Two-Layer Network Based Epidemic Model with Network Formal Context
FAN Min1,2, CHEN Rui1,2, LI Jinhai1,2
1. Data Science Research Center, Kunming University of Science and Technology, Kunming 650500; 2. Faculty of Science, Kunming University of Science and Technology, Kunming 650500
Abstract Two-layer network based epidemic models are one of the hot topics in complex network dynamics. However, existing studies overlook the impact of epidemic awareness and behavior on epidemic transmission. As a result, when there are significant differences in individual prevention behaviors, these models fail to accurately reflect real-world disease spread. To address this issue, a two-layer network based epidemic model is proposed by integrating formal concept analysis with the microscopic Markov chain approach(MMCA) from the perspective of behavioral pattern recognition. First, the two-layer network formal context, network concepts and their characteristic parameters are defined, and a bridge between formal concept analysis and epidemic models is established. This method not only describes the concepts and characteristic parameters corresponding to behavioral patterns in the two-layer network, but also defines a decay factor to further facilitate the integration of information across layers using MMCA. Second, the influence of mass media and policy interventions on information diffusion is taken into account, the mass media function and the MMCA model are improved, and the epidemic outbreak threshold is derived. Finally, simulation experiments are conducted to analyze the impact of several key parameters on epidemic spread scale and threshold.
Fund:National Natural Science Foundation of China(No.62476114), Yunnan Fundamental Research Projects(No.202401AV070009)
Corresponding Authors:
LI Jinhai, Ph.D., professor. His research interests include cognitive computing, granular computing, big data analysis, concept lattice and rough set.
About author:: FAN Min, Ph.D., associate professor. Her research interests include data mining, rough set, granular computing and social network analysis. CHEN RUI, Master student. His research interests include network formal context and two-layer network based epidemic model."
FAN Min,CHEN Rui,LI Jinhai. Two-Layer Network Based Epidemic Model with Network Formal Context[J]. Pattern Recognition and Artificial Intelligence, 2025, 38(2): 143-163.
[1] WILLE R. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts // IRIVAL I, ed. Ordered Sets. Berlin, Germany: Springer, 1982: 445-470. [2] GANTER B, WILLE R. Formal Concept Analysis: Mathematical Foun-dations. Berlin, Germany: Springer, 2012. [3] KUZNETSOV S O. Machine Learning on the Basis of Formal Concept Analysis. Automation and Remote Control, 2001, 62: 1543-1564. [4] MEDDOURI N, KHOUFI H, MADDOURI M. Parallel Learning and Classification for Rules Based on Formal Concepts. Procedia Computer Science, 2014, 35: 358-367. [5] KHOR S, GROGONO P. Using a Genetic Algorithm and Formal Concept Analysis to Generate Branch Coverage Test Data Automatically // Proc of the 19th International Conference on Automated Software Engineering. Washington, USA: IEEE, 2004. DOI: 10.1109/ASE.2004.1342761. [6] GRIGORIEV P A, YEVTUSHENKO S A. QuDA: Applying Formal Concept Analysis in a Data Mining Environment // Proc of the 2nd International Conference on Formal Concept Analysis. Berlin, Germany: Springer, 2004: 386-393. [7] 梁涛巨,林艺东,林梦雷,等.基于属性加权的概念认知学习模型.模式识别与人工智能, 2023, 36(8): 749-763. (LIANG T J, LIN Y D, LIN M L, et al. Weighted Attributes-Based Concept-Cognitive Learning Model. Pattern Recognition and Artificial Intelligence, 2023, 36(8): 749-763.) [8] GUO D D, XU W H, DING W P, et al. Concept-Cognitive Lear-ning Survey: Mining and Fusing Knowledge from Data. Information Fusion, 2024, 109. DOI: 10.1016/j.inffus.2024.102426. [9] LIU M, ZHU P. Fuzzy Object-Induced Network Three-Way Concept Lattice and its Attribute Reduction. International Journal of Approximate Reasoning, 2024, 173. DOI: 10.1016/j.ijar.2024.109251. [10] 马娜,范敏,李金海. 复杂网络下的概念认知学习.南京大学学报(自然科学版), 2019, 55(4): 609-623. (MA N, FAN M, LI J H. Concept-Cognitive Learning under Complex Network. Journal of Nanjing University(Natural Sciences), 2019, 55(4): 609-623.) [11] FENZA G, GALLO M, LOIA V, et al. Concept-Drift Detection Index Based on Fuzzy Formal Concept Analysis for Fake News Cla-ssifiers. Technological Forecasting and Social Change, 2023, 194. DOI: 10.1016/j.techfore.2023.122640. [12] BENÍTEZ-CABALLERO M J, MEDINA J, RAMÍREZ-POUSSA E, et al. Rough-Set-Driven Approach for Attribute Reduction in Fuzzy Formal Concept Analysis. Fuzzy Sets and Systems, 2020, 391: 117-138. [13] LI J H, MEI C L, XU W H, et al. Concept Learning via Granular Computing: A Cognitive Viewpoint. Information Sciences, 2015, 298: 447-467. [14] KANG X P, MIAO D Q. A Study on Information Granularity in Formal Concept Analysis Based on Concept-Bases. Knowledge-Based Systems, 2016, 105: 147-159. [15] WEI L, LIU L, QI J J, et al. Rules Acquisition of Formal Decision Contexts Based on Three-Way Concept Lattices. Information Sciences, 2020, 516: 529-544. [16] QI J J, WEI L, YAO Y Y. Three-Way Formal Concept Analysis // Proc of the 9th International Conference on Rough Sets and Knowledge Technology. Berlin, Germany: Springer, 2014: 732-741. [17] LIU Z M, LI J H, ZHANG X, et al. Multi-level Information Fusion for Missing Multi-label Learning Based on Stochastic Concept Clustering. Information Fusion, 2025, 115. DOI: 10.1016/j.inffus.2024.102775. [18] 汤亚强,范敏,李金海. 三元形式概念分析下的认知系统模型及信息粒转化方法.山东大学学报(理学版), 2014, 49(8): 102-106. (TANG Y Q, FAN M, LI J H. Cognitive System Model and App-roach to Transformation of Information Granules under Triadic Formal Concept Analysis. Journal of Shandong University (Natural Science), 2014, 49(8): 102-106.) [19] ZHI H L, LI J H. Component Similarity Based Conflict Analysis: An Information Fusion Viewpoint. Information Fusion, 2024, 104. DOI: 10.1016/j.inffus.2023.102157. [20] LIU Z H, ZENG X F, LI J H, et al. Individual Entity Induced Label Concept Set for Classification: An Information Fusion Viewpoint. Information Fusion, 2024. DOI: 10.1016/j.inffus.2024.102495. [21] FAN M, LUO S, LI J H. Network Rule Extraction under the Network Formal Context Based on Three-Way Decision. Applied Inte-lligence, 2023, 53(5): 5126-5145. [22] 范敏,郭瑞欣,李金海. 网络决策形式背景下基于因果力的邻域推荐算法.模式识别与人工智能, 2022, 35(11): 977-988. (FAN M, GUO R X, LI J H. Neighborhood Recommendation Algorithm Based on Causality Force under Network Formal Decision Context. Pattern Recognition and Artificial Intelligence, 2022, 35(11): 977-988.) [23] FAN M, LI H. Graph Classification Method Based on Fuzzy Entropy Causality in a Network Formal Context. IEEE Transactions on Fuzzy Systems, 2024, 32(9): 5018-5032. [24] YAN M Y, LI J H. Knowledge Discovery and Updating under the Evolution of Network Formal Contexts Based on Three-Way Decision. Information Sciences, 2022, 601: 18-38. [25] 范敏,任文秀,李金海. 网络形式背景下的知识流动方法研究.模糊系统与数学, 2023, 37(1): 58-74. (FAN M, REN W X, LI J H. Research on Knowledge Flow Me-thods Based on Network Formal Context. Fuzzy Systems and Mathematics, 2023, 37(1): 58-74.) [26] MORENS D M, FAUCI A S. Emerging Infectious Diseases: Threats to Human Health and Global Stability. PLoS Pathogens, 2013, 9(7). DOI: 10.1371/journal.ppat.1003467. [27] GE X Y, LI J L, YANG X L, et al. Isolation and Characterization of a Bat SARS-Like Coronavirus that Uses the ACE2 Receptor. Nature, 2013, 503(7477): 535-538. [28] WANG B H, CHEN W S, WANG J C, et al. Cooperative Tracking Control of Multiagent Systems: A Heterogeneous Coupling Network and Intermittent Communication Framework. IEEE Transactions on Cybernetics, 2019, 49(12): 4308-4320. [29] GRANELL C, GÓMEZ S, ARENAS A. Dynamical Interplay Between Awareness and Epidemic Spreading in Multiplex Networks. Physical Review Letters, 2013, 111(12). DOI: 10.1103/PhysRevLett.111.128701. [30] GRANELL C, GÓMEZ S, ARENAS A. Competing Spreading Pro-cesses on Multiplex Networks: Awareness and Epidemics. Physical Review E, 2014, 90(1). DOI: 10.1103/PhysRevE.90.012808. [31] WANG Z S, XIA C Y, CHEN Z Q, et al. Epidemic Propagation with Positive and Negative Preventive Information in Multiplex Networks. IEEE Transactions on Cybernetics, 2021, 51(3): 1454-1462. [32] HE L, ZHU L H. Modeling the COVID-19 Epidemic and Awareness Diffusion on Multiplex Networks. Communications in Theoretical Physics, 2021, 73(3). DOI: 10.1088/1572-9494/abd84a. [33] GUO H L, WANG Z S, SUN S W, et al. Interplay Between Epidemic Spread and Information Diffusion on Two-Layered Networks with Partial Mapping. Physics Letters A, 2021, 398. DOI: 10.1016/j.physleta.2021.127282. [34] GUO H L, YIN Q, XIA C Y, et al. Impact of Information Diffusion on Epidemic Spreading in Partially Mapping Two-Layered Time-Varying Networks. Nonlinear Dynamics, 2021, 105(4): 3819-3833. [35] MA W C, ZHANG P, ZHAO X, et al. The Coupled Dynamics of Information Dissemination and SEIR-Based Epidemic Spreading in Multiplex Networks. Physica A: Statistical Mechanics and Its Applications, 2022, 588. DOI: 10.1016/j.physa.2021.126558. [36] XIA C Y, WANG Z S, ZHENG C Y, et al. A New Coupled Disease-Awareness Spreading Model with Mass Media on Multiplex Networks. Information Sciences, 2019, 471: 185-200. [37] LI D D, XIE W J, HAN D, et al. A Multi-information Epidemic Spreading Model on a Two-Layer Network. Information Sciences, 2023, 651. DOI: 10.1016/j.ins.2023.119723. [38] WANG H, MA C, CHEN H S, et al. Effects of Asymptomatic Infection and Self-Initiated Awareness on the Coupled Disease-Awareness Dynamics in Multiplex Networks. Applied Mathematics and Computation, 2021, 400. DOI: 10.1016/j.amc.2021.126084. [39] ZHOU J L, LIU H Y. Modeling the Impact of Virtual Contact Network with Community Structure on the Epidemic Spreading. Complexity, 2022, 2022(1). DOI: 10.1155/2022/9551912. [40] FENG M Y, LI X X, LI Y H, et al. The Impact of Nodes of Information Dissemination on Epidemic Spreading in Dynamic Multiplex Networks. Chaos, 2023, 33(4). DOI: 10.1063/5.0142386. [41] HU X, WANG Z S, SUN Q Y, et al. Coupled Propagation Between One Communicable Disease and Related Two Types of Information on Multiplex Networks with Simplicial Complexes. Physica A: Statistical Mechanics and Its Applications, 2024, 645. DOI: 10.1016/j.physa.2024.129832. [42] 张玉朋,李香菊,李超,等.基于Transformer与异质图神经网络的新闻推荐模型.模式识别与人工智能, 2022, 35(9): 839-848. (ZHANG Y P, LI X J, LI C, et al. News Recommendation Model Based on Transformer and Heterogeneous Graph Neural Network. Pattern Recognition and Artificial Intelligence, 2022, 35(9): 839-848.) [43] 吴志泽,陈盛,檀明,等.基于跨通道特征增强图卷积网络的骨架行为识别.模式识别与人工智能, 2024, 37(8): 703-714. (WU Z Z, CHEN S, TAN M, et al. Cross-Channel Feature-Enhanced Graph Convolutional Network for Skeleton-Based Action Recognition. Pattern Recognition and Artificial Intelligence, 2024, 37(8): 703-714.) [44] 杜永萍,牛晋宇,王陆霖,等.基于时间卷积注意力神经网络的序列推荐模型.模式识别与人工智能, 2022, 35(5): 472-480. (DU Y P, NIU J Y, WANG L L, et al. Sequential Recommendation Model Based on Temporal Convolution Attention Neural Network. Pattern Recognition and Artificial Intelligence, 2022, 35(5): 472-480.) [45] LECUN Y, BENGIO Y, HINTON G. Deep Learning. Nature, 2015, 521(7553): 436-444. [46] 薛峰,刘凯,王东,等.基于深度神经网络和加权隐反馈的个性化推荐.模式识别与人工智能, 2020, 33(4): 295-302. (XUE F, LIU K, WANG D, et al. Personalized Recommendation Algorithm Based on Deep Neural Network and Weighted Implicit Feedback. Pattern Recognition and Artificial Intelligence, 2020, 33(4): 295-302.) [47] WANG Z S, XIA C Y. Co-evolution Spreading of Multiple Information and Epidemics on Two-Layered Networks under the Influence of Mass Media. Nonlinear Dynamics, 2020, 102: 3039-3052. [48] BERNHEIM B D. A Theory of Conformity. Journal of Political Eco-nomy, 1994, 102(5): 841-877. [49] CIALDINI R B, GOLDSTEIN N J. Social Influence: Compliance and Conformity. Annual Review of Psychology, 2004, 55(1): 591-621. [50] IHME COVID-19 Health Service Utilization Forecasting Team. Fore-casting the Impact of The First Wave of The COVID-19 Pandemic on Hospital Demand and Deaths for the USA and European Economic Area Countries[J/OL]. [2024-12-15]. https://www.medrxiv.org/content/10.1101/2020.04.21.20074732v1.full.pdf. [51] ROGERS E M, SINGHAL A, QUINLAN M M. Diffusion of Innovations. 5th Edition. New York, USA: Free Press, 2003. [52] GÓMEZ S, ARENAS A, BORGE-HOLTHOEFER J, et al. Discrete-Time Markov Chain Approach to Contact-Based Disease Sprea-ding in Complex Networks. Europhysics Letters, 2010, 89(3). DOI: 10.1209/0295-5075/89/38009. [53] GÓMEZ S, GÓMEZ-GARDEÑES J, MORENO Y, et al. Nonperturbative Heterogeneous Mean-Field Approach to Epidemic Spreading in Complex Networks. Physical Review E, 2011, 84(3). DOI: 10.1103/PhysRevE.84.036105.
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