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Optimal impulse control of bi-virus SIR epidemics with application to heterogeneous Internet of Things

With the emerging Internet of Things (IoT) technologies, malware spreading over increasingly connected networks becomes a new security concern. To capture the heterogeneous nature of the IoT networks, we propose a continuous-time Susceptible-Infected-Recovered (SIR) epidemic model with two types of malware for heterogeneous populations over a large network of devices. The malware control mechanism is to patch an optimal fraction of the infected nodes at discrete points in time, which leads to an impulse controller. We use the Pontryagin's minimum principle for impulsive systems to obtain an optimal structure of the controller and use numerical experiments to demonstrate the computation of the optimal control and the controlled dynamics.