Estimating the state probability distribution for epidemic spreading in complex networks

Front. Appl. Math. Stat.

2018

Self Cite

In this paper the problem of designing an output-feedback control for the stabilization of the extinction steady-state in a virus spreading process over a complex network with quarantine is considered. Sufficient conditions are established for the choice of those nodes for which sensor information is necessary and those which should be controlled using notions from constructive control theory. A simple output-feedback control is proposed which exponentially stabilizes the extinction state. Numerical simulation results are provided to illustrate the functioning of the proposed control scheme for a scale-free network of N = 10 6 nodes.

Section: Linear Feedback Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Alarcon-Ramos

Front. Appl. Math. Stat.

2018

Self Cite

“…Spreading processes in complex networks have attracted recent attention for the purpose of analyzing the intertwined dynamics of epidemics [ 8 , 9 , 10 , 11 , 12 , 13 ] or information transmission in [ 14 , 15 , 16 , 17 , 18 ]. The control of such problems has to address fundamental questions as (i) which parameters of the system are amenable to manipulation and (ii) which nodes must be actively controlled.…”

Section: Introductionmentioning

confidence: 99%

“…Spreading processes in complex networks have attracted recent attention for the purpose of analyzing the intertwined dynamics of epidemics [8][9][10][11][12][13] or information transmission in [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Spreading Control in Two-Layer Multiplex Networks

Ramos

2020

Entropy

Self Cite

The problem of controlling a spreading process in a two-layer multiplex networks in such a way that the extinction state becomes a global attractor is addressed. The problem is formulated in terms of a Markov-chain based susceptible-infected-susceptible (SIS) dynamics in a complex multilayer network. The stabilization of the extinction state for the nonlinear discrete-time model by means of appropriate adaptation of system parameters like transition rates within layers and between layers is analyzed using a dominant linear dynamics yielding global stability results. An answer is provided for the central question about the essential changes in the step from a single to a multilayer network with respect to stability criteria and the number of nodes that need to be controlled. The results derived rigorously using mathematical analysis are verified using statical evaluations about the number of nodes to be controlled and by simulation studies that illustrate the stability property of the multilayer network induced by appropriate control action.

“…In recent years, Markov chain-based models for a Susceptible-Infected-Susceptible (SIS) dynamics over complex networks have been used [8][9][10][11][12]24]. Using these models, it is possible to determine the macroscopic properties of the system, as well as the description of the dynamics of individual nodes.…”

Section: Introductionmentioning

confidence: 99%

Output-Feedback Control for Discrete-Time Spreading Models in Complex Networks

Ramos

2018

Entropy

Self Cite

Abstract:The problem of stabilizing the spreading process to a prescribed probability distribution over a complex network is considered, where the dynamics of the nodes in the network is given by discrete-time Markov-chain processes. Conditions for the positioning and identification of actuators and sensors are provided, and sufficient conditions for the exponential stability of the desired distribution are derived. Simulations results for a network of N = 10 6 corroborate our theoretical findings.