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Volumn 2012, Issue , 2012, Pages

A lie algebra approach to susceptible-infected-susceptible epidemics

Author keywords

Epidemic dynamics; Lie algebra; Riccati equation; Susceptible infected susceptible

Indexed keywords


EID: 84871693073     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (51)

References (26)
  • 1
    • 0036739709 scopus 로고    scopus 로고
    • Extinction dynamics in mainland-island metapopulations: An N- patch stochastic model
    • D. Alonso, A. McKane; Extinction dynamics in mainland-island metapopulations: an N- patch stochastic model, Bull. Math. Biol. 64(2002) 913-958.
    • (2002) Bull. Math. Biol , vol.64 , pp. 913-958
    • Alonso, D.1    McKane, A.2
  • 2
    • 79956135264 scopus 로고    scopus 로고
    • High-order commutator-free exponential time-propagation of driven quantum systems
    • A. Alvermann, H. Fehske; High-order commutator-free exponential time-propagation of driven quantum systems, J. Comput. Phys. 230(2011) 5930-5956.
    • (2011) J. Comput. Phys , vol.230 , pp. 5930-5956
    • Alvermann, A.1    Fehske, H.2
  • 4
    • 84864394072 scopus 로고    scopus 로고
    • A law of large numbers approximation for Markov population processes with countably many types, Probab
    • A. D. Barbour, M. J. Luczak; A law of large numbers approximation for Markov population processes with countably many types, Probab. Theory Relat. Fields 153(2012) 727-757.
    • (2012) Theory Relat. Fields , vol.153 , pp. 727-757
    • Barbour, A.D.1    Luczak, M.J.2
  • 5
    • 18044384806 scopus 로고    scopus 로고
    • Dynamical patterns of epidemic outbreaks in complex heterogeneous networks
    • M. Barthélémy, A. Barrat, R. Pastor-Satorras, A. Vespignani; Dynamical patterns of epidemic outbreaks in complex heterogeneous networks, J. Theor. Biol. 235(2005) 275-288.
    • (2005) J. Theor. Biol , vol.235 , pp. 275-288
    • Barthélémy, M.1    Barrat, A.2    Pastor-Satorras, R.3    Vespignani, A.4
  • 6
    • 58149396539 scopus 로고    scopus 로고
    • The Magnus expansion and some of its applications
    • S. Blanes, F. Casas, J. A. Oteo, J. Ros; The Magnus expansion and some of its applications, Phys. Rep. 470(2009) 151-238.
    • (2009) Phys. Rep , vol.470 , pp. 151-238
    • Blanes, S.1    Casas, F.2    Oteo, J.A.3    Ros, J.4
  • 7
    • 80052974589 scopus 로고    scopus 로고
    • Nonperturbative heterogeneous mean- field approach to epidemic spreading in complex networks
    • S. Gómez, J. Gómez-Gardeñes, Y. Moreno, A. Arenas; Nonperturbative heterogeneous mean- field approach to epidemic spreading in complex networks, Phys. Rev. E 84(2011) 036105.
    • (2011) Phys. Rev. E , vol.84 , pp. 036105
    • Gómez, S.1    Gómez-Gardeñes, J.2    Moreno, Y.3    Arenas, A.4
  • 8
    • 84871704277 scopus 로고    scopus 로고
    • Lie algebra solution of population models based on time-inhomogeneous Markov chains
    • T. House; Lie algebra solution of population models based on time-inhomogeneous Markov chains, J. Appl. Probab. 49(2012) 472-481.
    • (2012) J. Appl. Probab , vol.49 , pp. 472-481
    • House, T.1
  • 10
    • 37249009073 scopus 로고    scopus 로고
    • On methods for studing stochastic disease dynamics
    • M. J. Keeling, J. V. Ross; On methods for studing stochastic disease dynamics, J. R. Soc. Interface 5(2008) 171-181.
    • (2008) J. R. Soc. Interface , vol.5 , pp. 171-181
    • Keeling, M.J.1    Ross, J.V.2
  • 11
    • 0000998185 scopus 로고
    • A contribution to the mathematical theory of epidemics
    • W. O. Kermack, A. G. McKendrick; A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. A 115(1927) 700-721.
    • (1927) Proc. R. Soc. Lond. A , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 12
    • 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
  • 13
    • 0003781238 scopus 로고    scopus 로고
    • Cambridge University Press, New York
    • J. R. Norris; Markov Chains, Cambridge University Press, New York, 1997.
    • (1997) Markov Chains
    • Norris, J.R.1
  • 14
    • 42149170100 scopus 로고    scopus 로고
    • Dynamics of epidemics on random networks
    • M. Marder; Dynamics of epidemics on random networks, Phys. Rev. E 75(2007) 066103.
    • (2007) Phys. Rev. E , vol.75 , pp. 066103
    • Marder, M.1
  • 15
    • 0035528749 scopus 로고    scopus 로고
    • The quasistationary distribution of the stochastic logistic model
    • O. Ovaskainen; The quasistationary distribution of the stochastic logistic model, J. Appl. Probab. 38(2001) 898-907.
    • (2001) J. Appl. Probab , vol.38 , pp. 898-907
    • Ovaskainen, O.1
  • 16
    • 0035794256 scopus 로고    scopus 로고
    • Epidemic spreading in scale-free networks
    • R. Pastor-Satorras, 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
  • 18
    • 76449089417 scopus 로고    scopus 로고
    • Computationally exact methods for stochastic periodic dynamics spatiotemporal dispersal and temporally forced transmission
    • J. V. Ross; Computationally exact methods for stochastic periodic dynamics spatiotemporal dispersal and temporally forced transmission, J. Theor. Biol. 262(2010) 14-22.
    • (2010) J. Theor. Biol , vol.262 , pp. 14-22
    • Ross, J.V.1
  • 19
    • 78650301212 scopus 로고    scopus 로고
    • Likelihood estimation for stochastic epidemics with heterogeneous mixing popula- tions
    • Y. Shang; Likelihood estimation for stochastic epidemics with heterogeneous mixing popula- tions, Int. J. Comput. Math. Sci. 6(2012) 34-38.
    • (2012) Int. J. Comput. Math. Sci , vol.6 , pp. 34-38
    • Shang, Y.1
  • 20
    • 84863102920 scopus 로고    scopus 로고
    • Distribution dynamics for SIS model on random networks
    • Y. Shang; Distribution dynamics for SIS model on random networks, J. Biol. Syst. 20(2012) 213-220.
    • (2012) J. Biol. Syst , vol.20 , pp. 213-220
    • Shang, Y.1
  • 21
    • 84856946171 scopus 로고    scopus 로고
    • Optimal attack strategies in a dynamic botnet defense model
    • Y. Shang; Optimal attack strategies in a dynamic botnet defense model, Appl. Math. Inf. Sci. 6(2012)29-33.
    • (2012) Appl. Math. Inf. Sci , vol.6 , pp. 29-33
    • Shang, Y.1
  • 22
    • 84880947651 scopus 로고    scopus 로고
    • Optimal control strategies for virus spreading in inhomogeneous epidemic dynam- ics
    • doi:10.4153/CMB-2012-007-2
    • Y. Shang; Optimal control strategies for virus spreading in inhomogeneous epidemic dynam- ics, Canad. Math. Bull. doi:10.4153/CMB-2012-007-2.
    • Canad. Math. Bull
    • Shang, Y.1
  • 23
    • 84872130172 scopus 로고    scopus 로고
    • Mixed SI(R) epidemic dynamics in random graphs with general degree distribu- tions
    • doi:10.1016/j.amc.2012.11.026
    • Y. Shang; Mixed SI(R) epidemic dynamics in random graphs with general degree distribu- tions, Appl. Math. Comput. doi:10.1016/j.amc.2012.11.026.
    • Appl. Math. Comput
    • Shang, Y.1
  • 24
    • 0007347727 scopus 로고
    • Lie algebra solution of linear differential equations
    • J. Wei, E. Norman; Lie algebra solution of linear differential equations, J. Math. Phys. 4(1963)575-581.
    • (1963) J. Math. Phys , vol.4 , pp. 575-581
    • Wei, J.1    Norman, E.2
  • 25
    • 0002618815 scopus 로고
    • On the asymptotic behavior of the stochastic and deterministic models of an epidemic
    • G. H. Weiss, M. Dishon; On the asymptotic behavior of the stochastic and deterministic models of an epidemic, Math. Biosci. 11(1971) 261-265.
    • (1971) Math. Biosci , vol.11 , pp. 261-265
    • Weiss, G.H.1    Dishon, M.2
  • 26
    • 0042638530 scopus 로고
    • Exponential operators and parameter differentiation in quantum physics
    • R. M. Wilcox; Exponential operators and parameter differentiation in quantum physics, J. Math. Phys. 8(1967) 962-982.
    • (1967) J. Math. Phys , vol.8 , pp. 962-982
    • Wilcox, R.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.