Optimal Control for Antivirus Routing in Epidemiological-Based Heterogeneous Computer Network Clusters

Maintaining productivity in computer networks under virus threats has been an ongoing research. Existing works have adopted epidemiological-based ordinary differentiation equations (ODEs) to model virus and antivirus propagation. However, these models tend to oversimplify by not accounting for the heterogeneity among different computer network clusters and ignoring real-world protocol constraints, e.g., nodes cannot communicate simultaneously with nodes in different groups. In this work, we develop a novel model that acknowledges these constraints and incorporates heterogeneity. We first propose a single-cluster ODE model in which both the virus and antivirus propagate. We then generalize this single-cluster model to a model for networks with heterogeneous clusters. Leveraging these models, we formulate the maximum productivity objective as an optimization problem that could be solved using quasi-Newton methods. We also numerically formalize the optimal control's validity in the single-cluster model through Pontryagin's Maximum Principle (PMP). By experimentation and simulation, we find that the optimal control policy follows a bang-bang structure and performs guided prioritization for the heterogeneity of clusters.