Stability analysis for virus spreading in complex networks with quarantine and non-homogeneous transition rates

Spreading Control in Two-Layer Multiplex Networks

“…In comparison with the single-layer setup considered, e.g., in [ 36 , 37 , 38 ] the additional dependency on introduces stronger conditions. This will most probably imply a higher number of nodes to be controlled in the case of interconnecting the network with another one, i.e., the number of nodes that need to be controlled to ensure an asymptotically stable interconnection will be larger then the sum of the numbers of nodes that need to be controlled in each sub-network to achieve individual asymptotic stability.…”

“…It should be mentioned that even though network controllability ensures that a desired state can be reached or stabilized, it does not necessarily guide the way for the design of a decentralized control but typically leads to centralized control strategies. On the other hand, the control of networks has been explicitly addressed using stabilization and stability analysis leading the way to the choice of nodes to be controlled with implicit decentralized parametric control strategies [ 35 , 36 , 37 , 38 ]. In particular, the approach followed in [ 36 , 37 , 38 ] yields global stability assessments by means of the derivation of a global dominant linear dynamics.…”

“…On the other hand, the control of networks has been explicitly addressed using stabilization and stability analysis leading the way to the choice of nodes to be controlled with implicit decentralized parametric control strategies [35][36][37][38]. In particular, the approach followed in [36][37][38] yields global stability assessments by means of the derivation of a global dominant linear dynamics. Furthermore, optimization based approaches for parameter adaptation and node or link removal have been widely discussed, as has been summarized in [39].…”

Output-Feedback Control of Virus Spreading in Complex Networks With Quarantine

“…This pioneering work gave birth to the SIS (Susceptible-Infected-Susceptible) model mainly because many diseases do not confer any immunity. Extensions such as the SIQ (Susceptible-Infected-Quarantine) model (see e.g., [15][16][17]) appeared in order to account for the dynamics of the spreading of infections when quarantine has been implemented as a means to control the massive spreading of the infectious disease. Accordingly, a new class of quarantined individuals is included.…”

“…In the present work we will study the spreading of diseases using a Markov-chain based model for a Susceptible-Infected-Quarentine (SIQ) dynamics over a complex network that has been used in a simplified version for the determination of stability tresholds in recent studies by the authors [15,17]. We will show that, even when the built-in control strategy of quarantine is not able to ensure virus extinction, it is always possible to solve the problem of epidemic spreading extinction.…”