Epidemic spreading on one-way-coupled networks. (English) Zbl 1400.92548
Summary: Numerous real-world networks (e.g., social, communicational, and biological networks) have been observed to depend on each other, and this results in interconnected networks with different topology structures and dynamics functions. In this paper, we focus on the scenario of epidemic spreading on one-way-coupled networks comprised of two subnetworks, which can manifest the transmission of some zoonotic diseases. By proposing a mathematical model through mean-field approximation approach, we prove the global stability of the disease-free and endemic equilibria of this model. Through the theoretical and numerical analysis, we obtain interesting results: the basic reproduction number \(R_0\) of the whole network is the maximum of the basic reproduction numbers of the two subnetworks; \(R_0\) is independent of the cross-infection rate and cross contact pattern; \(R_0\) increases rapidly with the growth of inner infection rate if the inner contact pattern is scale-free; in order to eradicate zoonotic diseases from human beings, we must simultaneously eradicate them from animals; bird-to-bird infection rate has bigger impact on the human’s average infected density than bird-to-human infection rate.
References:
| [1] | Watts, D. J., The ‘new’ science of networks, Ann. Rev. Sociology, 30, 243-270 (2004) |
| [2] | Watts, D. J.; Strogatz, S. H., Collective dynamics of small-world networks, Nature, 393, 440-442 (1998) · Zbl 1368.05139 |
| [3] | Newman, M. E.J., The structure and function of complex networks, SIAM Rev., 45, 167-256 (2003) · Zbl 1029.68010 |
| [4] | Liu, H.; Cao, M.; Wu, C. W.; Lu, J. A.; Tse, C. K., Synchronization in directed complex networks using graph comparison tools, IEEE Trans. Circuits Syst. I. Regul. Pap., 62, 4, 1185-1194 (2015) · Zbl 1468.94912 |
| [5] | Castellano, C.; Pastor-Satorras, R., Competing activation mechanisms in epidemics on networks, Sci. Rep., 2, 371-376 (2012) |
| [6] | Pastor-Satorras, R.; Vespignani, A., Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86, 3200-3203 (2001) |
| [7] | Keeling, M. J.; Eames, K. T., Networks and epidemic models, J. R. Soc. Interface, 2, 4, 295-307 (2005) |
| [8] | Kivela, M.; Arenas, A.; Barthelemy, M., Multilayer networks, J. Complex Netw., 2, 3, 203-271 (2014) |
| [9] | Boccaletti, S.; Bianconi, G.; Criado, R., The structure and dynamics of multilayer networks, Phys. Rep., 544, 1, 1-122 (2014) |
| [10] | Gao, J.; Buldyrev, S. V.; Stanley, H. E., Networks formed from interdependent networks, Nat. Phys., 8, 40-48 (2012) |
| [11] | Saumell-Mendiola, A.; Serrano, M. A.; Boguna, M., Epidemic spreading on interconnected networks, Phys. Rev. E, 86, Article 026106 pp. (2012) |
| [12] | Son, S. W.; Bizhani, G.; Christensen, C., Percolation theory on interdependent networks based on epidemic spreading, Europhys. Lett., 97, 1, 16006 (2012) |
| [13] | Dickison, M.; Havlin, S.; Stanley, H. E., Epidemics on interconnected networks, Phys. Rev. E, 85, Article 066109 pp. (2012) |
| [14] | Zhao, D.; Li, L.; Peng, H., Multiple routes transmitted epidemics on multiplex networks, Phys. Lett. A, 378, 770-776 (2014) · Zbl 1323.92216 |
| [15] | Liu, M.; Li, D.; Qin, P., Epidemics in interconnected small-world networks, PLoS ONE, 10, 3, e0120701 (2015) |
| [16] | Sahneh, F. D.; Scoglio, C.; Fahmida, N. C., Effect of coupling on the epidemic threshold in interconnected complex networks: a spectral analysis, Amer. Contr. Conf. (ACC) IEEE, 2013, 2307-2312 (2013) |
| [17] | Granell, C.; Gomez, S.; Arenas, A., Dynamical interplay between awareness and epidemic spreading in multiplex networks, Phys. Rev. Lett., 111, Article 128701 pp. (2013) |
| [18] | Wang, H.; Li, Q.; DAgostino, G., Effect of the interconnected network structure on the epidemic threshold, Phys. Rev. E, 88, Article 022801 pp. (2013) |
| [19] | Bonaccorsi, S.; Ottaviano, S.; Pellegrini, F. D., Epidemic outbreaks in two-scale community networks, Phys. Rev. E, 90, Article 012810 pp. (2014) |
| [20] | Fu, X. C.; Small, M.; Chen, G. R., Networked models for SARS and avian influenza, (Propagation Dynamics on Complex Networks: Models, Methods and Stability Analysis (2014), John Wiley & Sons, Inc.: John Wiley & Sons, Inc. Hoboken, NJ), Higher Education Press, Beijing, Ch.4 · Zbl 1308.92005 |
| [22] | Hsieh, Y.; Wu, J.; Fang, J., Quantification of bird-to-bird and bird-to-human infections during 2013 novel H7N9 avian influenza outbreak in China, PLoS ONE, 9, 12, e111834 (2014) |
| [23] | Che, S.; Xue, Y.; Ma, L., The stability of highly pathogenic avian influenza epidemic model with saturated contact rate, Appl. Math., 5, 3365-3371 (2014) |
| [24] | Wang, R.; Jin, Z.; Liu, Q., A simple stochastic model with environmental transmission explains multi-year periodicity in outbreaks of avian flu, PLoS ONE, 7, 2, e28873 (2012) |
| [25] | Zhang, J.; Jin, Z.; Sun, G. Q., Determination of original infection source of H7N9 avian influenza by dynamical model, Sci. Rep., 4, 4846 (2014) |
| [26] | Pastor-Satorras, R.; Vespignani, A., Epidemic dynamics in finite size scale-free networks, Phys. Rev. E, 65, Article 035108 pp. (2002) |
| [27] | May, R. M.; Lioyd, A. L., Infection dynamics on scale-free networks, Phys. Rev. E, 64, Article 066112 pp. (2001) |
| [28] | den Driessche, P. V.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29-48 (2002) · Zbl 1015.92036 |
| [29] | Zhao, X. Q.; Jing, Z. J., Global asymptotic behavior in some cooperative systems of functional diferential equations, Canadian Appl. Math. Quarterly, 4, 421-444 (1996) · Zbl 0888.34038 |
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.
