control Theory Approach to Modeling and Optimal Control of Zoonoses: Case Study of Brucellosis Transmission in Sub-Saharan Africa
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. 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. 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. Zoonotic diseases (ones that infect both animals and humans) exact a significant economic and human cost, especially in developing economies. Developing effective policies for mitigating zoonotic infections is often challenging, both because of the complexity of their spread and because very limited resources must be allocated among a range of control options. It is increasingly becoming clear that mathematical modeling, and in particular network modeling, of disease spread can aid in analyzing and mitigating these spreads. Here, we develop a network model for the spread and control of a zoonotic infection, focusing particularly on a case study of brucellosis transmission and control among wildlife, cattle herds, and human subpopulations in an agricultural community. After motivating and formulating the model, we introduce tools for 1) parameterization of the model from time-course and snapshot data, 2) simulation and analysis of the model, and 3) optimal design of control policies using the model. The study shows that the network model can inform design of heterogeneous control policies that mitigate zoonotic disease spread with limited resources.