Optimal Patching in Clustered Malware Epidemics

Abstract

Abstract—Studies of propagation of malware in mobile network 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, clustered nature of the network, etc. In this paper, we propose a general formal framework to leverage such heterogeneity information into devising 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, we analytically prove that in the mean-field deterministic regime optimal patch disseminations are simple single-threshold policies which are amenable to implementation in a distributed manner. Through numerical calculations, we investigate the behavior of optimal patching policies in sample topologies and demonstrate their advantages. I.