TY - JOUR

T1 - Distributed feedback control on the SIS network model

T2 - 21st IFAC World Congress 2020

AU - Ye, Mengbin

AU - Liu, Ji

AU - Anderson, Brian D.O.

AU - Cao, Ming

N1 - Publisher Copyright:
Copyright © 2020 The Authors.

PY - 2020

Y1 - 2020

N2 - This paper considers the deterministic Susceptible-Infected-Susceptible (SIS) epidemic network model, over strongly connected networks. It is well known that there exists an endemic equilibrium (the disease persists in all nodes of the network) if and only if the effective reproduction number of the network is greater than 1. In fact, the endemic equilibrium is unique and is asymptotically stable for all feasible nonzero initial conditions. We consider the recovery rate of each node as a control input. Using results from differential topology and monotone systems, we establish that it is impossible for a large class of distributed feedback controllers to drive the network to the healthy equilibrium (where every node is disease free) if the uncontrolled network has a reproduction number greater than 1. In fact, a unique endemic equilibrium exists in the controlled network, and it is exponentially stable for all feasible nonzero initial conditions. We illustrate our impossibility result using simulations, and discuss the implications on the problem of control over epidemic networks.

AB - This paper considers the deterministic Susceptible-Infected-Susceptible (SIS) epidemic network model, over strongly connected networks. It is well known that there exists an endemic equilibrium (the disease persists in all nodes of the network) if and only if the effective reproduction number of the network is greater than 1. In fact, the endemic equilibrium is unique and is asymptotically stable for all feasible nonzero initial conditions. We consider the recovery rate of each node as a control input. Using results from differential topology and monotone systems, we establish that it is impossible for a large class of distributed feedback controllers to drive the network to the healthy equilibrium (where every node is disease free) if the uncontrolled network has a reproduction number greater than 1. In fact, a unique endemic equilibrium exists in the controlled network, and it is exponentially stable for all feasible nonzero initial conditions. We illustrate our impossibility result using simulations, and discuss the implications on the problem of control over epidemic networks.

KW - Complex networks

KW - Control of networked systems

KW - Deterministic epidemic models

KW - Differential topology

KW - Monotone systems

KW - Susceptible-Infected-Susceptible (SIS) model

UR - http://www.scopus.com/inward/record.url?scp=85105116370&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2020.12.2844

DO - 10.1016/j.ifacol.2020.12.2844

M3 - Conference article

AN - SCOPUS:85105116370

SN - 2405-8963

VL - 53

SP - 10955

EP - 10962

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 2

Y2 - 12 July 2020 through 17 July 2020

ER -