Stability properties of infected networks with low curing rates

Khanafer, Ali; Başar, Tamer; Gharesifard, Bahman

doi:10.1109/acc.2014.6859418

Cited by 48 publications

(36 citation statements)

References 13 publications

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“…However, studying the existence, uniqueness, and stability of the endemic state is more relevant while being more challenging. In this section, we provide a non-trivial extension of our stability results for undirected graph in [8] to the directed case. In particular, we study the stability of the n-intertwined Markov model for both strongly and weakly connected graphs.…”

Section: Existence and Stability Of An Endemic Statementioning

confidence: 99%

“…We will select the curing rates over G 1 to be low to make R 1 o > 1. For the remaining nodes, we will set δ i = j =i a ji β j + 0.5, which is a sufficient condition to ensure R i o < 1, for all i [8]. The infection rates β i and the weights a ij are all selected to be equal to 1.…”

Section: Numerical Studiesmentioning

confidence: 99%

“…However, when the curing rates are low, an endemic state emerges and a residual infection persists in the network. Having studied the stability properties of this model over undirected graphs in [8], our focus here will be stability over directed networks. In general, communication and interaction among people, animals, and computers are not necessarily symmetric, which highlights the importance of studying epidemics over directed graphs.…”

Section: Introductionmentioning

confidence: 99%

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Stability properties of infection diffusion dynamics over directed networks

Khanafer

Başar

Gharesifard

2014

53rd IEEE Conference on Decision and Control

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We analyze the stability properties of a susceptible-infected-susceptible diffusion model over directed networks. Similar to the majority of infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the all-healthy state is globally asymptotically stable (GAS). Otherwise, an endemic state arises and the entire network could become infected. Using notions from positive systems theory, we prove that the endemic state is GAS in strongly connected networks. When the graph is weakly connected, we provide conditions for the existence, uniqueness, and global asymptotic stability of weak and strong endemic states. Several simulations demonstrate our results. 53rd IEEE Conference on Decision and Control

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Section: Existence and Stability Of An Endemic Statementioning

confidence: 99%

Section: Numerical Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability properties of infection diffusion dynamics over directed networks

Khanafer

Başar

Gharesifard

2014

53rd IEEE Conference on Decision and Control

Self Cite

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“…The socalled N -intertwined SIS model has been well studied. The remarkable property that there exists an epidemic threshold is given in [9] and the stability of the equilibria in metastable states is proved in [10]. However, no results on node-based SIRS model are reported, which motivates our work in this paper.…”

Section: Introductionmentioning

confidence: 96%

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

Liu

Buss

2016

2016 American Control Conference (ACC)

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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.

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“…From the proof of statement (iv), we know that, around the unique fixed point, the linearized system is y(t + 1) = M y(t), where M is a Metzler matrix and is Hurwitz stable. Usually the Metzler matrices are presented in continuous-time network dynamics models, e.g., the epidemic spreading model [35], [36]. In the proof of Theorem 10 (iv), we provide an example of the Metzler matrix in a stable discrete-time system.…”

Section: Map According To the Proof For Statement (I)mentioning

confidence: 99%

Modeling and analysis of competitive propagation with social conversion

Mei

Bullo

2014

53rd IEEE Conference on Decision and Control

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Abstract-In this paper we propose a class of propagation models for multiple competing products over a social network. We consider two propagation mechanisms: social conversion and self conversion, corresponding, respectively, to endogenous and exogenous factors. A novel concept, the product-conversion graph, is proposed to characterize the interplay among competing products. According to the chronological order of social and self conversions, we develop two Markov-chain models and, based on the independence approximation, we approximate them with two corresponding difference equations systems. Our theoretical analysis on these two approximated models reveals the dependency of their asymptotic behavior on the structures of both the product-conversion graph and the social network, as well as the initial condition. In addition to the theoretical work, we investigate via numerical analysis the accuracy of the independence approximation and the asymptotic behavior of the Markov-chain model, for the case where social conversion occurs before self conversion. Finally, we propose two classes of games based on the competitive propagation model: the repeated one-shot game and the dynamic infinite-horizon game. We characterize the quality-seeding trade-off for the first game and the Nash equilibrium in both games.

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Stability properties of infected networks with low curing rates

Cited by 48 publications

References 13 publications

Stability properties of infection diffusion dynamics over directed networks

Stability properties of infection diffusion dynamics over directed networks

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

Modeling and analysis of competitive propagation with social conversion

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