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Methodology and Computing in Applied Probability
Volumn 13, Issue 3, 2011, Pages 603-618
Approximating the Quasi-stationary Distribution of the SIS Model for Endemic Infection
Author keywords

Cumulant equations; Endemic disease; Moment closure; Stochastic infection model
Indexed keywords

EID: 79960292204     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-010-9177-8     Document Type: Article
Times cited : (16)
References (17)
  • 1
    • 0001892427 scopus 로고
    • Deterministic and stochastic models for recurrent epidemics
    • Berkeley: University of California Press
    • Bartlett MS (1956) Deterministic and stochastic models for recurrent epidemics. In: Proc. third Berkeley symp. math. statist. and probab., vol 4. University of California Press, Berkeley, pp 81-109.
    • (1956) Proc. Third Berkeley Symp. Math. Statist. And Probab , vol.4 , pp. 81-109
    • Bartlett, M.S.1
  • 2
    • 0000851843 scopus 로고
    • Quasi-stationary distributions of birth-and-death processes
    • Cavender JA (1978) Quasi-stationary distributions of birth-and-death processes. Adv Appl Probab 10: 570-586.
    • (1978) Adv Appl Probab , vol.10 , pp. 570-586
    • Cavender, J.A.1
  • 3
    • 0041774290 scopus 로고    scopus 로고
    • Approximations for the long-term behavior of an open-population epidemic model
    • Clancy D, O'Neill PD, Pollett PK (2001) Approximations for the long-term behavior of an openpopulation epidemic model. Methodol Comput Appl Probab 3: 75-95.
    • (2001) Methodol Comput Appl Probab , vol.3 , pp. 75-95
    • Clancy, D.1    O'Neill, P.D.2    Pollett, P.K.3
  • 4
    • 0001383449 scopus 로고
    • On quasi-stationary distributions in absorbing continuous-time finite Markov chains
    • Darroch J, Seneta E (1967) On quasi-stationary distributions in absorbing continuous-time finite Markov chains. J Appl Probab 4: 192-196.
    • (1967) J Appl Probab , vol.4 , pp. 192-196
    • Darroch, J.1    Seneta, E.2
  • 5
    • 0034698011 scopus 로고    scopus 로고
    • Multiplicative moments and measures of persistence in ecology
    • Keeling MJ (2000) Multiplicative moments and measures of persistence in ecology. J Theor Biol 205: 269-281.
    • (2000) J Theor Biol , vol.205 , pp. 269-281
    • Keeling, M.J.1
  • 6
    • 19044383593 scopus 로고    scopus 로고
    • Novel moment closure approximations in stochastic epidemics
    • Krishnarajah I, Cook A, Marion G, Gibson G (2005) Novel moment closure approximations in stochastic epidemics. Bull Math Biol 67: 855-873.
    • (2005) Bull Math Biol , vol.67 , pp. 855-873
    • Krishnarajah, I.1    Cook, A.2    Marion, G.3    Gibson, G.4
  • 7
    • 0000311552 scopus 로고
    • On the extinction of the S-I-S stochastic logistic epidemic
    • Kryscio R, Lefèvre C (1989) On the extinction of the S-I-S stochastic logistic epidemic. J Appl Probab 27: 685-694.
    • (1989) J Appl Probab , vol.27 , pp. 685-694
    • Kryscio, R.1    Lefèvre, C.2
  • 8
    • 0000635179 scopus 로고    scopus 로고
    • The quasi-stationary distribution of the closed endemic SIS model
    • Nåsell I (1996) The quasi-stationary distribution of the closed endemic SIS model. Adv Appl Probab 28: 895-932.
    • (1996) Adv Appl Probab , vol.28 , pp. 895-932
    • Nåsell, I.1
  • 9
    • 2542509066 scopus 로고    scopus 로고
    • On the quasi-stationary distribution of the stochastic logistic epidemic
    • Nåsell I (1999a) On the quasi-stationary distribution of the stochastic logistic epidemic. Math Biosci 156: 21-40.
    • (1999) Math Biosci , vol.156 , pp. 21-40
    • Nåsell, I.1
  • 10
    • 0033475339 scopus 로고    scopus 로고
    • On the time to extinction in recurrent epidemics
    • Nåsell I (1999b) On the time to extinction in recurrent epidemics. J R Stat Soc B 61: 309-330.
    • (1999) J R Stat Soc B , vol.61 , pp. 309-330
    • Nåsell, I.1
  • 11
    • 17944394670 scopus 로고    scopus 로고
    • Moment closure and the stochastic logistic model
    • Nåsell I (2003a) Moment closure and the stochastic logistic model. Theor Popul Biol 63: 159-168.
    • (2003) Theor Popul Biol , vol.63 , pp. 159-168
    • Nåsell, I.1
  • 12
    • 0347506351 scopus 로고    scopus 로고
    • An extension of the moment closure method
    • Nåsell I (2003b) An extension of the moment closure method. Theor Popul Biol 64: 233-239.
    • (2003) Theor Popul Biol , vol.64 , pp. 233-239
    • Nåsell, I.1
  • 13
    • 16244363078 scopus 로고    scopus 로고
    • A new look at the critical community size for childhood infections
    • Nåsell I (2005) A new look at the critical community size for childhood infections. Theor Popul Biol 67: 203-216.
    • (2005) Theor Popul Biol , vol.67 , pp. 203-216
    • Nåsell, I.1
  • 14
    • 0035528749 scopus 로고    scopus 로고
    • The quasistationary distribution of the stochastic logistic model
    • Ovaskainen O (2001) The quasistationary distribution of the stochastic logistic model. J Appl Probab 38: 898-907.
    • (2001) J Appl Probab , vol.38 , pp. 898-907
    • Ovaskainen, O.1
  • 15
    • 0000381122 scopus 로고
    • Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes
    • van Doorn EA (1991) Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes. Adv Appl Probab 23: 683-700.
    • (1991) Adv Appl Probab , vol.23 , pp. 683-700
    • van Doorn, E.A.1
  • 16
    • 0002618815 scopus 로고
    • On the asymptotic behaviour of the stochastic and deterministic models of an epidemic
    • Weiss GH, Dishon M (1971) On the asymptotic behaviour of the stochastic and deterministic models of an epidemic. Math Biosci 11: 261-265.
    • (1971) Math Biosci , vol.11 , pp. 261-265
    • Weiss, G.H.1    Dishon, M.2
  • 17
    • 0001637131 scopus 로고
    • On the use of the normal approximation in the treatment of stochastic processes
    • Whittle P (1957) On the use of the normal approximation in the treatment of stochastic processes. J R Stat Soc B 19: 268-281.
    • (1957) J R Stat Soc B , vol.19 , pp. 268-281
    • Whittle, P.1

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