Node-based SIRS model on heterogeneous networks: Analysis and control

Abstract

Abstract-In this paper, a node-base susceptible-infectedrecovered-susceptible (SIRS) model on heterogeneous networks is proposed. The condition for global exponential stability of the origin in the disease-free case is obtained via Lyapunov theory. Furthermore, aiming at regulating the probabilities of being infected and recovered to desired values, the controlled recovering rates are designed. Taking practical implementation into consideration, an alternative approach is provided to calculate the feasible control inputs. Finally, several numerical simulations validate our results.

A Persistent-Excitation-Free Method for System Disturbance Estimation Using Concurrent Learning

“…W = [w i j ] ∈ R n×n is the adjacency matrix of G. Here, we only consider a graph G with no self-loops, i.e., w ii = 0, ∀ i ∈ V. We also confine ourselves that w i j > 0, ∀ i, j ∈ V, if there exists an edge from j to i. Then, the discrete-time dynamic model of the SIS model is [53] x (23) i ∈ V, where for each note i, x i (k) denotes its infection probability at time step k ∈ N ≥0 , d i ∈ R ≥0 is the proactive infection rate, δ i ∈ R ≥0 is the passive curing rate at instant k, and h ∈ R + is the sampling period. Under appropriate assumptions [54], the infection probability x i (k), for all k ∈ N ≥0 and i ∈ V, is well defined, i.e., given any initial condition x i (0) ∈ [ 0, 1 ], the system state is confined by x i (k) ∈ [ 0, 1 ].…”

On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

“…In this case, epidemic diffusion process can be generally described as a graph-based Markov chain. Particularly, for the infection process of one agent, the transition rate is dependent on the states of her neighbors Liu and Buss (2016); Qu and Wang (2017). However, the exact Markov chain model faces difficulties due to the great number of states especially in large-scale networks.…”