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∞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.