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Volumn 275, Issue , 2016, Pages 255-267

Threshold behavior of a stochastic SIS model with Lévy jumps

Author keywords

Extinction; Ito formula; L vy jumps; Persistence; Stochastic SIS epidemic model

Indexed keywords

EPIDEMIOLOGY; LIGHT EXTINCTION; STOCHASTIC SYSTEMS;

EID: 84950986062     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2015.11.077     Document Type: Article
Times cited : (73)

References (32)
  • 1
    • 79960370338 scopus 로고    scopus 로고
    • A stochastic differential equation SIS epidemic model
    • A. Gray, and 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
  • 2
    • 84862005170 scopus 로고    scopus 로고
    • The SIS epidemic model with Markovian switching
    • A. Gray, and et al. The SIS epidemic model with Markovian switching J. Math. Anal. Appl. 394 2012 496 516
    • (2012) J. Math. Anal. Appl. , vol.394 , pp. 496-516
    • Gray, A.1
  • 3
    • 84887260929 scopus 로고    scopus 로고
    • Stationary distribution of a stochastic SIS epidemic model
    • Y. Lin, D. Jiang, and S. Wang Stationary distribution of a stochastic SIS epidemic model Phys. A 394 2014 187 197
    • (2014) Phys. A , vol.394 , pp. 187-197
    • Lin, Y.1    Jiang, D.2    Wang, S.3
  • 4
    • 67649118104 scopus 로고    scopus 로고
    • Stability of a stochastic delayed SIR model
    • G. Chen, and T. Li Stability of a stochastic delayed SIR model Stoch. Dyn. 9 2009 231 252
    • (2009) Stoch. Dyn. , vol.9 , pp. 231-252
    • Chen, G.1    Li, T.2
  • 5
    • 19944381861 scopus 로고    scopus 로고
    • Stability of a stochastic SIR system
    • E. Tornatore, S. Buccellato, and P. Vetro 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.2    Vetro, P.3
  • 6
    • 84355161643 scopus 로고    scopus 로고
    • Dynamics of a multigroup SIR epidemic model with stochastic perturbation
    • C. Ji, and et al. Dynamics of a multigroup SIR epidemic model with stochastic perturbation Automatica 48 2012 121 131
    • (2012) Automatica , vol.48 , pp. 121-131
    • Ji, C.1
  • 7
    • 0036846225 scopus 로고    scopus 로고
    • A general model for stochastic SIR epidemics with two levels of mixing
    • B. Frank, and N. Peter A general model for stochastic SIR epidemics with two levels of mixing Math. Biosci. 180 2002 73 102
    • (2002) Math. Biosci. , vol.180 , pp. 73-102
    • Frank, B.1    Peter, N.2
  • 8
    • 68049121846 scopus 로고    scopus 로고
    • Global stability of two-group SIR model with random perturbation
    • J. Yu, D. Jiang, and N. Shi Global stability of two-group SIR model with random perturbation J. Math. Anal. Appl. 360 2009 235 244
    • (2009) J. Math. Anal. Appl. , vol.360 , pp. 235-244
    • Yu, J.1    Jiang, D.2    Shi, N.3
  • 9
    • 0036293119 scopus 로고    scopus 로고
    • Stochastic models of some endemic infections
    • N. Ingemar Stochastic models of some endemic infections Math. Biosci. 179 2002 1 19
    • (2002) Math. Biosci. , vol.179 , pp. 1-19
    • Ingemar, N.1
  • 10
    • 84455169402 scopus 로고    scopus 로고
    • The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence
    • Q. Yang, and et al. The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence J. Math. Anal. Appl. 388 2012 248 271
    • (2012) J. Math. Anal. Appl. , vol.388 , pp. 248-271
    • Yang, Q.1
  • 11
    • 36148991049 scopus 로고    scopus 로고
    • Mean-square stability of a stochastic model for bacteriophage infection with time delays
    • M. Carletti Mean-square stability of a stochastic model for bacteriophage infection with time delays Math. Biosci. 210 2 2007 395 414
    • (2007) Math. Biosci. , vol.210 , Issue.2 , pp. 395-414
    • Carletti, M.1
  • 12
    • 84873535867 scopus 로고    scopus 로고
    • Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence
    • A. Lahrouz, and L. Omari Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence Stat. Probab. Lett. 83 2013 960 968
    • (2013) Stat. Probab. Lett. , vol.83 , pp. 960-968
    • Lahrouz, A.1    Omari, L.2
  • 13
    • 84879092827 scopus 로고    scopus 로고
    • Long-time behaviour of a perturbed SIR model by white noise
    • Y. Lin, and D. Jiang Long-time behaviour of a perturbed SIR model by white noise Discret. Cont. Dyn. Syst. Ser. B 18 2013 1873 1887
    • (2013) Discret. Cont. Dyn. Syst. Ser. B , vol.18 , pp. 1873-1887
    • Lin, Y.1    Jiang, D.2
  • 14
    • 84903978036 scopus 로고    scopus 로고
    • The threshold of a stochastic SIS epidemic model with vaccination
    • Y. Zhao, and D. Jiang The threshold of a stochastic SIS epidemic model with vaccination Appl. Math. Comput. 243 2014 718 727
    • (2014) Appl. Math. Comput. , vol.243 , pp. 718-727
    • Zhao, Y.1    Jiang, D.2
  • 15
    • 84908507682 scopus 로고    scopus 로고
    • Threshold behaviour of a stochastic SIR model
    • C. Ji, and D. Jiang Threshold behaviour of a stochastic SIR model Appl. Math. Model. 38 2014 5067 5079
    • (2014) Appl. Math. Model. , vol.38 , pp. 5067-5079
    • Ji, C.1    Jiang, D.2
  • 17
    • 0025159677 scopus 로고
    • On the definition and computation of the basic reproductive ratio in models for infectious diseases in heterogeneous population
    • O. Diekmann, and et al. On the definition and computation of the basic reproductive ratio in models for infectious diseases in heterogeneous population J. Math. Biol. 28 4 1990 365 382
    • (1990) J. Math. Biol. , vol.28 , Issue.4 , pp. 365-382
    • Diekmann, O.1
  • 18
    • 84875736026 scopus 로고    scopus 로고
    • Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps
    • M. Liu, and K. Wang Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps Nonlinear Anal. 85 2013 204 213
    • (2013) Nonlinear Anal. , vol.85 , pp. 204-213
    • Liu, M.1    Wang, K.2
  • 19
    • 80051597036 scopus 로고    scopus 로고
    • Competitive Lotka-Volterra population dynamics with jumps
    • J. Bao, and et al. Competitive Lotka-Volterra population dynamics with jumps Nonlinear Anal. 74 2011 6601 6616
    • (2011) Nonlinear Anal. , vol.74 , pp. 6601-6616
    • Bao, J.1
  • 21
    • 38248999613 scopus 로고
    • Pricing options on securities with discontinuous
    • I. Bardhan, and X. Chao Pricing options on securities with discontinuous Stoch. Proc. Appl. 48 1993 123 137
    • (1993) Stoch. Proc. Appl. , vol.48 , pp. 123-137
    • Bardhan, I.1    Chao, X.2
  • 22
    • 34248474317 scopus 로고
    • Option pricing when underlying stock returns are discontinuous
    • R. Merton Option pricing when underlying stock returns are discontinuous J. Financ. Econ. 3 1976 125 144
    • (1976) J. Financ. Econ. , vol.3 , pp. 125-144
    • Merton, R.1
  • 23
    • 34548131034 scopus 로고    scopus 로고
    • Flights towards defection in economic transactions
    • M. Perc Flights towards defection in economic transactions Econ. Lett. 97 2007 58 63
    • (2007) Econ. Lett. , vol.97 , pp. 58-63
    • Perc, M.1
  • 24
    • 33846813336 scopus 로고    scopus 로고
    • Transition from Gaussion to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma game
    • M. Perc Transition from Gaussion to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma game Phy. Rev. E 75 2007 022101
    • (2007) Phy. Rev. e , vol.75 , pp. 022101
    • Perc, M.1
  • 25
    • 84905041397 scopus 로고    scopus 로고
    • The Mattew effect in empirical data
    • M. Perc The Mattew effect in empirical data J. R. Soc. Interface 11 2014 20140378
    • (2014) J. R. Soc. Interface , vol.11 , pp. 20140378
    • Perc, M.1
  • 26
    • 84888072869 scopus 로고    scopus 로고
    • Fat tails in marine microbial population fluctuations
    • A. Segura, and et al. Fat tails in marine microbial population fluctuations Oikos 122 2013 1739 1745
    • (2013) Oikos , vol.122 , pp. 1739-1745
    • Segura, A.1
  • 27
    • 84877792643 scopus 로고    scopus 로고
    • Stochastic SIR model with jumps
    • X. Zhang, and K. Wang Stochastic SIR model with jumps Appl. Math. Lett. 26 2013 867 874
    • (2013) Appl. Math. Lett. , vol.26 , pp. 867-874
    • Zhang, X.1    Wang, K.2
  • 28
    • 84900834468 scopus 로고    scopus 로고
    • Stochastic SEIR model with jumps
    • X. Zhang, and K. Wang Stochastic SEIR model with jumps Appl. Math. Comput. 2399 2014 133 143
    • (2014) Appl. Math. Comput. , vol.2399 , pp. 133-143
    • Zhang, X.1    Wang, K.2
  • 29
    • 32044460132 scopus 로고    scopus 로고
    • Perspectives on the basic reproductive ratio
    • J. Heffernan, R. Smith, and L. WahI Perspectives on the basic reproductive ratio J. R. Soc. Interface 2 4 2005 281 293
    • (2005) J. R. Soc. Interface , vol.2 , Issue.4 , pp. 281-293
    • Heffernan, J.1    Smith, R.2    WahI, L.3
  • 31
    • 84655161375 scopus 로고    scopus 로고
    • Stochastic persistence and stationary distribution in a Holling-Tanner type prey-predator model
    • P. Mandal, and M. Banerjee Stochastic persistence and stationary distribution in a Holling-Tanner type prey-predator model Phys. A 391 2012 1216 1233
    • (2012) Phys. A , vol.391 , pp. 1216-1233
    • Mandal, P.1    Banerjee, M.2
  • 32
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • D. Higham An algorithmic introduction to numerical simulation of stochastic differential equations SIAM Rev. 43 2001 525 546
    • (2001) SIAM Rev. , vol.43 , pp. 525-546
    • Higham, D.1


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