A stochastic SIS epidemic model with heterogeneous contacts

Physica A: Statistical Mechanics and its Applications

Volumn 421, Issue , 2015, Pages 78-97

  Economou, A ^a   Gomez Corral A ^b,c   Lopez Garcia M ^d  

^a UNIVERSITY OF ATHENS   (Greece)

^b INSTITUTO DE CIENCIAS MATEMÁTICAS   (Spain)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^d UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Basic reproduction number; Markov chain model; Maximum number of infected individuals; Number of infections; Quasi stationary regime; SIS epidemic; Stochastic

Indexed keywords

CELL PROLIFERATION; CONTINUOUS TIME SYSTEMS; EPIDEMIOLOGY; INVERSE PROBLEMS; ITERATIVE METHODS; MARKOV CHAINS; RANDOM VARIABLES; STOCHASTIC SYSTEMS;

BASIC REPRODUCTION NUMBER; MARKOV CHAIN MODELS; MAXIMUM NUMBER OF INFECTED INDIVIDUALS; NUMBER OF INFECTIONS; QUASI-STATIONARY REGIME; STOCHASTIC;

STOCHASTIC MODELS;

EID: 84918839615     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2014.10.054     Document Type: Article

References (41)

1. L.J.S. Allen An Introduction to Stochastic Processes with Applications to Biology 2003 Pearson Education, Inc. New Jersey
2. A. Yates, R. Antia, and R.R. Regoes How do pathogen evolution and host heterogeneity interact in disease emergence? Proc. R. Soc. B Biol. Sci. 273 2006 3075 3083
3. P. Van Mieghem, J. Omic, and R. Kooij Virus spread in networks IEEE/ACM Trans. Netw. 17 2009 1 14
4. M.E.J. Newman Networks. An Introduction 2010 Oxford University Press Oxford
5. F. Vega-Redondo Complex Social Networks 2007 Cambridge University Press New York
6. J.O. Kephart, S.R. White, Directed-graph epidemiological models of computer viruses, in: Proceedings of the 1991 IEEE Computer Society Symposium on Research in Security and Privacy, 1991, pp. 343-359.
7. M. Moslonka-Lefebvre, M. Pautasso, and M.J. Jeger Disease spread in small-size directed networks: epidemic threshold, correlation between links to and from nodes, and clustering J. Theoret. Biol. 260 2009 402 411
8. M.J. Keeling, and K.T.D. Eames Networks and epidemic models J. R. Soc. Interface 2 2005 295 307
9. L. Danon, A.P. Ford, T. House, C.P. Jewell, M.J. Keeling, G.O. Roberts, J.V. Ross, and M.C. Vernon Networks and the epidemiology of infectious disease Interdiscip. Perspect. Infect. Dis. 2012 2011 28 Article ID 284909
10. M. Pautasso, M. Moslonka-Lefebvre, and M.J. Jeger The number of links to and from the starting node as a predictor of epidemic size in small-size directed networks Ecol. Complex. 7 2010 424 432
11. X. Zhang, G.Q. Sun, Y.X. Zhu, J. Ma, and Z. Jin Epidemic dynamics on semi-directed complex networks Math. Biosci. 246 2013 242 251
12. L.A. Meyers, M.E.J. Newman, and B. Pourbohloul Predicting epidemics on directed contact networks J. Theoret. Biol. 240 2006 400 418
13. K.J. Sharkey, C.F. Fernandez, K.L. Morgam, E. Peeler, M. Thrush, J.F. Turnbull, and R.G. Bowers Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks J. Math. Biol. 53 2006 61 85
14. R.R. Wilkinson, and K.J. Sharkey An exact relationship between invasion probability and endemic prevalence for Markovian SIS dynamics on networks PLoS One 8 7 2013 e69028 10.1371/journal.pone.0069028
15. K. Saito, M. Kimura, and H. Motoda Discovering influential nodes for SIS models in social networks Discovery Science Lecture Notes in Computer Science vol. 5808 2009 302 316
16. K. Saito, M. Kimura, K. Ohara, and H. Motoda Efficient discovery of influential nodes for SIS models in social networks Knowl. Inf. Syst. 30 2012 613 635
17. F.S.W. Brimblecombe, R. Cruickshank, P.L. Masters, D.D. Reid, and G.T. Stewart Family studies of respiratory infections Br. Med. J. 18 1958 119 128
18. K. Grimwood, G.D. Abbott, D.M. Fergusson, L.C. Jennings, and J.M. Allan Spread of rotavirus within families: a community based study Br. Med. J. 287 1983 575 577
19. F. Chamchod, and S. Ruan Modeling the spread of methicillin-resistant Staphylococcus aureus in nursing homes for elderly PLoS One 7 2012 8 Article ID e29757
20. J.R. Artalejo On the Markovian approach for modeling the dynamics of nosocomial infections Acta Biotheor. 62 2014 15 34
21. D.J. Austin, M.J.M. Bonten, R.A. Weinstein, S. Slaughter, and R.M. Anderson Vancomycin-resistant enterococci in intensive-care hospital settings: transmission dynamics, persistence, and the impact of infection control programs Proc. Natl. Acad. Sci. 96 1999 6908 6913
22. B.S. Cooper, G.F. Medley, and G.M. Scott Preliminary analysis of the transmission dynamics of nosocomial infections: stochastic and management effects J. Hosp. Infect. 43 1999 131 147
23. M. Forrester, and A.N. Pettitt Use of stochastic epidemic modeling to quantify transmission rates of colonization with methicillin-resistant Staphylococcus aureus in an intensive care unit Infect. Control Hosp. Epidemiol. 26 2005 598 606
24. E.S. McBryde, A.N. Pettitt, and D.L.S. McElwain A stochastic mathematical model of methicillin resistant Staphylococcus aureus transmission in an intensive care unit: predicting the impact of interventions J. Theoret. Biol. 245 2007 470 481
25. J. Verdasca, M.M. Telo da Gama, A. Nunes, N.R. Bernardino, J.M. Pacheco, and M.C. Gomes Recurrent epidemics in small world networks J. Theoret. Biol. 233 2005 553 561
26. D.J. Watts, and S.H. Strogatz Collective dynamics of 'small-world' networks Nature 393 1998 440 442
27. P.L. Simon, M. Taylor, and I.Z. Kiss Exact epidemic models on graphs using graph-automorphism driven lumping J. Math. Biol. 62 2011 479 508
28. P. Van Mieghem, and E. Cator Epidemics in networks with nodal-infection and the epidemic threshold Phys. Rev. E 86 2012 10 Article ID 016116
29. M. Taylor, P.L. Simon, D.M. Green, T. House, and I.Z. Kiss From Markovian to pairwise epidemic models and the performance of moment closure approximations J. Math. Biol. 64 2012 1021 1042
30. A.L. Hill, D.G. Rand, M.A. Nowak, and N.A. Christakis Emotions as infectious diseases in a large social network: the SISa model Proc. R. Soc. B 277 2010 3827 3835
31. F.D. Sahneh, C. Scoglio, and P. Van Mieghem Generalized epidemic mean-field model for spreading processes over multilayer complex networks IEEE/ACM Trans. Netw. 21 2013 1609 1620
32. T.J. Taylor, and I.Z. Kiss Interdependency and hierarchy of exact and approximate epidemic models on networks J. Math. Biol. 69 2014 183 211
33. S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks Phys. Rev. E 84 2011 7 Article ID 036105
34. J.R. Artalejo, and M.J. Lopez-Herrero On the exact measure of the disease spread in stochastic epidemic models Bull. Math. Biol. 75 2013 1031 1050
35. G. Latouche, V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM Series on Statistics and Applied Probability, Philadelphia, 1999.
36. P.G. Ciarlet Introduction to Numerical Linear Algebra and Optimisation 1989 Cambridge University Press Cambridge
37. E.A. Van Doorn, and P.K. Pollett Quasi-stationary distributions for discrete-state models European J. Oper. Res. 230 2013 1 14
38. J.N. Darroch, and E. Seneta On quasi-stationary distributions in absorbing continuous-time finite Markov chains J. Appl. Probab. 4 1967 192 196
39. O. Diekmann, H. Heesterbeek, and T. Britton Mathematical Tools for Understanding Infectious Disease Dynamics 2013 Princeton University Press Princeton, NJ
40. J.J. Hunter Mathematical Techniques of Applied Probability. Discrete Time Models: Basic Theory, Vol. 1 1983 Academic Press New York
41. A. Valentin, and P. Ferdinande Recommendations on basic requirements for intensive care units: structural and organizational aspects Intensive Care Med. 37 10 2011 1575 1587