Estimating thresholds for asynchronous susceptible-infected-removed model on complex networks
Abstract: We use the pair heterogeneous mean-field (PHMF) approximation for an asynchronous version of the susceptible-infected-removed (SIR) model to estimate the epidemic thresholds on complex quenched networks. Our results indicate an improvement compared to the heuristic heterogeneous mean-field theory developed for one vertex (HMF) when the dynamic evolves on top random regular and power-law networks. However, there is a slight overestimation of the transition point for the later network type. We also analyze scaling for random regular networks near the thresholds. For this region, collapses were shown at the subcritical and supercritical phases.
- W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics–i. 1927., Bulletin of mathematical biology 53 (1991) 33–55.
- W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics. ii.—the problem of endemicity, Proceedings of the Royal Society of London. Series A, containing papers of a mathematical and physical character 138 (1932) 55–83.
- W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics. iii.—further studies of the problem of endemicity, Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character 141 (1933) 94–122.
- T. Hasegawa, K. Nemoto, Outbreaks in susceptible-infected-removed epidemics with multiple seeds, Phys. Rev. E 93 (2016) 032324. URL: https://link.aps.org/doi/10.1103/PhysRevE.93.032324. doi:10.1103/PhysRevE.93.032324.
- Droplet finite-size scaling theory of asynchronous sir model on quenched scale-free networks, Physica A: Statistical Mechanics and its Applications 626 (2023) 129102. URL: https://www.sciencedirect.com/science/article/pii/S037843712300657X. doi:https://doi.org/10.1016/j.physa.2023.129102.
- Epidemic processes in complex networks, Rev. Mod. Phys. 87 (2015) 925–979.
- Phys. Lett. A 384 (2020) 126063.
- T. Tomé, M. J. de Oliveira, Susceptible-infected-recovered and susceptible-exposed-infected models, Journal of Physics A: Mathematical and Theoretical 44 (2011) 095005. URL: https://dx.doi.org/10.1088/1751-8113/44/9/095005. doi:10.1088/1751-8113/44/9/095005.
- T. Tomé, R. M. Ziff, Phys. Rev. E 82 (2010) 051921.
- Phys. Rev. E 71 (2005) 027103.
- A.-L. Barabási, R. Albert, Emergence of scaling in random networks, science 286 (1999) 509–512.
- A. Barrat, R. Pastor-Satorras, Rate equation approach for correlations in growing network models, Phys. Rev. E 71 (2005) 036127. URL: https://link.aps.org/doi/10.1103/PhysRevE.71.036127. doi:10.1103/PhysRevE.71.036127.
- Heterogeneous pair-approximation for the contact process on complex networks, New Journal of Physics 16 (2014) 053006. URL: https://dx.doi.org/10.1088/1367-2630/16/5/053006. doi:10.1088/1367-2630/16/5/053006.
- A. S. Mata, S. C. Ferreira, Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks, Europhysics Letters 103 (2013) 48003. URL: https://dx.doi.org/10.1209/0295-5075/103/48003. doi:10.1209/0295-5075/103/48003.
- Q. Wu, T. Hadzibeganovic, Pair quenched mean-field approach to epidemic spreading in multiplex networks, Applied Mathematical Modelling 60 (2018) 244–254. URL: https://www.sciencedirect.com/science/article/pii/S0307904X18301276. doi:https://doi.org/10.1016/j.apm.2018.03.011.
- T. Tomé, R. M. Ziff, Critical behavior of the susceptible-infected-recovered model on a square lattice, Physical Review E 82 (2010) 051921.
- Epidemic outbreaks on random voronoi–delaunay triangulations, Physica A: Statistical Mechanics and its Applications 541 (2020) 122800. URL: https://www.sciencedirect.com/science/article/pii/S0378437119315882. doi:https://doi.org/10.1016/j.physa.2019.122800.
- Epidemic outbreaks on two-dimensional quasiperiodic lattices, Physics Letters A 384 (2020) 126063.
- R. Albert, A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74 (2002) 47–97.
- Critical phenomena in complex networks, Rev. Mod. Phys. 80 (2008) 1275–1335.
- Droplet finite-size scaling of the contact process on scale-free networks revisited, International Journal of Modern Physics C 34 (2023) 2350105.
- Comparison of theoretical approaches for epidemic processes with waning immunity in complex networks, Phys. Rev. E 106 (2022) 034317. URL: https://link.aps.org/doi/10.1103/PhysRevE.106.034317. doi:10.1103/PhysRevE.106.034317.
- Generation of uncorrelated random scale-free networks, Physical review e 71 (2005) 027103.
- Cut-offs and finite size effects in scale-free networks, The European Physical Journal B 38 (2004) 205–209.
- M. E. Newman, R. M. Ziff, Fast monte carlo algorithm for site or bond percolation, Physical Review E 64 (2001) 016706.
- J. Stat. Mech. 2011 (2011) 27202.
- E. Ben-Naim, P. Krapivsky, Size of outbreaks near the epidemic threshold, Physical Review E 69 (2004) 050901.
- D. A. Kessler, N. M. Shnerb, Solution of an infection model near threshold, Phys. Rev. E 76 (2007) 010901. URL: https://link.aps.org/doi/10.1103/PhysRevE.76.010901. doi:10.1103/PhysRevE.76.010901.
- Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks, Chaos: An Interdisciplinary Journal of Nonlinear Science 25 (2015).
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