Optimal Impulse Control of SIR Epidemics Over Scale-Free Networks

Abstract

Recent wide spreading of Ransomware has created new challenges for cybersecurity over large-scale networks. The densely connected networks can exacerbate the spreading and makes the containment and control of the malware more challenging. In this work, we propose an impulse optimal control framework for epidemics over networks. The hybrid nature of discretetime control policy of continuous-time epidemic dynamics together with the network structure poses a challenging optimal control problem. We leverage the Pontryagin's minimum principle for impulsive systems to obtain an optimal structure of the controller and use numerical experiments to corroborate our results.

Nash equilibria in nonzero-sum differential games with impulse control

“…One of the well-studied impulse control problems is the central bank intervention problem, where the bank intervenes in the foreign exchange market and continuously controls the domestic interest rate to keep the exchange rate close to a target value (see, e.g., [11] and [15]). The characterization of optimal impulse control in a one-decision-maker setting has been the topic of a long series of contributions in diverse fields, e.g, finance [16]; management [17,18,19,20,21]; and epidemiology [22]. In contrast, the literature in differential games with impulse controls has been very limited, and has predominantly dealt with zero-sum games (see, e.g., [23] and [24]).…”