메뉴 건너뛰기




Volumn 447, Issue 2, 2017, Pages 736-757

Global threshold dynamics of a stochastic differential equation SIS model

Author keywords

Basic reproduction number; Fokker Planck equation; Global threshold dynamics; Invariant density; SIS epidemic model; Stochastic differential equation

Indexed keywords


EID: 85002542228     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2016.10.041     Document Type: Article
Times cited : (35)

References (19)
  • 1
    • 0037746789 scopus 로고    scopus 로고
    • An Introduction to Stochastic Processes with Applications to Biology
    • Pearson Prentice Hall Upper Saddle River
    • [1] Allen, L.J.S., An Introduction to Stochastic Processes with Applications to Biology. 2003, Pearson Prentice Hall, Upper Saddle River.
    • (2003)
    • Allen, L.J.S.1
  • 2
    • 0003677583 scopus 로고
    • Infectious Diseases of Humans: Dynamics and Control
    • Oxford University Press Oxford
    • [2] Anderson, R.M., May, R.M., Infectious Diseases of Humans: Dynamics and Control. 1992, Oxford University Press, Oxford.
    • (1992)
    • Anderson, R.M.1    May, R.M.2
  • 3
    • 84873746359 scopus 로고    scopus 로고
    • Lyapunov exponent of a stochastic SIRS model
    • [3] Chen, G., Li, T., Liu, C., Lyapunov exponent of a stochastic SIRS model. C. R. Acad. Sci. Paris, Ser. I 351 (2013), 33–35.
    • (2013) C. R. Acad. Sci. Paris, Ser. I , vol.351 , pp. 33-35
    • Chen, G.1    Li, T.2    Liu, C.3
  • 4
    • 33750368835 scopus 로고    scopus 로고
    • A stochastic model of AIDS and condom use
    • [4] Dalal, N., Greenhalgh, D., Mao, X., A stochastic model of AIDS and condom use. J. Math. Anal. Appl. 325 (2007), 36–53.
    • (2007) J. Math. Anal. Appl. , vol.325 , pp. 36-53
    • Dalal, N.1    Greenhalgh, D.2    Mao, X.3
  • 5
    • 0003426971 scopus 로고    scopus 로고
    • Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation
    • Wiley New York
    • [5] Diekmann, O., Heesterbeek, J.A.P., Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. 2000, Wiley, New York.
    • (2000)
    • Diekmann, O.1    Heesterbeek, J.A.P.2
  • 7
    • 84966207705 scopus 로고
    • Diffusion processes in one dimension
    • [7] Feller, W., Diffusion processes in one dimension. Trans. Amer. Math. Soc. 77 (1954), 1–31.
    • (1954) Trans. Amer. Math. Soc. , vol.77 , pp. 1-31
    • Feller, W.1
  • 8
    • 79960370338 scopus 로고    scopus 로고
    • A stochastic differential equation SIS epidemic model
    • [8] Gray, A., et al. A stochastic differential equation SIS epidemic model. SIAM J. Appl. Math. 71 (2011), 876–902.
    • (2011) SIAM J. Appl. Math. , vol.71 , pp. 876-902
    • Gray, A.1
  • 9
    • 0003020529 scopus 로고
    • Gonorrhea Transmission Dynamics and Control
    • Springer-Verlag Berlin
    • [9] Hethcote, H.W., Yorke, J.A., Gonorrhea Transmission Dynamics and Control. Lecture Notes in Biomath., vol. 56, 1984, Springer-Verlag, Berlin.
    • (1984) Lecture Notes in Biomath. , vol.56
    • Hethcote, H.W.1    Yorke, J.A.2
  • 10
    • 0021404302 scopus 로고
    • Ergodicity of randomly perturbed Lorenz model
    • [10] It̂o, H.M., Ergodicity of randomly perturbed Lorenz model. J. Stat. Phys. 35 (1984), 151–158.
    • (1984) J. Stat. Phys. , vol.35 , pp. 151-158
    • It̂o, H.M.1
  • 11
    • 0003242243 scopus 로고    scopus 로고
    • Brownian Motion and Stochastic Calculus
    • 2nd ed. Springer Verlag New York
    • [11] Karatzas, I., Shreve, S., Brownian Motion and Stochastic Calculus. 2nd ed. Graduate Texts in Math., vol. 113, 1997, Springer Verlag, New York.
    • (1997) Graduate Texts in Math. , vol.113
    • Karatzas, I.1    Shreve, S.2
  • 12
    • 0000998185 scopus 로고
    • A contribution to the mathematical theory of epidemics. Part I
    • [12] Kermack, W.O., McKendrick, A.G., A contribution to the mathematical theory of epidemics. Part I. Proc. R. Soc. Lond. Ser. A 115 (1927), 700–721.
    • (1927) Proc. R. Soc. Lond. Ser. A , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 13
    • 0003802044 scopus 로고
    • Stability of Systems of Differential Equations under Random Perturbation of Their Parameters
    • Nauka Moscow (in Russian)
    • [13] Khasiminsky, R.Z., Stability of Systems of Differential Equations under Random Perturbation of Their Parameters. 1969, Nauka, Moscow (in Russian).
    • (1969)
    • Khasiminsky, R.Z.1
  • 14
    • 0003228410 scopus 로고
    • Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics
    • 2nd ed. Springer New York
    • [14] Lasota, A., Mackey, M.C., Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics. 2nd ed. Appl. Math. Sci., vol. 97, 1994, Springer, New York.
    • (1994) Appl. Math. Sci. , vol.97
    • Lasota, A.1    Mackey, M.C.2
  • 15
    • 84879092827 scopus 로고    scopus 로고
    • Long-time behaviour of a perturbed SIR model by white noise
    • [15] Lin, Y., Jiang, D., Long-time behaviour of a perturbed SIR model by white noise. Discrete Contin. Dyn. Syst. Ser. B 18 (2013), 1873–1887.
    • (2013) Discrete Contin. Dyn. Syst. Ser. B , vol.18 , pp. 1873-1887
    • Lin, Y.1    Jiang, D.2
  • 16
    • 67649440965 scopus 로고    scopus 로고
    • Stability of SIRS system with random perturbations
    • [16] Lu, Q., Stability of SIRS system with random perturbations. Phys. A 388 (2009), 3677–3686.
    • (2009) Phys. A , vol.388 , pp. 3677-3686
    • Lu, Q.1
  • 17
    • 0001663606 scopus 로고
    • Noise-induced global asymptotic stability
    • [17] Mackey, M.C., Longtin, A., Lasota, A., Noise-induced global asymptotic stability. J. Stat. Phys. 60 (1990), 735–751.
    • (1990) J. Stat. Phys. , vol.60 , pp. 735-751
    • Mackey, M.C.1    Longtin, A.2    Lasota, A.3
  • 18
    • 19944381861 scopus 로고    scopus 로고
    • Stability of a stochastic SIR system
    • [18] Tornatore, E., Buccellato, S.M., Vetro, P., Stability of a stochastic SIR system. Phys. A 354 (2005), 111–126.
    • (2005) Phys. A , vol.354 , pp. 111-126
    • Tornatore, E.1    Buccellato, S.M.2    Vetro, P.3
  • 19
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • [19] van den Driessche, P., Watmough, J., 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.