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- Liu, Ji, et al.
(author)
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Analysis and Control of a Continuous-Time Bi-Virus Model
- 2019
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In: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 64:12, s. 4891-4906
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Journal article (peer-reviewed)abstract
- This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the equilibria of the system and their stability. Specifically, when the two viruses spread over possibly different directed infection graphs, the system may have the following: first, a unique equilibrium, the healthy state, which is globally stable, implying that both viruses will eventually be eradicated, second, two equilibria including the healthy state and a dominant virus state, which is almost globally stable, implying that one virus will pervade the entire network causing a single-virus epidemic while the other virus will be eradicated, or third, at least three equilibria including the healthy state and two dominant virus states, depending on certain conditions on the healing and infection rates. When the two viruses spread over the same directed infection graph, the system may have zero or infinitely many coexisting epidemic equilibria, which represents the pervasion of the two viruses. Sensitivity properties of some nontrivial equilibria are investigated in the context of a decentralized control technique, and an impossibility result is given for a certain type of distributed feedback controller.
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- Pare, Philip E., et al.
(author)
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Networked Infectious Disease-Contaminated Water Model
- 2019
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In: 2019 18TH EUROPEAN CONTROL CONFERENCE (ECC). - : IEEE. ; , s. 2018-2023
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Conference paper (peer-reviewed)abstract
- This paper proposes a continuous-time virus spreading model that includes a human-contact network and a water component that may be contaminated. The main motivating applications are modeling infectious waterborne diseases such as cholera, SARS, and amoebiasis (hand-to-mouth). We present the model and its derivation, explore the equilibria of the model, and analyze the healthy equilibria. We illustrate the behavior of the model via simulation, and demonstrate how the proposed model captures the behavior of Dr. John Snow's pioneering cholera dataset.
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- Wang, Dan, et al.
(author)
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Controlling a Networked SIS Model via a Single Input over Undirected Graphs
- 2020
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In: IFAC PAPERSONLINE. - : Elsevier BV. - 2405-8963. ; , s. 10981-10986
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Conference paper (peer-reviewed)abstract
- This paper formulates and studies the problem of controlling a networked SIS model using a single input in which the network structure is described by a connected undirected graph. A necessary and sufficient condition on the values of curing and infection rates for the healthy state to be exponentially stable is obtained via the analysis of signed Laplacians when the control input is the curing budget of a single agent. In the case when the healthy state is stabilizable, an explicit expression for the minimum curing budget is provided. The utility of the algorithm is demonstrated using a simulation over a network of cities in the northeastern United States.
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- Zhang, Ciyuan, et al.
(author)
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A Networked Competitive Multi-Virus SIR Model : Analysis and Observability
- 2022
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In: IFAC Papersonline. - : Elsevier BV. - 2405-8963. ; , s. 13-18
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Conference paper (peer-reviewed)abstract
- This paper proposes a novel discrete-time multi-virus SIR (susceptible-infected-recovered) model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses' infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be locally observable. We propose a Luenberger observer for the system state estimation and show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out. Copyright
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