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The dynamical analysis of simplicial SAIS epidemic model with awareness programs by media

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  • Liu, Maoxing
  • Ren, Xuejie
  • Peng, Yu
  • Sun, Yongzheng

Abstract

In this paper, we propose an SAIS epidemic model with awareness programs by media on higher-order networks to study the impact of media and higher-order networks on disease transmission, in which the simplicial complex is utilized to construct a social network that describes connections between nodes, where a single link can connect more than two individuals. We use the cumulative density of awareness programs to quantify the impact of media and use the Microscopic Markov Chains method to get the probability evolution equation of each node. In order to solve the computational difficulties caused by the excessively high dimension of the equation, we use the mean field method to reduce the dimension of the equation to get the equilibrium of the system. Through dynamical analysis, we obtain the threshold of disease outbreak and conditions for the existence and stability of the disease-free equilibrium and the endemic equilibrium. The numerical simulations of SAIS model prove that the mean field method has good predictive performance. We also obtain the influence of parameters on threshold and system dynamical behavior through sensitivity analysis. The results show that: on one hand, the introduce of 2-simplex increases the probability of disease transmission in healthy populations, and the system appears discontinuous transition and bistable coexistence of health state and disease epidemic state, on the other hand, awareness programs by media can increase the threshold of disease outbreak, decrease the final density of infected individuals and inhibit the explosive growth of disease, thus effectively control the spread of diseases.

Suggested Citation

  • Liu, Maoxing & Ren, Xuejie & Peng, Yu & Sun, Yongzheng, 2024. "The dynamical analysis of simplicial SAIS epidemic model with awareness programs by media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 649(C).
    • Handle: RePEc:eee:phsmap:v:649:y:2024:i:c:s0378437124004825
    DOI: 10.1016/j.physa.2024.129973
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Li, WenYao & Xue, Xiaoyu & Pan, Liming & Lin, Tao & Wang, Wei, 2022. "Competing spreading dynamics in simplicial complex," Applied Mathematics and Computation, Elsevier, vol. 412(C).
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    1. Qin, Yuyan & Yang, Lixin & Li, Jia & Li, Mengjiao & Du, Meng Meng, 2024. "A simplicial SSIS epidemic model with the outgoing pressure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 654(C).
    2. Liu, Maoxing & Peng, Yu & Ren, Xuejie & Zhang, Juping, 2026. "Dynamical analysis of simplicial epidemic model with demographic and aware effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 483-504.

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