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| Algebraic form and analysis of SIR epidemic dynamics over probabilistic dynamic networks |
| HongxingYuan1,ZengqiangChen1,ZhipengZhang2,RuiZhu1,ZhongxinLiu1 |
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| (1 College of Artificial Intelligence, Nankai University, Tianjin 300350, China;2 School of Artificial Intelligence, Tiangong University, Tianjin 300387, China) |
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| 摘要: |
| The outbreak of corona virus disease 2019 has profoundly affected people’s way of life. It is increasingly necessary to
investigate epidemics over social networks. This paper studies susceptible-infected-removed (SIR) epidemics via the semitensor
product. First, a formal susceptible-infected-removed epidemic dynamic model over probabilistic dynamic networks
(SIRED-PDN) is given. Based on an evolutionary rule, the algebraic form for the dynamics of individual states and network
topologies is given, respectively. Second, the SIRED-PDN can be described by a probabilistic mix-valued logical network.
After providing an algorithm, all possible final spreading equilibria can be obtained for any given initial epidemic state and
network topology by seeking attractors of the network. And the shortest time for all possible initial epidemic state and network
topology profiles to evolve to the final spreading equilibria can be obtained by seeking the transient time of the network.
Finally, an illustrative example is given to show the effectiveness of our model. |
| 关键词: SIR epidemic · Probabilistic dynamic networks · Final spreading equilibria · Semi-tensor product of matrices · Algebraic form |
| DOI：https://doi.org/10.1007/s11768-023-00143-0 |
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| 基金项目:This work was supported by the National Natural Science Foundation of China (Nos. 61973175, 62203328), the Tianjin Natural Science Foundation (Nos. 20JCYBJC01060, 21JCQNJC00840) and the General Terminal IC Interdisciplinary Science Center of Nankai University. |
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| Algebraic form and analysis of SIR epidemic dynamics over probabilistic dynamic networks |
| Hongxing Yuan1,Zengqiang Chen1,Zhipeng Zhang2,Rui Zhu1,Zhongxin Liu1 |
| (1 College of Artificial Intelligence, Nankai University, Tianjin 300350, China;2 School of Artificial Intelligence, Tiangong University, Tianjin 300387, China) |
| Abstract: |
| The outbreak of corona virus disease 2019 has profoundly affected people’s way of life. It is increasingly necessary to
investigate epidemics over social networks. This paper studies susceptible-infected-removed (SIR) epidemics via the semitensor
product. First, a formal susceptible-infected-removed epidemic dynamic model over probabilistic dynamic networks
(SIRED-PDN) is given. Based on an evolutionary rule, the algebraic form for the dynamics of individual states and network
topologies is given, respectively. Second, the SIRED-PDN can be described by a probabilistic mix-valued logical network.
After providing an algorithm, all possible final spreading equilibria can be obtained for any given initial epidemic state and
network topology by seeking attractors of the network. And the shortest time for all possible initial epidemic state and network
topology profiles to evolve to the final spreading equilibria can be obtained by seeking the transient time of the network.
Finally, an illustrative example is given to show the effectiveness of our model. |
| Key words: SIR epidemic · Probabilistic dynamic networks · Final spreading equilibria · Semi-tensor product of matrices · Algebraic form |
