Optimal Patching in Clustered Malware Epidemics
This work addresses malware containment in mobile networks, offering a theoretical and practical approach to reduce costs, though it is incremental as it builds on existing epidemic models.
The paper tackles the problem of minimizing costs from malware spread and patching in mobile networks by proposing a formal framework for optimal patching policies, proving analytically that single-threshold policies are optimal in deterministic regimes and demonstrating advantages through simulations.
Studies on the propagation of malware in mobile networks have revealed that the spread of malware can be highly inhomogeneous. Platform diversity, contact list utilization by the malware, clustering in the network structure, etc. can also lead to differing spreading rates. In this paper, a general formal framework is proposed for leveraging such heterogeneity to derive optimal patching policies that attain the minimum aggregate cost due to the spread of malware and the surcharge of patching. Using Pontryagin's Maximum Principle for a stratified epidemic model, it is analytically proven that in the mean-field deterministic regime, optimal patch disseminations are simple single-threshold policies. Through numerical simulations, the behavior of optimal patching policies is investigated in sample topologies and their advantages are demonstrated.