메뉴 건너뛰기




Volumn 237, Issue , 2014, Pages 474-488

Global dynamics of a network epidemic model for waterborne diseases spread

Author keywords

Basic reproduction number; Complex networks; Global stability; Immunization strategies; Kirchhoff's matrix tree theorem; Transmission routes

Indexed keywords

COMPLEX NETWORKS; FORESTRY; HETEROGENEOUS NETWORKS; IMMUNIZATION;

EID: 84899119114     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.03.148     Document Type: Article
Times cited : (77)

References (80)
  • 2
    • 0000998185 scopus 로고
    • A contribution to the mathematical theory of epidemics
    • W.O. Kermack, and A.G. McKendrick A contribution to the mathematical theory of epidemics Proc. R. Soc. A 115 1927 700 721
    • (1927) Proc. R. Soc. A , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 4
    • 79953280211 scopus 로고    scopus 로고
    • On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls
    • Article ID 281612
    • M. De la Sen, R.P. Agarwal, A. Ibeas, and A. Alonso-Quesada On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls Adv. Differ. Equ. 2010 2010 Article ID 281612
    • (2010) Adv. Differ. Equ. , vol.2010
    • De La Sen, M.1    Agarwal, R.P.2    Ibeas, A.3    Alonso-Quesada, A.4
  • 5
    • 84875377047 scopus 로고    scopus 로고
    • Endemic threshold results for an age-structured SIS epidemic model with periodic parameters
    • T. Kuniya, and H. Inaba Endemic threshold results for an age-structured SIS epidemic model with periodic parameters J. Math. Anal. Appl. 402 2013 477 492
    • (2013) J. Math. Anal. Appl. , vol.402 , pp. 477-492
    • Kuniya, T.1    Inaba, H.2
  • 7
    • 84891749174 scopus 로고    scopus 로고
    • Robust uniform persistence and competitive exclusion in a nonautonomous multi-strain SIR epidemic model with disease-induced mortality
    • A.S. Ackleh, and P.L. Salceanu Robust uniform persistence and competitive exclusion in a nonautonomous multi-strain SIR epidemic model with disease-induced mortality J. Math. Biol. 68 2014 453 475
    • (2014) J. Math. Biol. , vol.68 , pp. 453-475
    • Ackleh, A.S.1    Salceanu, P.L.2
  • 10
  • 11
    • 70349763962 scopus 로고    scopus 로고
    • Cholera: Global surveillance summary
    • WHO Cholera: global surveillance summary Weekly Epidemiol. Record 84 2009 309 324
    • (2009) Weekly Epidemiol. Record , vol.84 , pp. 309-324
  • 12
    • 79957653823 scopus 로고    scopus 로고
    • Global stability for cholera epidemic models
    • J.P. Tian, and J. Wang Global stability for cholera epidemic models Math. Biosci. 232 2011 31 41
    • (2011) Math. Biosci. , vol.232 , pp. 31-41
    • Tian, J.P.1    Wang, J.2
  • 13
    • 0018704517 scopus 로고
    • A mathematical model for the 1973 cholera epidemic in the European Mediterranean region
    • V. Capasso, and S.L. Paveri-Fontana A mathematical model for the 1973 cholera epidemic in the European Mediterranean region Rev. Epidemiol. Sante Publique 27 1979 1973 121 132
    • (1973) Rev. Epidemiol. Sante Publique , vol.27 , Issue.1979 , pp. 121-132
    • Capasso, V.1    Paveri-Fontana, S.L.2
  • 14
    • 2942619997 scopus 로고    scopus 로고
    • Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir
    • C.T. Codeco Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir BMC Infectious Diseases 1 2001 1 14
    • (2001) BMC Infectious Diseases , vol.1 , pp. 1-14
    • Codeco, C.T.1
  • 15
    • 32044434020 scopus 로고    scopus 로고
    • Hyperinfectivity: A critical element in the ability of V. Cholerae to cause epidemics?
    • D.M. Hartley, J.G. Morris, and D.L. Smith Hyperinfectivity: a critical element in the ability of V. cholerae to cause epidemics? PLoS Med. 3 2006 0063 0069
    • (2006) PLoS Med. , vol.3 , pp. 0063-0069
    • Hartley, D.M.1    Morris, J.G.2    Smith, D.L.3
  • 16
    • 0025322504 scopus 로고
    • Person-to-person transmission of cholera in a psychiatric hospital
    • K. Goh, S. Teo, S. Lam, and M. Ling Person-to-person transmission of cholera in a psychiatric hospital J. Infection 20 1990 193 200
    • (1990) J. Infection , vol.20 , pp. 193-200
    • Goh, K.1    Teo, S.2    Lam, S.3    Ling, M.4
  • 17
    • 33745604544 scopus 로고    scopus 로고
    • Hyperinfectivity in cholera: A new mechanism for an old epidemiological model?
    • M. Pascual, K. Koelle, and A.P. Dobson Hyperinfectivity in cholera: a new mechanism for an old epidemiological model? PLoS Med. 3 2006 e280
    • (2006) PLoS Med. , vol.3 , pp. 280
    • Pascual, M.1    Koelle, K.2    Dobson, A.P.3
  • 18
    • 77955172112 scopus 로고    scopus 로고
    • Multiple transmission pathways and disease dynamics in a waterborne pathogen model
    • J.H. Tien, and D.J.D. Earn Multiple transmission pathways and disease dynamics in a waterborne pathogen model Bull. Math. Biol. 72 2010 1506 1533
    • (2010) Bull. Math. Biol. , vol.72 , pp. 1506-1533
    • Tien, J.H.1    Earn, D.J.D.2
  • 20
    • 2342570969 scopus 로고    scopus 로고
    • Microbial contamination of drinking water and disease outcomes in developing regions
    • N. Ashbolt Microbial contamination of drinking water and disease outcomes in developing regions Toxicology 198 2004 229 238
    • (2004) Toxicology , vol.198 , pp. 229-238
    • Ashbolt, N.1
  • 21
    • 0034907869 scopus 로고    scopus 로고
    • The association between extreme precipitation and waterborne disease outbreaks in the United States
    • F. Curriero, J. Patz, J. Rose, and S. Lele The association between extreme precipitation and waterborne disease outbreaks in the United States Am. J. Public Health 91 2001 1194 1199
    • (2001) Am. J. Public Health , vol.91 , pp. 1194-1199
    • Curriero, F.1    Patz, J.2    Rose, J.3    Lele, S.4
  • 22
    • 4644266545 scopus 로고    scopus 로고
    • Heavy rainfall and waterborne disease outbreaks: The Walkerton example
    • H. Auld, D. MacIver, and J. Klaassen Heavy rainfall and waterborne disease outbreaks: the Walkerton example J. Toxicol. Environ. Health A 67 2004 1879 1887
    • (2004) J. Toxicol. Environ. Health A , vol.67 , pp. 1879-1887
    • Auld, H.1    Maciver, D.2    Klaassen, J.3
  • 23
    • 0030955032 scopus 로고    scopus 로고
    • Environmental ecology of Cryptosporidium and public health implications
    • J. Rose Environmental ecology of Cryptosporidium and public health implications Annu. Rev. Public Health 18 1997 135 161
    • (1997) Annu. Rev. Public Health , vol.18 , pp. 135-161
    • Rose, J.1
  • 24
    • 0031792685 scopus 로고    scopus 로고
    • Epidemiology, genetics, and ecology of toxigenic Vibrio cholerae
    • S. Faruque, M. Albert, and J. Mekalanos Epidemiology, genetics, and ecology of toxigenic Vibrio cholerae Microbiol. Mol. Biol. Rev. 62 1998 1301 1314
    • (1998) Microbiol. Mol. Biol. Rev. , vol.62 , pp. 1301-1314
    • Faruque, S.1    Albert, M.2    Mekalanos, J.3
  • 26
    • 0035907006 scopus 로고    scopus 로고
    • How viruses spread among computers and people
    • A.L. Lloyd, and R.M. May How viruses spread among computers and people Science 292 2001 1316 1317
    • (2001) Science , vol.292 , pp. 1316-1317
    • Lloyd, A.L.1    May, R.M.2
  • 27
    • 37649029105 scopus 로고    scopus 로고
    • Email networks and the spread of computer viruses
    • M.E.J. Newman, S. Forrest, and J. Balthrop Email networks and the spread of computer viruses Phys. Rev. E 66 2002 035101(R)
    • (2002) Phys. Rev. e , vol.66
    • Newman, M.E.J.1    Forrest, S.2    Balthrop, J.3
  • 28
    • 0022357743 scopus 로고
    • Social networks and the spread of infectious diseases: The AIDS example
    • A.S. Klovdahl Social networks and the spread of infectious diseases: the AIDS example Soc. Sci. Med. 21 1985 1203 1216
    • (1985) Soc. Sci. Med. , vol.21 , pp. 1203-1216
    • Klovdahl, A.S.1
  • 29
    • 0023091646 scopus 로고
    • Transmission dynamics of HIV infection
    • R.M. May, and R.M. Anderson Transmission dynamics of HIV infection Nature 326 1987 137 142
    • (1987) Nature , vol.326 , pp. 137-142
    • May, R.M.1    Anderson, R.M.2
  • 30
    • 0035794256 scopus 로고    scopus 로고
    • Epidemic spreading in scale-free networks
    • R. Pastor-Satorras, and A. Vespignani Epidemic spreading in scale-free networks Phys. Rev. Lett. 86 2001 3200 3203
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 3200-3203
    • Pastor-Satorras, R.1    Vespignani, A.2
  • 31
    • 0035363452 scopus 로고    scopus 로고
    • Epidemic dynamics and endemic states in complex networks
    • R. Pastor-Satorras, and A. Vespignani Epidemic dynamics and endemic states in complex networks Phys. Rev. E 63 2001 066117
    • (2001) Phys. Rev. e , vol.63 , pp. 066117
    • Pastor-Satorras, R.1    Vespignani, A.2
  • 32
    • 41349112686 scopus 로고    scopus 로고
    • Epidemic dynamics in finite size scale-free networks
    • R. Pastor-Satorras, and A. Vespignani Epidemic dynamics in finite size scale-free networks Phys. Rev. E 65 2002 035108(R)
    • (2002) Phys. Rev. e , vol.65
    • Pastor-Satorras, R.1    Vespignani, A.2
  • 33
    • 0035689341 scopus 로고    scopus 로고
    • Infection dynamics on scale-free networks
    • R.M. May, and A.L. Lloyd Infection dynamics on scale-free networks Phys. Rev. E 64 2001 066112
    • (2001) Phys. Rev. e , vol.64 , pp. 066112
    • May, R.M.1    Lloyd, A.L.2
  • 35
    • 41349106348 scopus 로고    scopus 로고
    • Spread of epidemic disease on networks
    • M.E.J. Newman Spread of epidemic disease on networks Phys. Rev. E 66 2002 016128
    • (2002) Phys. Rev. e , vol.66 , pp. 016128
    • Newman, M.E.J.1
  • 36
    • 33751230072 scopus 로고    scopus 로고
    • Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation
    • J. Joo, and J.L. Lebowitz Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation Phys. Rev. E 69 2004 066105
    • (2004) Phys. Rev. e , vol.69 , pp. 066105
    • Joo, J.1    Lebowitz, J.L.2
  • 37
    • 33751017682 scopus 로고    scopus 로고
    • Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity
    • T. Zhou, J.G. Liu, W.J. Bai, G.R. Chen, and B.H. Wang Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity Phys. Rev. E 74 2006 056109
    • (2006) Phys. Rev. e , vol.74 , pp. 056109
    • Zhou, T.1    Liu, J.G.2    Bai, W.J.3    Chen, G.R.4    Wang, B.H.5
  • 38
    • 40949107911 scopus 로고    scopus 로고
    • Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization
    • X.C. Fu, M. Small, D.M. Walker, and H.F. Zhang Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization Phys. Rev. E 77 2008 036113
    • (2008) Phys. Rev. e , vol.77 , pp. 036113
    • Fu, X.C.1    Small, M.2    Walker, D.M.3    Zhang, H.F.4
  • 39
    • 61349124265 scopus 로고    scopus 로고
    • Spreading of epidemics on scale-free networks with nonlinear infectivity
    • H.F. Zhang, and X.C. Fu Spreading of epidemics on scale-free networks with nonlinear infectivity Nonlinear Anal.: TMA 70 2009 3273 3278
    • (2009) Nonlinear Anal.: TMA , vol.70 , pp. 3273-3278
    • Zhang, H.F.1    Fu, X.C.2
  • 40
    • 80054965082 scopus 로고    scopus 로고
    • Global asymptotic stability and a property of the SIS model on bipartite networks
    • L.S. Wen, and J. Zhong Global asymptotic stability and a property of the SIS model on bipartite networks Nonlinear Anal.: RWA 13 2012 967 976
    • (2012) Nonlinear Anal.: RWA , vol.13 , pp. 967-976
    • Wen, L.S.1    Zhong, J.2
  • 41
    • 84874527279 scopus 로고    scopus 로고
    • Vaccination intervention on epidemic dynamics in networks
    • X.L. Peng, X.J. Xu, X.C. Fu, and T. Zhou Vaccination intervention on epidemic dynamics in networks Phys. Rev. E 87 2013 022813
    • (2013) Phys. Rev. e , vol.87 , pp. 022813
    • Peng, X.L.1    Xu, X.J.2    Fu, X.C.3    Zhou, T.4
  • 42
    • 84884661759 scopus 로고    scopus 로고
    • Impact of media coverage on epidemic spreading in complex networks
    • Y. Wang, J.D. Cao, Z. Jin, H.F. Zhang, and G.Q. Sun Impact of media coverage on epidemic spreading in complex networks Physica A 392 2013 5824 5835
    • (2013) Physica A , vol.392 , pp. 5824-5835
    • Wang, Y.1    Cao, J.D.2    Jin, Z.3    Zhang, H.F.4    Sun, G.Q.5
  • 45
    • 33748186988 scopus 로고    scopus 로고
    • The effect of contact heterogeneity and multiple routes of transmission on final epidemic size
    • I.Z. Kiss, D.M. Green, and R.R. Kao The effect of contact heterogeneity and multiple routes of transmission on final epidemic size Math. Biosci. 203 2006 124 136
    • (2006) Math. Biosci. , vol.203 , pp. 124-136
    • Kiss, I.Z.1    Green, D.M.2    Kao, R.R.3
  • 46
    • 38349171523 scopus 로고    scopus 로고
    • An SIS model with infective medium on complex networks
    • H.J. Shi, Z.S. Duan, and G.R. Chen An SIS model with infective medium on complex networks Physica A 387 2008 2133 2144
    • (2008) Physica A , vol.387 , pp. 2133-2144
    • Shi, H.J.1    Duan, Z.S.2    Chen, G.R.3
  • 49
    • 0017226769 scopus 로고
    • A deterministic model for gonorrhea in a nonhomogeneous population
    • A. Lajmanovich, and J.A. Yorke A deterministic model for gonorrhea in a nonhomogeneous population Math. Biosci. 28 1976 221 236
    • (1976) Math. Biosci. , vol.28 , pp. 221-236
    • Lajmanovich, A.1    Yorke, J.A.2
  • 50
    • 21844477622 scopus 로고    scopus 로고
    • Pathogen adaption to seasonal forcing and climate change
    • K. Koelle, M. Pascual, and Md. Yunus Pathogen adaption to seasonal forcing and climate change Proc. R. Soc. B 272 2005 971 977
    • (2005) Proc. R. Soc. B , vol.272 , pp. 971-977
    • Koelle, K.1    Pascual, M.2    Yunus, Md.3
  • 51
    • 0038483826 scopus 로고    scopus 로고
    • Emergence of scaling in random networks
    • A.L. Barabasi, and R. Albert Emergence of scaling in random networks Science 286 1999 509 512
    • (1999) Science , vol.286 , pp. 509-512
    • Barabasi, A.L.1    Albert, R.2
  • 52
    • 0036013593 scopus 로고    scopus 로고
    • Statistical mechanics of complex networks
    • R. Albert, and A.L. Barabasi Statistical mechanics of complex networks Rev. Mod. Phys. 74 2002 47 97
    • (2002) Rev. Mod. Phys. , vol.74 , pp. 47-97
    • Albert, R.1    Barabasi, A.L.2
  • 53
    • 84855247936 scopus 로고    scopus 로고
    • Global attractivity of a network-based epidemic SIS model with nonlinear infectivity
    • G. Zhu, X. Fu, and G. Chen Global attractivity of a network-based epidemic SIS model with nonlinear infectivity Commun. Nonlinear Sci. Numer. Simul. 17 2012 2588 2594
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 2588-2594
    • Zhu, G.1    Fu, X.2    Chen, G.3
  • 54
    • 84886292820 scopus 로고    scopus 로고
    • Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks
    • C. Li, C. Tsai, and S. Yang Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks Commun. Nonlinear Sci. Numer. Simul. 19 2014 1042 1054
    • (2014) Commun. Nonlinear Sci. Numer. Simul. , vol.19 , pp. 1042-1054
    • Li, C.1    Tsai, C.2    Yang, S.3
  • 55
    • 4043103722 scopus 로고    scopus 로고
    • Oscillatory epidemic prevalence in growing scale-free networks
    • Y. Hayashi, M. Minoura, and J. Matsukubo Oscillatory epidemic prevalence in growing scale-free networks Phys. Rev. E 69 2004 016112
    • (2004) Phys. Rev. e , vol.69 , pp. 016112
    • Hayashi, Y.1    Minoura, M.2    Matsukubo, J.3
  • 57
    • 0000145168 scopus 로고
    • The reproductive number in deterministic models of contagious diseases
    • J.A. Jacquez, C.P. Simon, and J. Koopman The reproductive number in deterministic models of contagious diseases Commun. Theor. Biol. 2 1991 159 209
    • (1991) Commun. Theor. Biol. , vol.2 , pp. 159-209
    • Jacquez, J.A.1    Simon, C.P.2    Koopman, J.3
  • 58
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H.W. Hethcote The mathematics of infectious diseases SIAM Rev. 42 2000 599 653
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 59
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • P. van den Driessche, and J. Watmough Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission Math. Biosci. 180 2002 29 48
    • (2002) Math. Biosci. , vol.180 , pp. 29-48
    • Van Den Driessche, P.1    Watmough, J.2
  • 61
    • 0000361466 scopus 로고
    • Uniform persistence and flows near a closed positively invariant set
    • H.I. Freedman, S. Ruan, and M. Tang Uniform persistence and flows near a closed positively invariant set J. Dyn. Differ. Equ. 6 1994 583 600
    • (1994) J. Dyn. Differ. Equ. , vol.6 , pp. 583-600
    • Freedman, H.I.1    Ruan, S.2    Tang, M.3
  • 62
    • 0032812296 scopus 로고    scopus 로고
    • Global dynamics of a SEIR model with varying total population size
    • 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 191 213
    • (1999) Math. Biosci. , vol.160 , pp. 191-213
    • Li, M.Y.1    Graef, J.R.2    Wang, L.3    Karsai, J.4
  • 64
    • 38049037455 scopus 로고    scopus 로고
    • Global stability of the endemic equilibrium of multigroup SIR epidemic models
    • H. Guo, M.Y. Li, and Z. Shuai Global stability of the endemic equilibrium of multigroup SIR epidemic models Can. Appl. Math. Q. 14 2006 259 284
    • (2006) Can. Appl. Math. Q. , vol.14 , pp. 259-284
    • Guo, H.1    Li, M.Y.2    Shuai, Z.3
  • 65
    • 70349388314 scopus 로고    scopus 로고
    • A graph-theoretic approach to the method of global Lyapunov functions
    • H. Guo, M.Y. Li, and Z. Shuai A graph-theoretic approach to the method of global Lyapunov functions Proc. Am. Math. Soc. 136 2008 2793 2802
    • (2008) Proc. Am. Math. Soc. , vol.136 , pp. 2793-2802
    • Guo, H.1    Li, M.Y.2    Shuai, Z.3
  • 66
    • 84872049589 scopus 로고    scopus 로고
    • Global stability for a multi-group SIRS epidemic model with varying population sizes
    • Y. Muroya, Y. Enatsu, and T. Kuniya Global stability for a multi-group SIRS epidemic model with varying population sizes Nonlinear Anal.: RWA 14 2013 1693 1704
    • (2013) Nonlinear Anal.: RWA , vol.14 , pp. 1693-1704
    • Muroya, Y.1    Enatsu, Y.2    Kuniya, T.3
  • 69
    • 0942268259 scopus 로고    scopus 로고
    • Efficient immunization strategies for computer networks and populations
    • R. Cohen, S. Havlin, and D. Ben-Avraham Efficient immunization strategies for computer networks and populations Phys. Rev. Lett. 91 2003 247901
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 247901
    • Cohen, R.1    Havlin, S.2    Ben-Avraham, D.3
  • 70
    • 77649238152 scopus 로고    scopus 로고
    • Efficient immunization strategies on complex networks
    • F.Z. Nian, and X.Y. Wang Efficient immunization strategies on complex networks J. Theor. Biol. 264 2010 77 83
    • (2010) J. Theor. Biol. , vol.264 , pp. 77-83
    • Nian, F.Z.1    Wang, X.Y.2
  • 72
    • 43649094607 scopus 로고    scopus 로고
    • A note on the global behaviour of the network-based SIS epidemic model
    • A. d'Onofrio A note on the global behaviour of the network-based SIS epidemic model Nonlinear Anal.: RWA 9 2008 1567 1572
    • (2008) Nonlinear Anal.: RWA , vol.9 , pp. 1567-1572
    • D'Onofrio, A.1
  • 73
    • 55149093653 scopus 로고    scopus 로고
    • Global stability of virus spreading in complex heterogeneous networks
    • L. Wang, and G.Z. Dai Global stability of virus spreading in complex heterogeneous networks SIAM. J. Appl. Math. 68 2008 1495 1502
    • (2008) SIAM. J. Appl. Math. , vol.68 , pp. 1495-1502
    • Wang, L.1    Dai, G.Z.2
  • 74
    • 79954614830 scopus 로고    scopus 로고
    • A modified SIS model with an infective medium on complex networks and its global stability
    • M. Yang, G.R. Chen, and X.C. Fu A modified SIS model with an infective medium on complex networks and its global stability Physica A 390 2011 2408 2413
    • (2011) Physica A , vol.390 , pp. 2408-2413
    • Yang, M.1    Chen, G.R.2    Fu, X.C.3
  • 75
    • 84865001434 scopus 로고    scopus 로고
    • Spreading dynamics and global stability of a generalized epidemic model on complex heterogeneous networks
    • G. Zhu, X.C. Fu, and G.R. Chen Spreading dynamics and global stability of a generalized epidemic model on complex heterogeneous networks Appl. Math. Model. 36 2012 5806 5817
    • (2012) Appl. Math. Model. , vol.36 , pp. 5806-5817
    • Zhu, G.1    Fu, X.C.2    Chen, G.R.3
  • 76
  • 77
    • 0002024701 scopus 로고
    • On the generalized Birth-and-Death process
    • D.G. Kendall On the generalized Birth-and-Death process Ann. Math. Stat. 19 1948 1 15
    • (1948) Ann. Math. Stat. , vol.19 , pp. 1-15
    • Kendall, D.G.1
  • 78
    • 78651255603 scopus 로고    scopus 로고
    • Epidemic spreading in evolving networks
    • Y. Schwarzkopf, A. Rakos, and D. Mukamel Epidemic spreading in evolving networks Phys. Rev. E 82 2010 036112
    • (2010) Phys. Rev. e , vol.82 , pp. 036112
    • Schwarzkopf, Y.1    Rakos, A.2    Mukamel, D.3
  • 79
    • 0018869039 scopus 로고
    • On the spread of a disease with gamma distributed latent and infectious periods
    • R. Anderson, and R. Watson On the spread of a disease with gamma distributed latent and infectious periods Biometrika 67 1980 191 198
    • (1980) Biometrika , vol.67 , pp. 191-198
    • Anderson, R.1    Watson, R.2
  • 80
    • 70349785039 scopus 로고    scopus 로고
    • Global-stability problem for coupled systems of differential equations on networks
    • M.Y. Li, and Z.S. Shuai Global-stability problem for coupled systems of differential equations on networks J. Differ. Equ. 248 2010 1 20
    • (2010) J. Differ. Equ. , vol.248 , pp. 1-20
    • Li, M.Y.1    Shuai, Z.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.