{"title":"Simplicial epidemic model with a threshold policy","authors":"","doi":"10.1016/j.physa.2024.130077","DOIUrl":null,"url":null,"abstract":"<div><p>We establish a simplicial empty-susceptible–infected (ESI) model with consideration of threshold policy to depict the network-based epidemic transmission, where the underlying propagation structures are expanded from edges to higher-order structures. To address the epidemic evolution in an explicit network, we formulate the quenched mean-field probability evolution about each site, which is composed of non-smooth differential equations based on network topology. Remarkably, under the combined action of non-smooth and high-order structures, a tristable state is observed in empirical social networks, which is consistent with the coexistence of three stable equilibria by analysis of the mean-field system. Moreover, we find that a sliding mode exists in empirical social networks, which is also indicated by the theoretical analysis of the mean-field probability equations. Finally, the system is divided into the free subsystem without the threshold policy and control subsystem with the threshold policy. Both subsystems admit a stable disease-free equilibrium and a stable endemic equilibrium, as well as coexistence of a stable disease-free equilibrium and a stable pseudo equilibrium in the system, thereby admitting three types of the bistable state under the policy with different critical levels.</p></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica A: Statistical Mechanics and its Applications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378437124005867","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a simplicial empty-susceptible–infected (ESI) model with consideration of threshold policy to depict the network-based epidemic transmission, where the underlying propagation structures are expanded from edges to higher-order structures. To address the epidemic evolution in an explicit network, we formulate the quenched mean-field probability evolution about each site, which is composed of non-smooth differential equations based on network topology. Remarkably, under the combined action of non-smooth and high-order structures, a tristable state is observed in empirical social networks, which is consistent with the coexistence of three stable equilibria by analysis of the mean-field system. Moreover, we find that a sliding mode exists in empirical social networks, which is also indicated by the theoretical analysis of the mean-field probability equations. Finally, the system is divided into the free subsystem without the threshold policy and control subsystem with the threshold policy. Both subsystems admit a stable disease-free equilibrium and a stable endemic equilibrium, as well as coexistence of a stable disease-free equilibrium and a stable pseudo equilibrium in the system, thereby admitting three types of the bistable state under the policy with different critical levels.
期刊介绍:
Physica A: Statistical Mechanics and its Applications
Recognized by the European Physical Society
Physica A publishes research in the field of statistical mechanics and its applications.
Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents.
Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.