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Compact pairwise methods for susceptible–infected–susceptible epidemics on weighted heterogeneous networks

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  • Wu, Qingchu
  • Kabir, K.M. Ariful

Abstract

We analyze the spreading of susceptible–infected–susceptible epidemics on random networks with general weight and degree distributions. We generalize the compact pairwise mean-field model from the unweighted network to the weighted network. By using the probability theory, we also develop an asymmetrical compact model, which takes into account the transitivity of edges where a vertex passes the disease to a neighboring node. Simulations show that the new model outperforms the previous method on scale-free networks. In addition, the condition of epidemic outbreak is analytically derived based on the perron complement of a matrix. Our results suggest that the heterogeneity of weight distribution can remarkably decrease the likelihood of an epidemic outbreak for the nonlinear transmission rate. Interestingly, the epidemic threshold can be slightly affected by the weight heterogeneity on a heterogeneous network but cannot on a homogeneous network for the linear transmission rate.

Suggested Citation

  • Wu, Qingchu & Kabir, K.M. Ariful, 2023. "Compact pairwise methods for susceptible–infected–susceptible epidemics on weighted heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    • Handle: RePEc:eee:phsmap:v:621:y:2023:i:c:s0378437123003606
    DOI: 10.1016/j.physa.2023.128805
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    References listed on IDEAS

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    1. Sun, Qingyi & Wang, Zhishuang & Zhao, Dawei & Xia, Chengyi & Perc, Matjaž, 2022. "Diffusion of resources and their impact on epidemic spreading in multilayer networks with simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Nie, Yanyi & Zhong, Xiaoni & Lin, Tao & Wang, Wei, 2022. "Homophily in competing behavior spreading among the heterogeneous population with higher-order interactions," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    3. Qu, Bo & Wang, Huiijuan, 2017. "SIS epidemic spreading with correlated heterogeneous infection rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 13-24.
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    5. Wu, Qingchu & Zhang, Fei, 2016. "Threshold conditions for SIS epidemic models on edge-weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 77-83.
    6. Nie, Yanyi & Li, Wenyao & Pan, Liming & Lin, Tao & Wang, Wei, 2022. "Markovian approach to tackle competing pathogens in simplicial complex," Applied Mathematics and Computation, Elsevier, vol. 417(C).
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