Optimal Patching in Clustered Epidemics of Malware

Studies on the propagation of malware in mobile networks have revealed that the spread of malware can be highly inhomogeneous across different regions. Heterogeneous rates of contact can also be due to diverse platforms, utilization of contact lists by the malware, the clustered nature of the network, etc. In this paper, a general formal framework is proposed for leveraging such information about 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 that are amenable to implementation in a distributed manner. Through numerical calculations, the behavior of optimal patching policies is investigated in sample topologies and their advantages are demonstrated.