Simplicial epidemic model with a threshold policy

Hui Leng, Yi Zhao and Jianfeng Luo

Physica A: Statistical Mechanics and its Applications, 2024, vol. 653, issue C

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.

Keywords: Epidemic spreading; Simplicial complex; Threshold policy; Tristable state (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:653:y:2024:i:c:s0378437124005867

DOI: 10.1016/j.physa.2024.130077

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