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An exploration and simulation of epidemic spread and its control in multiplex networks. (English) Zbl 1395.92166

Summary: The outbreak of an epidemic can trigger adaptive behavioral responses from individuals – these responses will then play an important role in the spread of the infection. In order to characterize the interaction between human adaptive behaviors and epidemic spread, we propose a concrete interplay model in quenched multiplex networks. We model interaction between individuals and spread of the infection, as individual layers within the multiplex networks. Susceptibility of each individual to infection can then be mitigated by the strength of his/her adaptive behaviors, which is a direct response to information transmission. The model we propose is generic and applicable to a range of public health scenarios. We provide a caricature model of individual opinion, coupled through information propagation to the opinion of others. As opinion synchronizes in the information network, infectivity is shown to decrease in the epidemic contact network. While simple, the model is a useful proxy for many real-life and more complex scenarios. In particular, we observe the phenomenon of oscillation in an epidemic network with adaptive behaviors, and find that the epidemic control strategy from the perspective of behavioral control is extremely relevant for epidemic control. As an example, our results on SARS, a potentially fatal disease, have demonstrated the improved understanding of behavioral effects on infectious disease dynamics and control.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations

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GenLouvain
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[1] R. M. Anderson, R. M. May, and B. Anderson, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1992.
[2] J. Arino, R. Jordan, and P. Van den Driessche, Quarantine in a multi-species epidemic model with spatial dynamics, Math. Biosci., 206 (2007), pp. 46–60. · Zbl 1124.92042
[3] F. Bagnoli, P. Lio, and L. Sguanci, Risk perception in epidemic modeling, Phys. Rev. E (3), 76 (2007), 061904.
[4] A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), pp. 509–512. · Zbl 1226.05223
[5] R. Barrera, M. Amador, and A. J. MacKay, Population dynamics of aedes aegypti and dengue as influenced by weather and human behavior in San Juan, Puerto Rico, PLoS Neglect. Trop. Dis., 5 (2011), e1378.
[6] C. T. Bauch and A. P. Galvani, Social factors in epidemiology, Science, 342 (2013), pp. 47–49.
[7] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics Appl. Math. 9, SIAM, Philadelphia, 1994. · Zbl 0815.15016
[8] G. Bianconi, Statistical mechanics of multiplex networks: Entropy and overlap, Phys. Rev. E (3), 87 (2013), 062806.
[9] S. M. Blower, A. R. Mclean, T. C. Porco, P. M. Small, P. C. Hopewell, M. A. Sanchez, and A. R. Moss, The intrinsic transmission dynamics of tuberculosis epidemics, Nature Med., 1 (1995), pp. 815–821.
[10] J. Borge-Holthoefer, R. A. Ban͂os, S. González-Bailón, and Y. Moreno, Cascading behaviour in complex socio-technical networks, J. Complex Netw., 1 (2013), pp. 3–24.
[11] A. Cardillo, C. Reyes-Suárez, F. Naranjo, and J. Gómez-Garden͂es, Evolutionary vaccination dilemma in complex networks, Phys. Rev. E (3), 88 (2013), 032803.
[12] T. Chen, X. Liu, and W. Lu, Pinning complex networks by a single controller, IEEE Trans. Circuits Syst. I Regul. Pap., 54 (2007), pp. 1317–1326. · Zbl 1374.93297
[13] G. Chowell, P. W. Fenimore, M. A. Castillo-Garsow, and C. Castillo-Chavez, Sars outbreaks in Ontario, Hong Kong and Singapore: The role of diagnosis and isolation as a control mechanism, J. Theoret. Biol., 224 (2003), pp. 1–8.
[14] O. Diekmann, J. A. P. Heesterbeek, and J. A. Metz, On the definition and the computation of the basic reproduction ratio r0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), pp. 365–382. · Zbl 0726.92018
[15] A. S. Fauci and D. M. Morens, Zika virus in the Americas—yet another arbovirus threat, New Engl. J. Med., 374 (2016), pp. 601–604.
[16] E. P. Fenichel, C. Castillo-Chavez, M. Ceddia, G. Chowell, P. A. G. Parra, G. J. Hickling, G. Holloway, R. Horan, B. Morin, C. Perrings, et al., Adaptive human behavior in epidemiological models, Proc. Natl. Acad. Sci. USA, 108 (2011), pp. 6306–6311.
[17] N. Ferguson, Capturing human behaviour, Nature, 446 (2007), pp. 733–733.
[18] H. Freedman, S. Ruan, and M. Tang, Uniform persistence and flows near a closed positively invariant set, J. Dynam. Differential Equations, 6 (1994), pp. 583–600. · Zbl 0811.34033
[19] F. Fu, D. I. Rosenbloom, L. Wang, and M. A. Nowak, Imitation dynamics of vaccination behaviour on social networks, R. Soc. Lond. Proc. Biol. Sci., 278 (2011), pp. 42–49.
[20] S. Funk, E. Gilad, C. Watkins, and V. A. Jansen, The spread of awareness and its impact on epidemic outbreaks, Proc. Natl. Acad. Sci. USA, 106 (2009), pp. 6872–6877. · Zbl 1203.91242
[21] S. Funk and V. A. Jansen, Interacting epidemics on overlay networks, Phys. Rev. E (3), 81 (2010), 036118.
[22] S. Funk, M. Salathé, and V. A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review, J. R. Soc. Interface, 7 (2010), pp. 1247–1256.
[23] J. W. Glasser, N. Hupert, M. M. Mccauley, and R. Hatchett, Modeling and public health emergency responses: Lessons from SARS, Epidemics, 3 (2011), pp. 32–37.
[24] S. Gómez, A. Arenas, J. Borge-Holthoefer, S. Meloni, and Y. Moreno, Discrete-time Markov chain approach to contact-based disease spreading in complex networks, EPL (Europhysics Letters), 89 (2010), 38009.
[25] J. Gómez-Gardenes, I. Reinares, A. Arenas, and L. M. Floría, Evolution of cooperation in multiplex networks, Sci. Rep., 2 (2012), p. 620.
[26] T. Gross and I. G. Kevrekidis, Robust oscillations in sis epidemics on adaptive networks: Coarse graining by automated moment closure, Europhys. Lett., 82 (2008), 38004.
[27] A. B. Gumel, S. Ruan, T. Day, J. Watmough, F. Brauer, P. Van den Driessche, D. Gabrielson, C. Bowman, M. E. Alexander, S. Ardal, et al., Modelling strategies for controlling SARS outbreaks, R. Soc. Lond. Proc. Biol. Sci., 271 (2004), pp. 2223–2232.
[28] V. Hatzopoulos, M. Taylor, P. L. Simon, and I. Z. Kiss, Multiple sources and routes of information transmission: Implications for epidemic dynamics, Math. Biosci., 231 (2011), pp. 197–209. · Zbl 1216.92053
[29] S.-B. Hsu and Y.-H. Hsieh, Modeling intervention measures and severity-dependent public response during severe acute respiratory syndrome outbreak, SIAM J. Appl. Math., 66 (2005), pp. 627–647. · Zbl 1087.92053
[30] M. J. Keeling and K. T. Eames, Networks and epidemic models, J. R. Soc. Interface, 2 (2005), pp. 295–307.
[31] S. Kitchovitch and P. Lio, Risk perception and disease spread on social networks, Procedia Comput. Sci., 1 (2010), pp. 2345–2354.
[32] J. P. LaSalle, The Stability of Dynamical Systems, CBMS-NSP Regional Conf. Ser. Appl. Math. 25, SIAM, Philadelphia 1976.
[33] K. Z. Li, Z. J. Ma, Z. Jia, M. Small, and X. C. Fu, Interplay between collective behavior and spreading dynamics on complex networks, Chaos, 22 (2012), 043113. · Zbl 1320.90010
[34] M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, Global dynamics of a SEIR model with varying total population size, Math. Biosci., 160 (1999), pp. 191–213. · Zbl 0974.92029
[35] M. Y. Li and Z. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Differential Equations, 248 (2010), pp. 1–20. · Zbl 1190.34063
[36] Z. Li, G. Feng, and D. Hill, Controlling complex dynamical networks with coupling delays to a desired orbit, Phys. Lett. A, 359 (2006), pp. 42–46. · Zbl 1209.93136
[37] J. O. Lloyd-Smith, A. P. Galvani, and W. M. Getz, Curtailing transmission of severe acute respiratory syndrome within a community and its hospital, R. Soc. Lond. Proc. Biol. Sci., 270 (2003), pp. 1979–1989.
[38] V. Marceau, P.-A. Noël, L. Hébert-Dufresne, A. Allard, and L. J. Dubé, Adaptive networks: Coevolution of disease and topology, Phys. Rev. E (3), 82 (2010), 036116.
[39] V. Marceau, P.-A. Noël, L. Hébert-Dufresne, A. Allard, and L. J. Dubé, Modeling the dynamical interaction between epidemics on overlay networks, Phys. Rev. E (3), 84 (2011), 026105.
[40] S. Melnik, J. A. Ward, J. P. Gleeson, and M. A. Porter, Multi-stage complex contagions, Chaos, 23 (2013), 013124.
[41] S. Meloni, N. Perra, A. Arenas, S. Gómez, Y. Moreno, and A. Vespignani, Modeling human mobility responses to the large-scale spreading of infectious diseases, Sci. Rep., 1 (2011), 62.
[42] L. A. Meyers, B. Pourbohloul, M. E. Newman, D. M. Skowronski, and R. C. Brunham, Network theory and SARS: Predicting outbreak diversity, J. Theoret. Biol., 232 (2005), pp. 71–81.
[43] P. J. Mucha, T. Richardson, K. Macon, M. A. Porter, and J.-P. Onnela, Community structure in time-dependent, multiscale, and multiplex networks, Science, 328 (2010), pp. 876–878. · Zbl 1226.91056
[44] R. Olinky and L. Stone, Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission, Phys. Rev. E (3), 70 (2004), 030902.
[45] H.-H. Pai, H. Yu-Jue, and E.-L. Hsu, Impact of a short-term community-based cleanliness campaign on the sources of dengue vectors: An entomological and human behavior study, J. Environ. Health, 68 (2006), 35.
[46] N. Perra, D. Balcan, B. Gonçalves, and A. Vespignani, Towards a characterization of behavior-disease models, PloS One, 6 (2011), e23084.
[47] A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge Nonlinear Sci. Ser. 12, Cambridge University Press, Cambridge, 2003. · Zbl 1219.37002
[48] T. C. Reluga and A. P. Galvani, A general approach for population games with application to vaccination, Math. Biosci., 230 (2011), pp. 67–78. · Zbl 1211.92049
[49] F. D. Sahneh, F. N. Chowdhury, and C. M. Scoglio, On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading, Sci. Rep., 2 (2012), 632.
[50] L. B. Shaw and I. B. Schwartz, Fluctuating epidemics on adaptive networks, Phys. Rev. E (3), 77 (2008), 066101.
[51] R. D. Smith, Responding to global infectious disease outbreaks: Lessons from SARS on the role of risk perception, communication and management, Soc. Sci. Med., 63 (2006), pp. 3113–3123.
[52] G. K. SteelFisher, R. J. Blendon, M. M. Bekheit, and K. Lubell, The public’s response to the 2009 H1N1 influenza pandemic, New Engl. J. Med., 362 (2010), e65.
[53] C. Sun, W. Yang, J. Arino, and K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Math. Biosci., 230 (2011), pp. 87–95. · Zbl 1211.92051
[54] M. Szell, R. Lambiotte, and S. Thurner, Multirelational organization of large-scale social networks in an online world, Proc. Natl. Acad. Sci. USA, 107 (2010), pp. 13636–13641.
[55] Z. Tai and T. Sun, Media dependencies in a changing media environment: The case of the 2003 SARS epidemic in China, New Media Soc., 9 (2007), pp. 987–1009.
[56] P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), pp. 29–48. · Zbl 1015.92036
[57] P. Van Mieghem, The n-intertwined SIS epidemic network model, Computing, 93 (2011), pp. 147–169. · Zbl 1293.68041
[58] B. Wang, L. Cao, H. Suzuki, and K. Aihara, Safety-information-driven human mobility patterns with metapopulation epidemic dynamics, Sci. Rep., 2 (2012), 887.
[59] D. J. Watts, A simple model of global cascades on random networks, Proc. Natl. Acad. Sci. USA, 99 (2002), pp. 5766–5771. · Zbl 1022.90001
[60] C. W. Wu and L. O. Chua, Synchronization in an array of linearly coupled dynamical systems, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 42 (1995), pp. 430–447. · Zbl 0867.93042
[61] Q. C. Wu, X. C. Fu, M. Small, and X.-J. Xu, The impact of awareness on epidemic spreading in networks, Chaos, 22 (2012), 013101. · Zbl 1331.92154
[62] G. Yan, Z.-Q. Fu, J. Ren, and W.-X. Wang, Collective synchronization induced by epidemic dynamics on complex networks with communities, Phys. Rev. E (3), 75 (2007), 016108.
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