Sparse linear and nonlinear controls for network spread processes

Sparse controls for network spread dynamics are explored, in the context of a linearized model for infection spread in networks. Limits and comparisons are established on the control performance, which hold regardless of the type of controller used (centralized or decentralized, dynamic or static, linear or nonlinear). More refined characterizations are obtained for proportional decentralized controls. These control schemes are found to always reduce spread but may not be tailored to address the source of the spread and, in special instances, may surprisingly cause a more oscillatory response. Finally, switching controls that are cheap and effective are motivated and developed, using an illustrative example.