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Epidemic spreading with migration in networked metapopulation. (English) Zbl 07840919

Summary: Migration plays a crucial role in epidemic spreading, and its dynamic can be studied by metapopulation model. Instead of the uniform mixing hypothesis, we adopt networked metapopulation to build the model of the epidemic spreading and the individuals’ migration. In these populations, individuals are connected by contact network and populations are coupled by individuals migration. With the network mean-field and the gravity law of migration, we establish the N-seat intertwined SIR model and obtain its basic reproduction number \(\mathscr{R}_0\). Meanwhile, we devise a non-Markov node-search algorithm for model statistical simulations. Through the static network migration ansatz and \(\mathscr{R}_0\) formula, we discover that migration will not directly increase the epidemic replication capacity. But when \(\mathscr{R}_0>1\), the migration will make the susceptive population evolve from metastable state (disease-free equilibrium) to stable state (endemic equilibrium), and then increase the influence area of epidemic. Re-evoluting the epidemic outbreak in Wuhan, top 94 cities empirical data validate the above mechanism. In addition, we estimate that the positive anti-epidemic measures taken by the Chinese government may have reduced 4 million cases at least during the first wave of COVID-19, which means those measures, such as the epidemiological investigation, nucleic acid detection in medium-high risk areas and isolation of confirmed cases, also play a significant role in preventing epidemic spreading after travel restriction between cities.

MSC:

92D30 Epidemiology
92D25 Population dynamics (general)

Software:

R0
Full Text: DOI

References:

[1] Chinazzi, M.; Davis, J. T.; Ajelli, M.; Gioannini, C.; Litvinova, M.; Merler, S., The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak, Science, 2020
[2] Davis, J. T.; Perra, N.; Zhang, Q.; Moreno, Y.; Vespignani, A., Phase transitions in information spreading on structured populations, Nat Phys, 1-7, 2020
[3] 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
[4] Salathé, M.; Kazandjieva, M.; Lee, J. W.; Levis, P.; Feldman, M. W.; Jones, J. H., A high-resolution human contact network for infectious disease transmission, Proc Nat Acad Sci, 107, 51, 22020-22025, 2010
[5] Sun, L.; Axhausen, K. W.; Lee, D.-H.; Huang, X., Understanding metropolitan patterns of daily encounters, Proc Nat Acad Sci, 110, 34, 13774-13779, 2013
[6] Barbosa, H.; Barthelemy, M.; Ghoshal, G.; James, C. R.; Lenormand, M.; Louail, T., Human mobility: Models and applications, Phys Rep, 734, 1-74, 2018 · Zbl 1395.91358
[7] Valdano, E.; Ferreri, L.; Poletto, C.; Colizza, V., Analytical computation of the epidemic threshold on temporal networks, Phys Rev X, 5, 2, Article 021005 pp., 2015
[8] Valdano, E.; Fiorentin, M. R.; Poletto, C.; Colizza, V., Epidemic threshold in continuous-time evolving networks, Phys Rev Lett, 120, 6, Article 068302 pp., 2018
[9] Koher, A.; Lentz, H. H.K.; Gleeson, J. P.; Hovel, P., Contact-based model for epidemic spreading on temporal networks, Phys Rev X, 9, 3, 1-20, 2019
[10] Wang, N.; Jin, Z.; Wang, Y.; Di, Z., Epidemics spreading in periodic double layer networks with dwell time, Phys A, 540, Article 123226 pp., 2020 · Zbl 07458014
[11] Arenas, A.; -Guilera, A. D.; Kurths, J.; Moreno, Y.; Zhou, C., Synchronization in complex networks, Phys Rep, 18, 3, Article 037111 pp., 2008
[12] Rodrigues, F. A.; Peron, T. K.D. M.; Ji, P.; Kurths, J., The Kuramoto model in complex networks, Phys Rep, 610, 1-98, 2016 · Zbl 1357.34089
[13] Acebron, J. A.; Bonilla, L. L.; Vicente, C. P.; Ritort, F.; Spigler, R., The Kuramoto model: A simple paradigm for synchronization phenomena, Rev Mod Phys, 77, 1, 137-185, 2005
[14] Doelling, K. B.; Assaneo, M. F.; Bevilacqua, D.; Pesaran, B.; Poeppel, D., An oscillator model better predicts cortical entrainment to music, Proc Nat Acad Sci, 116, 20, Article 201816414 pp., 2019
[15] Kralemann, B.; Fruhwirth, M.; Pikovsky, A.; Rosenblum, M.; Kenner, T.; Schaefer, J., In vivo cardiac phase response curve elucidates human respiratory heart rate variability, Nature Commun, 4, 1, 2418, 2013
[16] Erlander, S.; Stewart, N. F., The gravity model in transportation analysis: theory and extensions, 1990, Vsp · Zbl 0917.90115
[17] Barthélemy, M., Spatial networks, Phys Rep, 499, 1-3, 1-101, 2011
[18] Mckendrick, W. O.K. G., A contribution to the mathematical theory of epidemics, Proc R Soc Lond Ser A Math Phys Eng Sci, 115, 772, 700-721, 1927 · JFM 53.0517.01
[19] Van Mieghem, P.; Omic, J.; Kooij, R. E., Virus spread in networks, IEEE/ACM Trans Netw, 17, 1, 1-14, 2009
[20] Masuda, N., Effects of diffusion rates on epidemic spreads in metapopulation networks, New J Phys, 12, 9, Article 093009 pp., 2010
[21] Dreessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math Bio, 180, 1-2, 29-48, 2002 · Zbl 1015.92036
[22] Kiss IZ, Miller JC, Simon PL, et al. Mathematics of epidemics on networks. Springer; p. 384-9. · Zbl 1373.92001
[23] 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
[24] Moghadas, S., Analysis of an epidemic model with bistable equilibria using the Poincaré index, Appl Math Comput, 149, 3, 689-702, 2004 · Zbl 1034.92030
[25] Wang, W., Backward bifurcation of an epidemic model with treatment, Math Biosci, 201, 1-2, 58-71, 2006 · Zbl 1093.92054
[26] Lu, Y.; Jiang, G., Backward bifurcation and local dynamics of epidemic model on adaptive networks with treatment, Neurocomputing, 145, 113-121, 2014
[27] Jensen, G. G.; Uekermann, F.; Sneppen, K., Multi stability and global bifurcations in epidemic model with distributed delay SIRnS-model, Eur Phys J B, 92, 2, 28, 2019 · Zbl 1515.92073
[28] Rossman, G.; Fisher, J. C., Network hubs cease to be influential in the presence of low levels of advertising, Proc Nat Acad Sci, 118, 7, 2021
[29] Hu, B.; Qiu, J.; Chen, H.; Tao, V.; Wang, J.; Lin, H., First, second and potential third generation spreads of the COVID-19 epidemic in mainland China: An early exploratory study incorporating location-based service data of mobile devices, Int J Infect Dis, 96, 489-495, 2020
[30] Obadia, T.; Haneef, R.; Boëlle, P.-Y., The R0 package: A toolbox to estimate reproduction numbers for epidemic outbreaks, BMC Med Inform Decis Mak, 12, 1, 1-9, 2012
[31] Nishiura, H.; Linton, N. M.; Akhmetzhanov, A. R., Serial interval of novel coronavirus (COVID-19) infections, Int J Infect Dis, 93, 284-286, 2020
[32] Zhao, S.; Lin, Q.; Ran, J.; Musa, S. S.; Yang, G.; Wang, W., Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak, Int J Infect Dis, 92, 214-217, 2020
[33] Wallinga, J.; Lipsitch, M., How generation intervals shape the relationship between growth rates and reproductive numbers, Proc R Soc Lond [Biol], 274, 1609, 599-604, 2007
[34] Zhibin C. Chinese experts share experience in COVID-19 prevention and control at WHO information briefing, https://china.gov.cn.admin.kyber.vip/xinwen/2020-03/28/content_5496449.htm.
[35] National health commission of the People’s Republic of China, National Administration of Traditional Chinese Medicine. COVID-19 Diagnosis and Treatment Protocol (Trial Version 8), http://www.nhc.gov.cn/yzygj/s7653p/202008/0a7bdf12bd4b46e5bd28ca7f9a7f5e5a.shtml.
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