{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T05:12:16Z","timestamp":1779081136042,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,2]],"date-time":"2023-05-02T00:00:00Z","timestamp":1682985600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The impact of COVID-19 is global, and uncertain information will affect product quality and worker efficiency in the complex supply chain network, thus bringing risks. Aiming at individual heterogeneity, a partial mapping double-layer hypernetwork model is constructed to study the supply chain risk diffusion under uncertain information. Here, we explore the risk diffusion dynamics, drawing on epidemiology, and establish an SPIR (Susceptible\u2013Potential\u2013Infected\u2013Recovered) model to simulate the risk diffusion process. The node represents the enterprise, and hyperedge represents the cooperation among enterprises. The microscopic Markov chain approach (MMCA) is used to prove the theory. Network dynamic evolution includes two removal strategies: (i) removing aging nodes; (ii) removing key nodes. Using Matlab to simulate the model, we found that it is more conducive to market stability to eliminate outdated enterprises than to control key enterprises during risk diffusion. The risk diffusion scale is related to interlayer mapping. Increasing the upper layer mapping rate to strengthen the efforts of official media to issue authoritative information will reduce the infected enterprise number. Reducing the lower layer mapping rate will reduce the misled enterprise number, thereby weakening the efficiency of risk infection. The model is helpful for understanding the risk diffusion characteristics and the importance of online information, and it has guiding significance for supply chain management.<\/jats:p>","DOI":"10.3390\/e25050747","type":"journal-article","created":{"date-parts":[[2023,5,3]],"date-time":"2023-05-03T01:36:38Z","timestamp":1683077798000},"page":"747","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Supply Chain Risk Diffusion in Partially Mapping Double-Layer Hypernetworks"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8460-6701","authenticated-orcid":false,"given":"Ping","family":"Yu","sequence":"first","affiliation":[{"name":"School of Science, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4985-9003","authenticated-orcid":false,"given":"Zhiping","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya\u2019nan","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Science, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5164-4522","authenticated-orcid":false,"given":"Peiwen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.3389\/fpubh.2021.778671","article-title":"The Impact of COVID-19 Epidemic on the Development of the Digital Economy of China\u2014Based on the Data of 31 Provinces in China","volume":"9","author":"Xu","year":"2022","journal-title":"Front. Public Health"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2014","DOI":"10.1177\/00027642211003153","article-title":"The \u201cParallel Pandemic\u201d in the Context of China: The Spread of Rumors and Rumor-Corrections During COVID-19 in Chinese Social Media","volume":"65","author":"Song","year":"2021","journal-title":"Am. Behav. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhao, Z., Chen, D., Wang, L., and Han, C. (2018). Credit Risk Diffusion in Supply Chain Finance: A Complex Networks Perspective. Sustainability, 10.","DOI":"10.3390\/su10124608"},{"key":"ref_4","first-page":"5906901","article-title":"Research on Risk Diffusion Mechanism of Logistics Service Supply Chain in Urgent Scenarios","volume":"2020","author":"Zhang","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_5","first-page":"609","article-title":"Smart Supply Chain Risk Assessment in Intelligent Manufacturing","volume":"62","author":"Liu","year":"2022","journal-title":"J. Comput. Inf. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.isatra.2020.07.033","article-title":"An Intuitionistic Fuzzy Two Stage Supply Chain Network Design Problem with Multi-Mode Demand and Multi-Mode Transportation","volume":"107","author":"Niroomand","year":"2020","journal-title":"ISA Trans."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1186\/s13638-022-02209-0","article-title":"Blockchained Supply Chain Management Based on IoT Tracking and Machine Learning","volume":"2022","author":"Dong","year":"2022","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_8","first-page":"700","article-title":"A Contribution to the Mathematical Theory of Epidemics","volume":"115","author":"Kermack","year":"1927","journal-title":"Proc. R. Soc. Lond. Ser. A Contain. Pap. A Math. Phys. Character"},{"key":"ref_9","first-page":"94","article-title":"Contributions to the Mathematical Theory of Epidemics. III.\u2014Further Studies of the Problem of Endemicity","volume":"141","author":"Kermack","year":"1933","journal-title":"Proc. R. Soc. Lond. Ser. A Contain. Pap. A Math. Phys. Character"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.amc.2013.12.164","article-title":"How to Run a Campaign: Optimal Control of SIS and SIR Information Epidemics","volume":"231","author":"Kandhway","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"110259","DOI":"10.1016\/j.chaos.2020.110259","article-title":"Risk Transmission in Complex Supply Chain Network with Multi-Drivers","volume":"143","author":"Wang","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Liang, D., Bhamra, R., Liu, Z., and Pan, Y. (2022). Risk Propagation and Supply Chain Health Control Based on the SIR Epidemic Model. Mathematics, 10.","DOI":"10.3390\/math10163008"},{"key":"ref_13","first-page":"225","article-title":"The science of computing: Supernetworks","volume":"73","author":"Denning","year":"1985","journal-title":"Am. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/j.physa.2005.12.002","article-title":"Subgraph Centrality and Clustering in Complex Hyper-Networks","volume":"364","author":"Estrada","year":"2006","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.physa.2017.08.002","article-title":"Exploring the Evolutionary Mechanism of Complex Supply Chain Systems Using Evolving Hypergraphs","volume":"489","author":"Suo","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"122545","DOI":"10.1016\/j.physa.2019.122545","article-title":"Exploring the Dynamic Growth Mechanism of Social Networks Using Evolutionary Hypergraph","volume":"544","author":"Wang","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"127963","DOI":"10.1016\/j.physa.2022.127963","article-title":"Risk Propagation and Evolution Analysis of Multi-Level Handlings at Automated Terminals Based on Double-Layer Dynamic Network Model","volume":"605","author":"Li","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1051\/ro\/2022097","article-title":"Dual Channel Supply Chain Inventory Policies for Controllable Deteriorating Items Having Dynamic Demand under Trade Credit Policy with Default Risk","volume":"56","author":"Choudhury","year":"2022","journal-title":"RAIRO-Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"123506","DOI":"10.1016\/j.physa.2019.123506","article-title":"A New Model for Supply Chain Risk Propagation Considering Herd Mentality and Risk Preference under Warning Information on Multiplex Networks","volume":"545","author":"Huo","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"126226","DOI":"10.1016\/j.physa.2021.126226","article-title":"The Influence of Risk Attitude on Credit Risk Contagion\u2014Perspective of Information Dissemination","volume":"582","author":"Qian","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.physa.2018.08.169","article-title":"MM-SIS: Model for Multiple Information Spreading in Multiplex Network","volume":"513","author":"Xiao","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"125212","DOI":"10.1016\/j.physa.2020.125212","article-title":"Coupled Propagation Dynamics on Multiplex Activity-Driven Networks","volume":"561","author":"Hu","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s11036-018-1004-4","article-title":"Information Diffusion Model Based on Social Big Data","volume":"23","author":"Jin","year":"2018","journal-title":"Mob. Netw. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"115273","DOI":"10.1109\/ACCESS.2020.3004455","article-title":"Rumor Diffusion and Control Based on Double-Layer Dynamic Evolution Model","volume":"8","author":"Yin","year":"2020","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1140\/epjb\/e2010-00297-8","article-title":"Evolving Hypernetwork Model","volume":"77","author":"Wang","year":"2010","journal-title":"Eur. Phys. J. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.ins.2018.08.050","article-title":"A New Coupled Disease-Awareness Spreading Model with Mass Media on Multiplex Networks","volume":"471","author":"Xia","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yu, P., Wang, Z., Sun, Y., and Wang, P. (2022). Risk Diffusion and Control under Uncertain Information Based on Hypernetwork. Mathematics, 10.","DOI":"10.3390\/math10224344"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"126558","DOI":"10.1016\/j.physa.2021.126558","article-title":"The Coupled Dynamics of Information Dissemination and SEIR-Based Epidemic Spreading in Multiplex Networks","volume":"588","author":"Ma","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"964883","DOI":"10.3389\/fphy.2022.964883","article-title":"Effects of Individual Heterogeneity and Multi-Type Information on the Coupled Awareness-Epidemic Dynamics in Multiplex Networks","volume":"10","author":"Chen","year":"2022","journal-title":"Front. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3819","DOI":"10.1007\/s11071-021-06784-7","article-title":"Impact of Information Diffusion on Epidemic Spreading in Partially Mapping Two-Layered Time-Varying Networks","volume":"105","author":"Guo","year":"2021","journal-title":"Nonlinear Dyn."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/747\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:28:13Z","timestamp":1760124493000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/747"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,2]]},"references-count":30,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["e25050747"],"URL":"https:\/\/doi.org\/10.3390\/e25050747","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,2]]}}}