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Peng SL, Wang HJ, Peng H, Zhu XB, Li X, Han J, Zhao D, Hu ZL. NLSI: An innovative method to locate epidemic sources on the SEIR propagation model. CHAOS (WOODBURY, N.Y.) 2023; 33:083125. [PMID: 37549113 DOI: 10.1063/5.0152859] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2023] [Accepted: 07/12/2023] [Indexed: 08/09/2023]
Abstract
Epidemics pose a significant threat to societal development. Accurately and swiftly identifying the source of an outbreak is crucial for controlling the spread of an epidemic and minimizing its impact. However, existing research on locating epidemic sources often overlooks the fact that epidemics have an incubation period and fails to consider social behaviors like self-isolation during the spread of the epidemic. In this study, we first take into account isolation behavior and introduce the Susceptible-Exposed-Infected-Recovered (SEIR) propagation model to simulate the spread of epidemics. As the epidemic reaches a certain threshold, government agencies or hospitals will report the IDs of some infected individuals and the time when symptoms first appear. The reported individuals, along with their first and second-order neighbors, are then isolated. Using the moment of symptom onset reported by the isolated individuals, we propose a node-level classification method and subsequently develop the node-level-based source identification (NLSI) algorithm. Extensive experiments demonstrate that the NLSI algorithm is capable of solving the source identification problem for single and multiple sources under the SEIR propagation model. We find that the source identification accuracy is higher when the infection rate is lower, and a sparse network structure is beneficial to source localization. Furthermore, we discover that the length of the isolation period has little impact on source localization, while the length of the incubation period significantly affects the accuracy of source localization. This research offers a novel approach for identifying the origin of the epidemic associated with our defined SEIR model.
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Affiliation(s)
- Shui-Lin Peng
- College of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China
| | - Hong-Jue Wang
- School of Information, Beijing Wuzi University, Beijing 101149, China
| | - Hao Peng
- College of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China
| | - Xiang-Bin Zhu
- College of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China
| | - Xiang Li
- College of Science, National University of Defense Technology, Changsha 410073, China
| | - Jianmin Han
- College of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China
| | - Dandan Zhao
- College of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China
| | - Zhao-Long Hu
- College of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China
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2
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Zhang S, Zhao D, Xia C, Tanimoto J. Impact of simplicial complexes on epidemic spreading in partially mapping activity-driven multiplex networks. CHAOS (WOODBURY, N.Y.) 2023; 33:2895981. [PMID: 37307162 DOI: 10.1063/5.0151881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2023] [Accepted: 05/22/2023] [Indexed: 06/14/2023]
Abstract
Over the past decade, the coupled spread of information and epidemic on multiplex networks has become an active and interesting topic. Recently, it has been shown that stationary and pairwise interactions have limitations in describing inter-individual interactions , and thus, the introduction of higher-order representation is significant. To this end, we present a new two-layer activity-driven network epidemic model, which considers the partial mapping relationship among nodes across two layers and simultaneously introduces simplicial complexes into one layer, to investigate the effect of 2-simplex and inter-layer mapping rate on epidemic transmission. In this model, the top network, called the virtual information layer, characterizes information dissemination in online social networks, where information can be diffused through simplicial complexes and/or pairwise interactions. The bottom network, named as the physical contact layer, denotes the spread of infectious diseases in real-world social networks. It is noteworthy that the correspondence among nodes between two networks is not one-to-one but partial mapping. Then, a theoretical analysis using the microscopic Markov chain (MMC) method is performed to obtain the outbreak threshold of epidemics, and extensive Monte Carlo (MC) simulations are also carried out to validate the theoretical predictions. It is obviously shown that MMC method can be used to estimate the epidemic threshold; meanwhile, the inclusion of simplicial complexes in the virtual layer or introductory partial mapping relationship between layers can inhibit the spread of epidemics. Current results are conducive to understanding the coupling behaviors between epidemics and disease-related information.
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Affiliation(s)
- Shuofan Zhang
- Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384, China
| | - Dawei Zhao
- Shandong Provincial Key Laboratory of Computer Networks, Shandong Computer Science Center (National Supercomputer Center in Jinan), Qilu University of Technology (Shandong Academy of Sciences), Jinan 250014, China
| | - Chengyi Xia
- School of Artificial Intelligence, Tiangong University, Tianjin 300387, China
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
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Nie Y, Zhong M, Li R, Zhao D, Peng H, Zhong X, Lin T, Wang W. Digital contact tracing on hypergraphs. CHAOS (WOODBURY, N.Y.) 2023; 33:063146. [PMID: 37347642 DOI: 10.1063/5.0149384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 06/05/2023] [Indexed: 06/24/2023]
Abstract
The higher-order interactions emerging in the network topology affect the effectiveness of digital contact tracing (DCT). In this paper, we propose a mathematical model in which we use the hypergraph to describe the gathering events. In our model, the role of DCT is modeled as individuals carrying the app. When the individuals in the hyperedge all carry the app, epidemics cannot spread through this hyperedge. We develop a generalized percolation theory to investigate the epidemic outbreak size and threshold. We find that DCT can effectively suppress the epidemic spreading, i.e., decreasing the outbreak size and enlarging the threshold. DCT limits the spread of the epidemic to larger cardinality of hyperedges. On real-world networks, the inhibitory effect of DCT on the spread of epidemics is evident when the spread of epidemics is small.
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Affiliation(s)
- Yanyi Nie
- School of Public Health, Chongqing Medical University, Chongqing 400016, China
- College of Computer Science, Sichuan University, Chengdu 610065, China
| | - Ming Zhong
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Runchao Li
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Dandan Zhao
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Hao Peng
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Xiaoni Zhong
- School of Public Health, Chongqing Medical University, Chongqing 400016, China
| | - Tao Lin
- College of Computer Science, Sichuan University, Chengdu 610065, China
| | - Wei Wang
- School of Public Health, Chongqing Medical University, Chongqing 400016, China
- Research Center of Public Health Security, Chongqing Medical University, Chongqing 400016, China
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4
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Leng H, Zhao Y, Luo J, Ye Y. Simplicial epidemic model with birth and death. CHAOS (WOODBURY, N.Y.) 2022; 32:093144. [PMID: 36182376 DOI: 10.1063/5.0092489] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 08/29/2022] [Indexed: 06/16/2023]
Abstract
In this paper, we propose a simplicial susceptible-infected-susceptible (SIS) epidemic model with birth and death to describe epidemic spreading based on group interactions, accompanying with birth and death. The site-based evolutions are formulated by the quenched mean-field probability equations for each site, which is a high-dimensional differential system. To facilitate a theoretical analysis of the influence of system parameters on dynamics, we adopt the mean-field method for our model to reduce the dimension. As a consequence, it suggests that birth and death rates influence the existence and stability of equilibria, as well as the appearance of a bistable state (the coexistence of the stable disease-free and endemic states), which is then confirmed by extensive simulations on empirical and synthetic networks. Furthermore, we find that another type of the bistable state in which a stable periodic outbreak state coexists with a steady disease-free state also emerges when birth and death rates and other parameters satisfy the certain conditions. Finally, we illustrate how the birth and death rates shift the density of infected nodes in the stationary state and the outbreak threshold, which is also verified by sensitivity analysis for the proposed model.
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Affiliation(s)
- Hui Leng
- School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
| | - Yi Zhao
- School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
| | - Jianfeng Luo
- School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
| | - Yong Ye
- School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
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Zhu X, Wang Y, Zhang N, Yang H, Wang W. Influence of heterogeneity of infection thresholds on epidemic spreading with neighbor resource supporting. CHAOS (WOODBURY, N.Y.) 2022; 32:083124. [PMID: 36049956 DOI: 10.1063/5.0098328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Accepted: 07/20/2022] [Indexed: 06/15/2023]
Abstract
The spread of disease on complex networks has attracted wide attention in physics, mathematics, and epidemiology. Recent works have demonstrated that individuals always exhibit different criteria for disease infection in a network that significantly influences the epidemic dynamics. In this paper, considering the heterogeneity of node susceptibility, we proposed an infection threshold model with neighbor resource support. The infection threshold of an individual is associated with the degree, and a parameter follows the normal distribution. Based on improved heterogeneous mean-field theory and extensive numerical simulations, we find that the mean and standard deviation of the infection threshold model can affect the phase transition and epidemic outbreak size. As the mean of the normal distribution parameter increases from a small value to a large value, the system shows a change from a continuous phase transition to a discontinuous phase transition, and the disease even stops spreading. The disease spreads from a discontinuous phase transition to continuous for the sizeable mean value as the standard deviation increases. Furthermore, the standard deviation also varies in the outbreak size.
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Affiliation(s)
- Xuzhen Zhu
- State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China
| | - Yuxin Wang
- State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China
| | - Ningbo Zhang
- Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Hui Yang
- Institute of Southwestern Communication, Chengdu 610041, China
| | - Wei Wang
- School of Public Health, Chongqing Medical University, Chongqing 400016, China
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Zhao J, Wen T, Jahanshahi H, Cheong KH. The random walk-based gravity model to identify influential nodes in complex networks. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.07.084] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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7
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Chang X, Cai CR, Zhang JQ, Wang CY. Analytical solution of epidemic threshold for coupled information-epidemic dynamics on multiplex networks with alterable heterogeneity. Phys Rev E 2021; 104:044303. [PMID: 34781529 DOI: 10.1103/physreve.104.044303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 09/17/2021] [Indexed: 11/07/2022]
Abstract
The phase transition of epidemic spreading model on networks is one of the most important concerns of physicists to theoretical epidemiology. In this paper, we present an analytical expression of epidemic threshold for interplay between epidemic spreading and human behavior on multiplex networks. The threshold formula proposed in this paper reveals the relation between the threshold on single-layer networks and that on multiplex networks, which means that the theoretical conclusions of single-layer networks can be used to improve the threshold accuracy of multiplex networks. To verify how well our formula works in different networks, we build a network model with constant total number of edges but gradually changing the heterogeneity of the network, from scale-free network to Erdős-Rényi random network. By use of theoretical analysis and computer simulations, we find that the heterogeneity of information layer behaves as a "double-edged sword" on the epidemic threshold: The strong heterogeneity can effectively improve the epidemic threshold (which means the disease outbreak requires a higher infection probability) when the awareness probability α is low, while the opposite effect takes place for high α. Meanwhile, the weak heterogeneity of the information layer is effective in suppressing the epidemic prevalence when the awareness probability is neither too high nor too low.
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Affiliation(s)
- Xin Chang
- School of Physics, Northwest University, Xi'an 710069, China.,Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710069, China.,Institute of Modern Physics, Northwest University, Xi'an 710069, China
| | - Chao-Ran Cai
- School of Physics, Northwest University, Xi'an 710069, China.,Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710069, China
| | - Ji-Qiang Zhang
- School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China
| | - Chong-Yang Wang
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China.,Yangtze Delta Region Institute of University of Electronic Science and Technology of China, Huzhou, Zhejiang, 313000, China
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Li W, Zhou J, Jin Z, Lu JA. The combination of targeted vaccination and ring vaccination. CHAOS (WOODBURY, N.Y.) 2021; 31:063108. [PMID: 34241306 DOI: 10.1063/5.0048457] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 05/19/2021] [Indexed: 06/13/2023]
Abstract
Complex networks have become an important tool for investigating epidemic dynamics. A widely concerned research field for epidemics is to develop and study mitigation strategies or control measures. In this paper, we devote our attention to ring vaccination and targeted vaccination and consider the combination of them. Based on the different roles ring vaccination plays in the mixed strategy, the whole parameter space can be roughly divided into two regimes. In one regime, the mixed strategy performs poorly compared with targeted vaccination alone, while in the other regime, the addition of ring vaccination can improve the performance of targeted vaccination. This result gives us the more general and overall comparison between targeted and ring vaccination. In addition, we construct a susceptible-infected-recovered epidemic model coupled with the immunization dynamics on random networks. The comparison between stochastic simulations and numerical simulations confirms the validity of the model we propose.
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Affiliation(s)
- Weiqiang Li
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Jin Zhou
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
| | - Jun-An Lu
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
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Kabir KMA, Tanimoto J. Modelling and analysing the coexistence of dual dilemmas in the proactive vaccination game and retroactive treatment game in epidemic viral dynamics. Proc Math Phys Eng Sci 2019; 475:20190484. [PMID: 31892836 PMCID: PMC6936617 DOI: 10.1098/rspa.2019.0484] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Accepted: 10/30/2019] [Indexed: 12/21/2022] Open
Abstract
The dynamics of a spreadable disease are largely governed by four factors: proactive vaccination, retroactive treatment, individual decisions, and the prescribing behaviour of physicians. Under the imposed vaccination policy and antiviral treatment in society, complex factors (costs and expected effects of the vaccines and treatments, and fear of being infected) trigger an emulous situation in which individuals avoid infection by the pre-emptive or ex post provision. Aside from the established voluntary vaccination game, we propose a treatment game model associated with the resistance evolution of antiviral/antibiotic overuse. Moreover, the imperfectness of vaccinations has inevitably led to anti-vaccine behaviour, necessitating a proactive treatment policy. However, under the excessively heavy implementation of treatments such as antiviral medicine, resistant strains emerge. The model explicitly exhibits a dual social dilemma situation, in which the treatment behaviour changes on a local time scale, and the vaccination uptake later evolves on a global time scale. The impact of resistance evolution and the coexistence of dual dilemmas are investigated by the control reproduction number and the social efficiency deficit, respectively. Our investigation might elucidate the substantial impacts of both vaccination and treatment in the framework of epidemic dynamics, and hence suggest the appropriate use of antiviral treatment.
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Affiliation(s)
- K M Ariful Kabir
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan.,Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
| | - Jun Tanimoto
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan.,Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan
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Xia Y, Small M, Wu J. Introduction to Focus Issue: Complex Network Approaches to Cyber-Physical Systems. CHAOS (WOODBURY, N.Y.) 2019; 29:093123. [PMID: 31575131 DOI: 10.1063/1.5126230] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2019] [Accepted: 09/04/2019] [Indexed: 06/10/2023]
Affiliation(s)
- Yongxiang Xia
- School of Communication Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Michael Small
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Jiajing Wu
- School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510275, China
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