Epidemic control analysis: Designing targeted intervention strategies against epidemics propagated on contact networks

Journal of Theoretical Biology

Volumn 365, Issue , 2015, Pages 84-95

  Hadjichrysanthou, Christoforos ^a   Sharkey, Kieran J ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Heterogeneous networks; Individual based models; Methods of intervention; SIS

Indexed keywords

EPIDEMIC; EPIDEMIOLOGY; INDIVIDUAL-BASED MODEL; INFECTIVITY;

ARTICLE; CONTROL STRATEGY; DISEASE CONTROL; ENDEMIC DISEASE; EPIDEMIC; EPIDEMIC CONTROL ANALYSIS; PREDICTION; PREVENTION AND CONTROL; SIMULATION; STRATEGIC PLANNING; ANIMAL; BIOLOGICAL MODEL; COMMUNICABLE DISEASES; HUMAN; INFECTION CONTROL;

ANIMALS; COMMUNICABLE DISEASE CONTROL; COMMUNICABLE DISEASES; EPIDEMICS; HUMANS; MODELS, BIOLOGICAL;

EID: 84908637031     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2014.10.006     Document Type: Article

References (72)

1. Albert R., Barabási A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 2002, 74:47-97.
2. Albert R., Jeong H., Barabási A. Error and attack tolerance of complex networks. Nature 2000, 406:378-382.
3. Amaral, L.A.N., Scala, A., Barthélémy, M., Stanley, H.E., 2000. Classes of small-world networks. Proc. Natl. Acad. Sci. USA 97, 11149-11152.
4. Anderson R.M., May R.M. Infectious Diseases of Humans: Dynamics and Control 1992, Oxford University Press, New York.
5. Bansal S., Grenfell B.T., Meyers L.A. When individual behaviour matters. homogeneous and network models in epidemiology. J. R. Soc. Interface 2007, 4:879-891.
6. Barabási A.-L., Albert R. Emergence of scaling in random networks. Science 1999, 286:509-512.
7. Barrat A., Weigt M. On the properties of small-world network models. Eur. Phys. J. B 2000, 13:547-560.
8. Behzad M., Chartrand G., Lesniak-Foster L. Graphs & Digraphs 1979, Prindle, Weber and Schmidt, Boston.
9. Bollobás B. Random Graphs 1985, Academic Press, London.
10. Bonacich P. Factoring and weighting approaches to status scores and clique identification. J. Math. Sociol. 1972, 2:113-120.
11. Borgatti S.P. Centrality and network flow. Soc. Netw. 2005, 27:55-71.
12. Callaway D.S., Newman M.E.J., Strogatz S.H., Watts D.J. Network robustness and fragility. percolation on random graphs. Phys. Rev. Lett. 2000, 85:5468-5471.
13. Chakrabarti D., Wang Y., Wang C., Leskovec J., Faloutsos C. Epidemic thresholds in real networks. ACM Trans. Inf. Syst. Secur. 2008, 10:13.
14. Cheng X.-Q., Ren F.-X., Shen H.-W., Zhang Z.-K., Zhou T. Bridgeness. a local index on edge significance in maintaining global connectivity. J. Stat. Mech. 2010, 2010:P10011.
15. Christley R.M., Pinchbeck G.L., Bowers R.G., Clancy D., French N.P., Bennett R., Turner J. Infection in social networks. using network analysis to identify high-risk individuals. Am. J. Epidemiol. 2005, 162:1024-1031.
16. Cohen R., Erez K., ben-Avraham D., Havlin S. Resilience of the Internet to random breakdowns. Phys. Rev. Lett. 2000, 85:4626-4628.
17. Cohen R., Erez K., Ben-Avraham D., Havlin S. Breakdown of the Internet under intentional attack. Phys. Rev. Lett. 2001, 86:3682-3685.
18. Croft, D.P., Krause, J., James, R., 2004. Social networks in the guppy (poecilia reticulata). Proc. R. Soc. Lond. B Biol. Sci. 271, 516-519.
19. Danon L., Ford A.P., House T., Jewell C.P., Keeling M.J., Roberts G.O., Ross J.V., Vernon M.C. Networks and the epidemiology of infectious disease. Interdiscip. Perspect. Infect. Dis. 2011, 2011:284909.
20. Diekmann O., Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation 2000, Wiley, New York.
21. Dorogovtsev S.N., Mendes J.F.F. Evolution of Networks: From Biological Nets to the Internet and WWW 2003, Oxford University Press, New York.
22. Eames, K.T.D., Keeling, M.J., 2002. Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases. Proc. Natl. Acad. Sci. USA, 99, 13330-13335.
23. Enns E.A., Mounzer J.J., Brandeau M.L. Optimal link removal for epidemic mitigation. a two-way partitioning approach. Math. Biosci. 2012, 235:138-147.
24. Erdos P., Rényi A. On random graphs I. Publ. Math. (Debrecen) 1959, 6:290-297.
25. Fell D. Understanding the Control of Metabolism 1997, Portland Press, London.
26. Freeman L.C. A set of measures of centrality based on betweenness. Sociometry 1977, 40:35-41.
27. Freeman L.C. Centrality in social networks. conceptual clarification. Soc. Netw. 1978, 1:215-239.
28. Girvan, M., Newman, M.E.J., 2002. Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA, 99, 7821-7826.
29. 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, 89:38009.
30. Gross T., D'Lima C.J.D., Blasius B. Epidemic dynamics on an adaptive network. Phys. Rev. Lett. 2006, 96:208701.
31. Heinrich R., Rapoport T.A. A linear steady-state treatment of enzymatic chains. General properties, control and effector strength. Eur. J. Biochem. 1974, 42:89-95.
32. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. Soc. Ind. Appl. Math. 2000, 42:599-653.
33. Hethcote H.W., Yorke J.A. Gonorrhea Transmission Dynamics and Control. Lecture Notes in Biomathematics 1984, vol. 56. Springer-Verlag, Berlin.
34. Holme P., Kim B.J., Yoon C.N., Han S.K. Attack vulnerability of complex networks. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2002, 65:056109.
35. Jeong H., Tombor B., Albert R., Oltvai Z.N., Barabási A.-L. The large-scale organization of metabolic networks. Nature 2000, 407:651-654.
36. Jonkers A.R.T., Sharkey K.J., Christley R.M. Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales. J. R. Soc. Interface 2010, 7:695-701.
37. Kacser H., Burns J.A. The control of flux. Symp. Soc. Exp. Biol. 1973, 27:65-104. (Reprinted in: Biochem. Soc. Trans. 23, 1995, 341-366.).
38. Keeling, M.J., 1999. The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B Biol. Sci. 266, 859-867.
39. Keeling M.J., Eames K.T.D. Networks and epidemic models. J. R. Soc. Interface 2005, 2:295-307.
40. Keeling M.J., Shattock A. Optimal but unequitable prophylactic distribution of vaccine. Epidemics 2012, 4:78-85.
41. Kephart, J.O., White, S.R., 1991. Directed-graph epidemiological models of computer viruses. In: IEEE Computer Society Symposium on Research in Security and Privacy. IEEE Computer Society Press, Oakland, CA, pp. 343-359.
42. Kermack W.O., McKendrick A.G. A contribution to the mathematical theory of epidemics. Proc. Math. Phys. Eng. Sci. 1927, 115:700-721.
43. Kirkwood J.G. Statistical mechanics of fluid mixtures. J. Chem. Phys. 1935, 3:300-313.
44. Klemm K., Serrano M.A., Eguíluz V.M., San Miguel M. A measure of individual role in collective dynamics. Sci. Rep. 2012, 2:292.
45. Liljeros F., Edling C.R., Nunes Amaral L.A., Stanley H.E., Aberg Y. The web of human sexual contacts. Nature 2001, 411:907-908.
46. Marcelino J., Kaiser M. Reducing influenza spreading over the airline network. PLoS Curr. 2009, 1:RRN1005.
47. Masuda N. Immunization of networks with community structure. N. J. Phys. 2009, 11:123018.
48. Matsuda H., Ogita N., Sasaki A., Sato K. Statistical mechanics of population. the lattice Lotka-Volterra model. Prog. Theor. Phys. 1992, 88:1035-1049.
49. Murray J.D. Mathematical Biology: An Introduction 1993, Springer-Verlag, New York.
50. Nagy N., Simon P.L. Monte Carlo simulation and analytic approximation of epidemic processes on large networks. Cent. Eur. J. Math. 2013, 11:800-815.
51. Newman M.E.J. The structure and function of complex networks. SIAM Rev. Soc. Ind. Appl. Math. 2003, 45:167-256.
52. Newman M.E.J. A measure of betweenness centrality based on random walks. Soc. Netw. 2005, 27:39-54.
53. Newman M.E.J. Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2006, 74:036104.
54. Omić, J., Martín-Hernández, J., van Mieghem, P., 2010. Network protection against worms and cascading failures using modularity partitioning. In: 22nd International Teletraffic Congress (ITC). Amsterdam, The Netherlands, pp. 1-8.
55. Pastor-Satorras R., Vespignani A. Immunization of complex networks. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2002, 65:036104.
56. Rand D. Advanced Ecological Theory: Principles and Applications 1999, Blackwell Science, Oxford, UK, (Ch. Correlation equations and pair approximations for spatial ecologies, pp. 100-142.).
57. Reder C. Metabolic control theory. a structural approach. J. Theor. Biol. 1988, 135:175-201.
58. Restrepo J.G., Ott E., Hunt B.R. Characterizing the dynamical importance of network nodes and links. Phys. Rev. Lett. 2006, 97:094102.
59. Röling W.F.M., van Breukelen B.M., Bruggeman F.J., Westerhoff H.V. Ecological control analysis. being(s) in control of mass flux and metabolite concentrations in anaerobic degradation processes. Environ. Microbiol. 2007, 9:500-511.
60. Sharkey K.J. Deterministic epidemiological models at the individual level. J. Math. Biol. 2008, 57:311-331.
61. Sharkey K.J. Deterministic epidemic models on contact networks. correlations and unbiological terms. Theor. Popul. Biol. 2011, 79:115-129.
62. Sharkey, K.J., Kiss, I.Z., Wilkinson, R.R., Simon, P.L., 2013. Exact equations for SIR epidemics on tree graphs. Bull. Math. Biol., in press. http://dx.doi.org/10.1007/s11538-013-9923-5.
63. Starnini M., Machens A., Cattuto C., Barrat A., Pastor-Satorras R. Immunization strategies for epidemic processes in time-varying contact networks. J. Theor. Biol. 2013, 337:89-100.
64. Taylor M., Taylor T.J., Kiss I.Z. Epidemic threshold and control in a dynamic network. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2012, 85:016103.
65. Tong, H., Prakash, B.A., Tsourakakis, C., Eliassi-Rad, T., Faloutsos, C., Chau, D.H., 2010. On the vulnerability of large graphs. In: IEEE 10th International Conference on Data Mining (ICDM). Sydney, NSW, pp. 1091-1096.
66. van Baalen M. The Geometry of Ecological Interactions: Simplifying Spatial Complexity 2000, Cambridge University Press, Cambridge, (Ch. Pair approximations for different spatial geometries, pp. 359-387.).
67. Volz, E., Meyers, L.A., 2007. Susceptible-infected-recovered epidemics in dynamic contact networks. Proc. R. Soc. Lond. B Biol. Sci., 274, 2925-2933.
68. Wang, Y., Chakrabarti, D., Wang, C., Faloutsos, C., 2003. Epidemic spreading in real networks: an eigenvalue viewpoint. In: Proceedings of the 22nd International Symposium on Reliable Distributed Systems. IEEE Computer Society Press, Los Alamitos, CA, pp. 25-34.
69. Watts D.J., Strogatz S.H. Collective dynamics of 'small-world' networks. Nature 1998, 393:440-442.
70. Weiss G.H., Dishon M. On the asymptotic behavior of the stochastic and deterministic models of an epidemic. Math. Biosci. 1971, 11:261-265.
71. Westerhoff H.V., Getz W.M., Bruggeman F., Hofmeyr J.H.S., Rohwer J.M., Snoep J.L. ECA. control in ecosystems. Mol. Biol. Rep. 2002, 29:113-117.
72. Wilkinson R.R., Sharkey K.J. Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2014, 89:022808.