A network model for Ebola spreading

Journal of Theoretical Biology

Volumn 394, Issue , 2016, Pages 212-222

  Rizzo, Alessandro ^a,b   Pedalino, Biagio ^c   Porfiri, Maurizio ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

^b POLITECNICO DI TORINO   (Italy)

^c CENTERS FOR DISEASE CONTROL AND PREVENTION   (United States)

Author keywords

Activity driven networks; Ebola virus disease; Epidemic model; Interventions; Liberia

Indexed keywords

DISEASE SPREAD; EPIDEMIC; INFECTIOUS DISEASE; NUMERICAL MODEL; VIRAL DISEASE;

ACTIVITY DRIVEN NETWORK; ARTICLE; DISEASE TRANSMISSION; EBOLA HEMORRHAGIC FEVER; HEALTH STATUS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; MOLECULAR EVOLUTION; NONHUMAN; PRIORITY JOURNAL; PROBABILITY; QUALITATIVE ANALYSIS; SIMULATION; SOCIAL INTERACTION; WORLD HEALTH ORGANIZATION; BIOLOGICAL MODEL; CALIBRATION; COMPUTER SIMULATION; EBOLAVIRUS; HEMORRHAGIC FEVER, EBOLA; HOSPITALIZATION; HUMAN; LIBERIA; PHYSIOLOGY; TIME FACTOR; TRANSMISSION; VIROLOGY;

LIBERIA [WEST AFRICA];

EBOLA VIRUS;

CALIBRATION; COMPUTER SIMULATION; EBOLAVIRUS; HEMORRHAGIC FEVER, EBOLA; HOSPITALIZATION; HUMANS; LIBERIA; MODELS, BIOLOGICAL; TIME FACTORS;

EID: 84957096063     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2016.01.015     Document Type: Article

References (97)

1. Ajelli M., Gonçalves B., Balcan D., Colizza V., Hu H., Ramasco J.J., Merler S., Vespignani A. Comparing large-scale computational approaches to epidemic modeling: agent-based versus structured metapopulation models. BMC Infect. Dis. 2010, 10:190.
2. Althaus C.L. Estimating the reproduction number of Ebola virus (EBOV) during the 2014 outbreak in West Africa. PLoS Curr. 2014, 6:1-7.
3. Apolloni A., Poletto C., Colizza V. Age-specific contacts and travel patterns in the spatial spread of 2009 H1N1 influenza pandemic. BMC Infect. Dis. 2013, 13:176.
4. Apolloni A., Poletto C., Ramasco J.J., Jensen P., Colizza V. Metapopulation epidemic models with heterogeneous mixing and travel behaviour. Theor. Biol. Med. Model. 2014, 11(1):3.
5. Bajardi P., Poletto C., Ramasco J.J., Tizzoni M., Colizza V., Vespignani A. Human mobility networks, travel restrictions, and the global spread of 2009 H1N1 pandemic. PLoS One 2011, 6(1):e16591.
6. Balcan D., Colizza V. Multiscale mobility networks and the spatial spreading of infectious diseases. Proc. Natl. Acad. Sci. 2009, 106(51):21484-21489.
7. Barrat A., Barthelemy M., Vespignani A. Dynamical Processes on Complex Networks 2008, Cambridge University Press, Cambridge, UK.
8. BBC, 2015. Ebola case undermines Liberia disease-free hopes. 〈〉. http://www.bbc.com/news/world-africa-31991748.
9. Boguñá M., Castellano C., Pastor-Satorras R. Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks. Phys. Rev. Lett. 2013, 111:068701.
10. Brauer F. Epidemic models with heterogeneous mixing and treatment. Bull. Math. Biol. 2008, 70(7):1869-1885. 10.1007/s11538-008-9326-1.
11. Brauer F., Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology 2011, Springer, New York.
12. Butts C.T. Revisiting the foundations of network analysis. Science 2009, 325(5939):414-416.
13. Camacho, A., Kucharski, A.J., Funk, S., Breman, J., Piot, P., Edmunds, W.J., 2014. Potential for large outbreaks of Ebola virus disease, Epidemics 9, 70-78.
14. Camacho, A., Kucharski, A., Aki-Sawyerr, Y., White, M.A., Flasche, S., Baguelin, M., Pollington, T., Carney, J.R., Glover, R., Smout, E., Tiffany, A., Edmunds, W.J., Funk, S., 2015. Temporal changes in Ebola transmission in Sierra Leone and implications for control requirements: a real-time modelling study. PLoS Curr. Outbreaks 7, 1-20.
15. Castellano C., Pastor-Satorras R. Thresholds for epidemic spreading in networks. Phys. Rev. Lett. 2010, 105:218701.
16. Cattuto C., Van den Broeck W., Colizza V., Pinton J.-F., Vespignani A. Dynamics of person-to-person interactions from distributed RFID sensor networks. PLoS One 2010, 5(7):e11596.
17. CDC Stacks, 2014. Generic EbolaResponse (ER): Modeling the spread of disease impact & intervention, Version 2.5, 〈〉. http://stacks.cdc.gov/view/cdc/24900.
18. Centers for Disease Control and Prevention, 2015. 2014 Ebola Outbreak in West Africa - Reported Cases Graphs, 〈〉. http://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/cumulative-cases-graphs.html.
19. Centers for Disease Control and Prevention, 2014a. Ebola Outbreak in West Africa - Case Counts, 〈〉. http://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/case-counts.html.
20. Centers for Disease Control and Prevention, 2014b. Cases of Ebola Diagnosed in the United States, 〈〉. http://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/united-states-imported-case.html.
21. Centers for Disease Control and Prevention, 2014c. Top 10 Ebola Response Planning Tips: Ebola Readiness Self-assessment for State and Local Public Health Officials, 〈〉. http://www.cdc.gov/vhf/ebola/outbreaks/prepared-ness/planning-tips-top10.html.
22. Centola D., González-Avella J.C., Eguíluz V.M., San Miguel M. Homophily, cultural drift, and the co-evolution of cultural groups. J. Confl. Resolut. 2007, 51(6):905-929.
23. Choe S., Lee S. Modeling optimal treatment strategies in a heterogeneous mixing model. Theor. Biol. Med. Model. 2015, 12(1):28.
24. Chowell G., Nishiura H. Transmission dynamics and control of Ebola virus disease (EVD): a review. BMC Med. 2014, 12(1):196.
25. Chowell G., Hengartner N.W., Castillo-Chavez C., Fenimore P.W., Hyman J.M. The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. J. Theor. Biol. 2004, 229:119-126.
26. Fasina F.O., Shittu A., Lazarus D., Tomori O., Simonsen L., Viboud C., Chowell G. Transmission dynamics and control of Ebola virus disease outbreak in Nigeria, July to September 2014. Eurosurveillance 2014, 19(40):20920.
27. Fenichel E.P. Adaptive human behavior in epidemiological models. Proc. Natl. Acad. Sci. U. S. A. 2011, 108(15):6306-6311.
28. Ferguson N. Capturing human behaviour. Nature 2007, 446(7137):733.
29. Fibich G., Gibori R. Aggregate diffusion dynamics in agent-based models with a spatial structure. Oper. Res. 2010, 58(5):1450-1468.
30. Fisman D., Khoo E., Tuite A. Early epidemic dynamics of the West African 2014 Ebola outbreak: estimates derived with a simple two-parameter model. PLoS Curr. 2014, 6:1-13.
31. Frasca M., Buscarino A., Rizzo A., Fortuna L., Boccaletti S. Dynamical network model of infective mobile agents. Phys. Rev. E 2006, 74(3):036110.
32. Funk S., Gilad E., Watkins C., Jansen V.A.A. The spread of awareness and its impact on epidemic outbreaks. Proc. Natl. Acad. Sci. 2009, 106(16):6872-6877.
33. Funk S., Salathé M., Jansen V.A. Modelling the influence of human behaviour on the spread of infectious diseases: a review. J. R. Soc. Interface 2010, 7(50):1247-1256.
34. Ghoshal G., Holme P. Attractiveness and activity in internet communities. Physica A: Stat. Mech. Appl. 2006, 364:603-609.
35. Goltsev A.V., Dorogovtsev S.N., Oliveira J.G., Mendes J.F.F. Localization and spreading of diseases in complex networks. Phys. Rev. Lett. 2012, 109:128702.
36. Gomes M.F.C., Pastore A., Rossi L., Chao D., Longini I., Halloran M.E., Vespignani A. Assessing the international spreading risk associated with the 2014 West African Ebola outbreak. PLoS Curr. 2014, 6:1-20.
37. Gómez S., Arenas A., Borge-Holthoefer J., Meloni S., Moreno Y. Discrete-time Markov chain approach to contact-based disease spreading in complex networks. Europhys. Lett. 2010, 89(3):38009.
38. González M.C., Hidalgo C.A., Barabási A. Understanding individual human mobility patterns. Nature 2008, 453(7196):779-782.
39. Holme P. Network reachability of real-world contact sequences. Phys. Rev. E 2005, 71:046119.
40. Holme P., Saramäki J. Temporal networks. Phys. Rep. 2012, 519(3):97-125.
41. House T. Modelling behavioural contagion. J. R. Soc. Interface/R. Soc. 2011, 8(59):909-912.
42. Jolad S., Liu W., Schmittmann B., Zia R.K.P. Epidemic spreading on preferred degree adaptive networks. PLoS One 2012, 7(11):e48686.
43. Keeling M.J., Eames K.T.D. Networks and epidemic models. J. R. Soc. Interface 2005, 2(4):295-307.
44. Keeling M.J., Rohani P. Modeling Infectious Diseases in Humans and Animals 2011, Princeton University Press, Princeton, NJ, USA.
45. Khan A.S., Tshioko F.K., Heymann D.L., Le Guenno B., Nabeth P., Kerstiens B., Fleerackers Y., Kilmarx P.H., Rodier G.R., Nkuku O., Rollin P.E., Sanchez A., Zaki S.R., Swanepoel R., Tomori O., Nichol S.T., Peters C.J., Muyembe-Tamfum J.J., Ksiazek T.G. The reemergence of Ebola hemorrhagic fever, Democratic Republic of the Congo, 1995. J. Infect. Dis. 1999, 179(Supplement 1):S76-S86.
46. Kiskowski M.A. A three-scale network model for the early growth dynamics of 2014 West Africa Ebola epidemic. PLoS Curr. 2014, 6:1-28.
47. Legrand J., Grais R.F., Boelle P.Y., Valleron A.J., Flahault A. Understanding the dynamics of Ebola epidemics. Epidemiol. Infect. 2007, 135(4):610-621.
48. Lewnard J.A., Ndeffo Mbah M.L., Alfaro-Murillo J.A., Altice F.L., Bawo L., Nyenswah T.G., Galvani A.P. Dynamics and control of Ebola virus transmission in Montserrado, Liberia: a mathematical modelling analysis. Lancet Infect. Dis. 2014, 14:1189-1195.
49. Liu S., Perra N., Karsai M., Vespignani A. Controlling contagion processes in activity driven networks. Phys. Rev. Lett. 2014, 112:118702.
50. LiveScience, 2015. Liberia, Guinea on Track to Contain Ebola, 〈〉. http://www.livescience.com/48962-ebola-transmission-rate-down.html.
51. Modeling the Interplay Between Human Behavior and the Spread of Infectious Diseases 2013, Springer-Verlag, New York, NY, USA. P. Manfredi, A. D'Onofrio (Eds.).
52. Medus A.D., Dorso C.O. Memory effects induce structure in social networks with activity-driven agents. J. Stat. Mech.: Theory Exp. 2014, 2014(9):P09009.
53. Meltzer M.I., Atkins C.Y., Santibanez S., Knust B., Petersen B.W., Ervin E.D., Nichol S.T., Damin I.K., Washington M.L. Estimating the future number of cases in the Ebola epidemic-Liberia and Sierra Leone, 2014-2015. Morb. Mortal. Wkly. Rep. Suppl. 2014, 63(3):1-14.
54. Merler S., Ajelli M., Fumanelli L., Gomes M.F.C., Pastore y Piontti A., Rossi L., Chao D.L., Longini I.M., Halloran M.E., Vespignani A. Spatiotemporal spread of the 2014 outbreak of Ebola virus disease in Liberia and the effectiveness of non-pharmaceutical interventions: a computational modelling analysis. Lancet Infect. Dis. 2015, 3099(14):1-8.
55. Moody J. The importance of relationship timing for diffusion. Soc. Forces 2002, 81(1):25-56.
56. Morris M., Kretzschmar M. Concurrent partnership and the spread of HIV. AIDS 1997, 11(5):641-648.
57. Newman M.E.J. Spread of epidemic disease on networks. Phys. Rev. E 2002, 66:016128.
58. Ni S., Weng W. Impact of travel patterns on epidemic dynamics in heterogeneous spatial metapopulation networks. Phys. Rev. E 2009, 79(1):016111.
59. Nishiura H., Chowell G. Early transmission dynamics of Ebola virus disease (EVD), West Africa, March to August 2014. Eurosurveillance 2014, 19(36):20894.
60. Nyenswah, T.G., Westercamp, M., Kamali, A.A., Qin, J., Zielinski-Gutierrez, E., Amegashie, F., Fallah, M., Gergonne, B., Nugba-Ballah, R., Singh, G., Aberle-Grasse, J.M., Havers, F., Montgomery, J.M., Bawo, L., Wang, S., Rosenberg, R., 2014. Evidence for declining numbers of Ebola cases-Montserrado County, Liberia, June-October 2014, Morb. Mortal. Wkly. Rep., 63, 1-5.
61. Onnela J.-P., Saramäki J., Hyvönen J., Szabó G., Lazer D., Kaski K., Kertész J., Barabási A.-L. Structure and tie strengths in mobile communication networks. Proc. Natl. Acad. Sci. 2007, 104(18):7332-7336.
62. Pandey A., Atkins K.E., Medlock J. Strategies for containing Ebola in West Africa. Science 2014, 16(6212):991-995.
63. Pastor-Satorras R., Vespignani A. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 2001, 86:3200-3203.
64. Pastor-Satorras R., Castellano C., Van Mieghem P., Vespignani A. Epidemic processes in complex networks. Rev. Mod. Phys. 2015, 87:925-979.
65. Perra N., Gonçalves B. Modeling and predicting human infectious diseases. Social Phenomena. From Data Analysis to Models 2015, 59-83. Springer International Publishing, Cham (ZG), Switzerland. B. Gonçalves, N. Perra (Eds.).
66. Perra N., Balcan D., Gonçalves B., Vespignani A. Towards a characterization of behavior-disease models. PloS One 2011, 6(8):e23084.
67. Perra N., Gonçalves B., Pastor-Satorras R., Vespignani A. Activity driven modeling of time varying networks. Sci. Rep. 2012, 2:469.
68. Poletti P., Caprile B., Ajelli M., Pugliese A., Merler S. Spontaneous behavioural changes in response to epidemics. J. Theor. Biol. 2009, 260(1):31-40.
69. Poletto C., Tizzoni M., Colizza V. Human mobility and time spent at destination: impact on spatial epidemic spreading. J. Theor. Biol. 2013, 338:41-58.
70. Poletto C., Gomes M.F., Pastore y Piontti A., Rossi L., Bioglio L., Chao D.L., Longini I.M., Halloran M.E., Colizza V., Vespignani A. Assessing the impact of travel restrictions on international spread of the 2014 West African Ebola epidemic. Eurosurveillance 2014, 19(42):20936.
71. Rhee I., Shin M., Hong S., Lee K. On the Levy-walk nature of human mobility. IEEE/ACM Trans. Netw. 2011, 19(3):630-643.
72. Rivers, C., 2014. Data for the 2014 Ebola Outbreak in West Africa, 〈〉. https://github.com/cmrivers/ebola.
73. Rivers C.M., Lofgren E.T.T., Marathe M., Eubank S., Lewis B.L. Modeling the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia. PLoS Curr. 2014, 6:1-16.
74. Rizzo A., Frasca M., Porfiri M. Effect of individual behavior on epidemic spreading in activity driven networks. Phys. Rev. E 2014, 90:042801.
75. Rizzo, A., Porfiri, M., 2016. Innovation diffusion on time-varying activity networks. Eur. Phys. J. B, 89 (1), 1-8.
76. Ruan S., Wang W., Levin S.A. The effect of global travel on the spread of SARS. Math. Biosci. Eng. 2006, 3(1):205-218.
77. Scholtes I., Wider N., Pfitzner R., Garas A., Tessone C.J., Schweitzer F. Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks. Nat. Commun. 2014, 5.
78. Schwartz I.B., Shaw L.B. Rewiring for adaptation. Physics 2010, 3:17.
79. Shaw L.B., Schwartz I.B. Enhanced vaccine control of epidemics in adaptive networks. Phys. Rev. E 2010, 81:046120.
80. Sousa da Mata A., Pastor-Satorras R. Slow relaxation dynamics and aging in random walks on activity driven temporal networks. Eur. Phys. J. B 2015, 88(2):1-8.
81. Starnini M., Pastor-Satorras R. Temporal percolation in activity-driven networks. Phys. Rev. E 2014, 89(3):032807.
82. Sun, K., Baronchelli, A., Perra, N., 2014. Epidemic spreading in non-Markovian time-varying networks, arXiv preprint,. http://arxiv.org/abs/1404.1006.
83. Tang J., Scellato S., Musolesi M., Mascolo C., Latora V. Small-world behavior in time-varying graphs. Phys. Rev. E 2010, 81:055101.
84. Ebola virus disease in West Africa-The first 9 months of the epidemic and forward projections. New Engl. J. Med. 2014, 371(16):1481-1495. The WHO Ebola Response Team.
85. Towers S., Patterson-Lomba O., Castillo-Chavez C. Temporal variations in the effective reproduction number of the 2014 West Africa Ebola outbreak. PLoS Curr. 2014, 6:1-13.
86. Valdano E., Ferreri L., Poletto C., Colizza V. Analytical computation of the epidemic threshold on temporal networks. Phys. Rev. X 2015, 5(2):021005.
87. Valdez L.D., Aragão Rêgo H.H., Stanley H.E., Braunstein L.A. Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies. Sci. Rep. 2015, 5:12172.
88. van den Broeck W., Gioannini C., Gonçalves B., Quaggiotto M., Colizza V., Vespignani A. The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale. BMC Infect. Dis. 2011, 11(1):37.
89. Vespignani A. Modelling dynamical processes in complex socio-technical systems. Nat. Phys. 2011, 8(1):32-39.
90. VirginiaTech Network Dynamics & Simulation Science and Laboratory, 2014. Modeling Updates, 〈〉. http://www.vbi.vt.edu/ndssl/ebola/modeling-view/modeling-the-ebola-outbreak-in-west-africa-august-11th-2014-update.
91. Volz E., Meyers L.A. Epidemic thresholds in dynamic contact networks. J. R. Soc. Interface 2008, 6(32):233-241.
92. Wang L., Zhang Y., Huang T., Li X. Estimating the value of containment strategies in delaying the arrival time of an influenza pandemic: a case study of travel restriction and patient isolation. Phys. Rev. E 2012, 86(3):032901.
93. Webb G., Browne C., Huo X., Seydi O., Seydi M., Magal P. A model of the 2014 Ebola epidemic in West Africa with contact tracing. PLoS Curr. 2015, 7:1-11.
94. World Health Organization, 2014a. Ebola Situation Reports, 〈〉. http://apps.who.int/ebola/en/current-situation/ebola-situation-report.
95. World Health Organization, 2014b. Ebola Virus Disease, 〈〉. http://www.who.int/mediacentre/factsheets/fs103/en/.
96. World Health Organization, 2015. The Ebola Outbreak in Liberia is Over, 〈〉. http://www.who.int/mediacentre/news/statements/2015/liberia-ends-ebola/en/.
97. Yang Wang, W., Chakrabarti, D., Wang, C., Faloutsos, C., 2003. Epidemic spreading in real networks: an eigenvalue viewpoint. In: 2003 Proceedings of 22nd International Symposium on Reliable Distributed Systems, pp. 25-34.