Optimal Induced Spreading of SIS Epidemics in Networks

A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic model

“…While optimal control strategies are recently employed to solve various online control problems over networks (Khanafer and Başar, 2014;Eshghi et al, 2016;Kandhway and Kuri, 2016;He and Van Mieghem, 2019;Dashtbali et al, 2020;Watkins et al, 2020), they fall short in practice. Specifically, they are based on unrealistically simplified deterministic models, have a computational burden that is intractable for large networks, and require complete knowledge of network geometry and dynamical parameters.…”

“…Unlike local linearization approaches (Khanafer and Başar, 2014), that are valid within a (small) neighborhood of invariant sets, Koopman eigenfunctions extend the validity of the linear model into the whole basin of attraction. Furthermore we offer computationally tractable solutions, in contrary to recent works that use nonlinear models for more accurate and stable control (He and Van Mieghem, 2019;Watkins et al, 2020) with recalcitrant nonlinear programmings with requirements about the exact knowledge of underlying dynamics, model parameters, and network geometry. Hence, the importance of this work remains in establishing an approach that does not ask for often-unknown network information over and enables practical linear control strategies that are valid over the state space.…”

“…This means that these allocation strategies are incapable of adapting to changing demands, leading to at best a non-optimal resource allocation, and at worst a failure to control the disease process due to changing network conditions. Optimal control strategies are employed to solve this issue by allowing the control allocation to vary over time (Khanafer and Başar, 2014;Eshghi et al, 2016); this approach is used in Kandhway and Kuri (2016); He and Van Mieghem (2019) for application in virus spreading problems and Dashtbali et al (2020) for investigating social distancing in response to epidemic using differential games approach. Watkins et al (2020) use MPC for optimal containment of epidemic over networks.…”