Epidemic thresholds identification of susceptible-infected-recovered model based on the eigen microstate. (English) Zbl 1511.92091
Summary: Epidemic threshold estimation plays a critical role in prevention strategies. Besides theoretical methods, some numerical methods estimate the threshold through the scale divergence of outbreak size near critical state. But the bimodal distribution of outbreak size may make the estimated threshold higher. In this paper, we extend the Eigen Microstate (EM) method to the susceptible-infected-recovered (SIR) epidemic model and devise the eigen measure to estimate the threshold using the scale divergence of singular values. Compared with the susceptibility and variability measure, the estimated threshold of eigen measure is closer to the theoretical results of the heterogeneous mean-field (HMF) and the quenched mean-field (QMF). In addition, better than the assortativity coefficient, network mean degree or dimension has a more significant effect on estimation accuracy. Under complex epidemic mechanisms, such as periodic time-varying networks and migration between networked populations, the threshold estimation of QMF models indicates that the eigen measure is more stable and accurate than the other two measures. Combined with renormalization group theory, our method may have practical significance in megalopolis epidemic warning.
MSC:
| 92D30 | Epidemiology |
Keywords:
epidemic threshold; eigen microstate; epidemic dynamics; double-layer network; networked metapopulationReferences:
| [1] | Green, M. S.; Swartz, T.; Mayshar, E.; Lev, B.; Shemer, J., When is an epidemic an epidemic?, Israel Medical Association Journal Imaj, 4, 1, 3-6 (2002) |
| [2] | Hindes, J.; Assaf, M.; Schwartz, I. B., Outbreak size distribution in stochastic epidemic models, Phys. Rev. Lett., 128, 7, 078301 (2022) |
| [3] | Rypdal, M.; Sugihara, G., Inter-outbreak stability reflects the size of the susceptible pool and forecasts magnitudes of seasonal epidemics, Nat Commun, 10, 1, 1-8 (2019) |
| [4] | Newman, M. E., Spread of epidemic disease on networks, Physical review E, 66, 1, 016128 (2002) |
| [5] | Keeling, M. J.; Eames, K. T., Networks and epidemic models, Journal of the royal society interface, 2, 4, 295-307 (2005) |
| [6] | Pastor-Satorras, R.; Castellano, C.; Van Mieghem, P.; Vespignani, A., Epidemic processes in complex networks, Rev Mod Phys, 87, 3, 925 (2015) |
| [7] | Wang, N.-N.; Jin, Z.; Wang, Y.-J.; Di, Z.-R., Epidemics spreading in periodic double layer networks with dwell time, Physica A, 540, 123226 (2020) · Zbl 07458014 |
| [8] | Hong, X.; Han, Y.; Wang, B., Impacts of detection and contact tracing on the epidemic spread in time-varying networks, Appl Math Comput, 439, 127601 (2023) · Zbl 07689962 |
| [9] | Guo, H.; Yin, Q.; Xia, C.; Dehmer, M., Impact of information diffusion on epidemic spreading in partially mapping two-layered time-varying networks, Nonlinear Dyn, 105, 4, 3819-3833 (2021) |
| [10] | Granell, C.; Gomez, S.; Arenas, A., Dynamical interplay between awareness and epidemic spreading in multiplex networks, Phys. Rev. Lett., 111, 12, 128701 (2013) |
| [11] | Wang, N.-N.; Wang, Y.-J.; Qiu, S.-H.; Di, Z.-R., Epidemic spreading with migration in networked metapopulation, Commun. Nonlinear Sci. Numer. Simul., 109, 106260 (2022) · Zbl 07840919 |
| [12] | Zhu, X.; Liu, Y.; Wang, S.; Wang, R.; Chen, X.; Wang, W., Allocating resources for epidemic spreading on metapopulation networks, Appl Math Comput, 411, 126531 (2021) · Zbl 1510.92259 |
| [13] | Ferreira, S. C.; Castellano, C.; Pastor-Satorras, R., Epidemic thresholds of the susceptible-infected-susceptible model on networks: a comparison of numerical and theoretical results, Physical Review E, 86, 4, 041125 (2012) |
| [14] | Shu, P.; Wang, W.; Tang, M.; Do, Y., Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25, 6, 063104 (2015) |
| [15] | Zhang, X.; Hu, G.; Zhang, Y.; Li, X.; Chen, X., Finite-size scaling of correlation functions in finite systems, Science China Physics, Mechanics & Astronomy, 61, 12, 120511 (2018) |
| [16] | Sun, Y.; Hu, G.; Zhang, Y.; Lu, B.; Lu, Z.; Fan, J.; Li, X.; Deng, Q.; Chen, X., Eigen microstates and their evolutions in complex systems, Commun Theor Phys, 73, 6, 065603 (2021) · Zbl 1521.82019 |
| [17] | Li, X.-T.; Chen, X.-S., Critical behaviors and finite-size scaling of principal fluctuation modes in complex systems, Commun Theor Phys, 66, 355-362 (2016) |
| [18] | Li, X.; Xue, T.; Sun, Y.; Fan, J.; Li, H.; Liu, M.; Han, Z.; Di, Z.; Chen, X., Discontinuous and continuous transitions of collective behaviors in living systems*, Chin. Phys. B, 30, 12, 128703 (2021) |
| [19] | Hu, G.; Liu, T.; Liu, M.; Chen, W.; Chen, X., Condensation of Eigen Microstate in statistical ensemble and phase transition, Science China Physics, Mechanics & Astronomy, 62, 9, 990511 (2019) |
| [20] | Marro, J.; Dickman, R., Nonequilibrium phase transitions in lattice models, Nonequilibrium Phase Transitions in Lattice Models (2005) |
| [21] | Saumell-Mendiola, A.; Serrano, M.Á.; Boguná, M., Epidemic spreading on interconnected networks, Physical Review E, 86, 2, 026106 (2012) |
| [22] | Christensen, K.; Moloney, N. R., Complexity and Criticality (2005), Complexity and Criticality |
| [23] | Kiss, I. Z.; Miller, J. C.; Simon, P. L., Mathematics of epidemics on networks: from exact to approximate models, volume 46 (2017), Springer International Publishing · Zbl 1373.92001 |
| [24] | Pastor-Satorras, R.; Vespignani, A., Epidemic dynamics and endemic states in complex networks, Physical Review E, 63, 6, 066117 (2001) |
| [25] | Kuznetsov, Y. A., Elements of applied bifurcation theory, applied mathematical sciences, 288, 2, 5-10 (2004) · Zbl 1082.37002 |
| [26] | Colizza, V.; Vespignani, A., Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations, J. Theor. Biol., 251, 3, 450-467 (2008) · Zbl 1398.92233 |
| [27] | Meloni, S.; Perra, N.; Arenas, A.; Gmez, S.; Vespignani, A., Modeling human mobility responses to the large-scale spreading of infectious diseases, Sci Rep, 1, 62, 62 (2011) |
| [28] | Poletto, C.; Tizzoni, M.; Colizza, V., Heterogeneous length of stay of hosts’ movements and spatial epidemic spread, Sci Rep, 2, 476 (2012) |
| [29] | Van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math Biosci, 180, 1-2, 29-48 (2002) · Zbl 1015.92036 |
| [30] | Liu, T.; Hu, G.-K.; Dong, J.-Q.; Fan, J.-F.; Liu, M.-X.; Chen, X.-S., Renormalization group theory of Eigen Microstates, Chin. Phys. Lett., 39, 8, 080503 (2022) |
| [31] | Pitaevskii, L.; Stringari, S., Bose-einstein condensation, Phys. Rev. Lett., 103, 20, 200402 (2009) |
| [32] | Boguá, M.; Pastor-Satorras, R.; Vespignani, A., Epidemic spreading in complex networks with degree correlations, Statistical Mechanics of Complex Networks, 127-147 (2003), Springer · Zbl 1132.92338 |
| [33] | Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F.F., Critical phenomena in complex networks, Rev Mod Phys, 80, 4, 1294-1296 (2008) |
| [34] | Wang, Y.; Ma, J.; Cao, J., Basic reproduction number for the sir epidemic in degree correlated networks, Physica D, 433, 133183 (2022) · Zbl 1486.92296 |
| [35] | Youssef, M.; Scoglio, C., An individual-based approach to sir epidemics in contact networks, J. Theor. Biol., 283, 1, 136 (2011) · Zbl 1397.92697 |
| [36] | Liu, L.; Luo, X.; Chang, L., Vaccination strategies of an sir pair approximation model with demographics on complex networks, Chaos Solitons & Fractals, 104, 282-290 (2017) · Zbl 1380.92076 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
