Optimal and robust epidemic response for multiple networks

This paper studies the optimization of malicious software removal or patch deployment processes across multiple networks. The well-known classical epidemic model is adapted to model malware propagation in this multi-network framework. The trade-off between the infection spread and the patching costs is captured in a cost function, leading to an optimal control problem. In the single network case the optimal feedback controller is found by solving an associated Hamilton-Jacobi-Bellman equation. This control law is numerically compared to the proportional response strategy typically assumed by the epidemic model. In the higher dimensional multiple-networks case, the system is linearized to derive feedback controllers using pole-placement, linear quadratic regulator (LQR) optimal control, and H^∞ optimal control, where the measurement errors in the number of infected clients are explicitly modeled. The resulting patching strategies are analyzed numerically and their results are compared.