Dynamic behavior of a stochastic SIQS epidemic model with Lévy jumps

In this paper, we propose a stochastic SIQS epidemic model with Lévy jumps and investigate sufficient conditions of the extinction and persistence of the disease. Then, we analyze the asymptotic behavior of the solution of the model around the endemic equilibrium of the corresponding deterministic model. We find that Lévy jumps can suppress the disease outbreak. Numerical simulations are carried out and approve our results.

[1]  Jiajia Yu,et al.  Asymptotic behavior of global positive solution to a stochastic SIR model , 2011, Math. Comput. Model..

[2]  Yun Kang,et al.  A stochastic SIRS epidemic model with infectious force under intervention strategies , 2015 .

[3]  Zhidong Teng,et al.  Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients , 2017 .

[4]  Yanan Zhao,et al.  The threshold of a stochastic SIS epidemic model with vaccination , 2014, Appl. Math. Comput..

[5]  Tasawar Hayat,et al.  Analysis of a delayed vaccinated SIR epidemic model with temporary immunity and Lévy jumps , 2018 .

[6]  Jiabo Xu,et al.  Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps , 2016 .

[7]  Hong Xiang,et al.  Dynamics of the deterministic and stochastic SIQS epidemic model with non-linear incidence , 2014, Appl. Math. Comput..

[8]  Juan Li,et al.  Persistence and ergodicity of plant disease model with markov conversion and impulsive toxicant input , 2017, Commun. Nonlinear Sci. Numer. Simul..

[9]  R. Liptser.  A strong law of large numbers for local martingales , 1980 .

[10]  Xinzhu Meng,et al.  Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis , 2016 .

[11]  Chuanzhi Bai,et al.  Dynamics of a stochastic one-prey two-predator model with Lévy jumps , 2016, Appl. Math. Comput..

[12]  Hong Xiang,et al.  Dynamics of an SAITS alcoholism model on unweighted and weighted networks , 2018 .

[13]  X. Mao,et al.  Competitive Lotka–Volterra population dynamics with jumps , 2011, 1102.2163.

[14]  Sanling Yuan,et al.  The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence , 2016 .

[15]  Z. Teng,et al.  Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate , 2016 .

[16]  Xinzhu Meng,et al.  Stochastic inequalities and applications to dynamics analysis of a novel SIVS epidemic model with jumps , 2017, Journal of Inequalities and Applications.

[17]  Daqing Jiang,et al.  The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence , 2012 .

[18]  Qun Liu,et al.  Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence , 2015 .

[19]  H. Hethcote,et al.  Effects of quarantine in six endemic models for infectious diseases. , 2002, Mathematical biosciences.

[20]  Xuerong Mao,et al.  THE THRESHOLD OF A STOCHASTIC SIRS EPIDEMIC MODEL IN A POPULATION WITH VARYING SIZE , 2015 .

[21]  Meng Liu,et al.  Optimal harvesting of a stochastic mutualism model with Lévy jumps , 2016, Appl. Math. Comput..

[22]  N. Shi,et al.  Dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases driven by Lévy jumps , 2018 .

[23]  Daqing Jiang,et al.  Threshold behaviour of a stochastic SIR model , 2014 .

[24]  Fengying Wei,et al.  Stochastic permanence of an SIQS epidemic model with saturated incidence and independent random perturbations , 2016 .

[25]  Meng Liu,et al.  Analysis of stochastic two-prey one-predator model with Lévy jumps , 2016 .

[26]  Daqing Jiang,et al.  Stationary distribution of a stochastic SIS epidemic model with vaccination , 2014 .

[27]  Yanli Zhou,et al.  Threshold of a stochastic SIR epidemic model with Lévy jumps , 2016 .

[28]  Liangjian Hu,et al.  A Stochastic Differential Equation SIS Epidemic Model , 2011, SIAM J. Appl. Math..

[29]  Ahmed Alsaedi,et al.  Stochastic mutualism model with Lévy jumps , 2017, Commun. Nonlinear Sci. Numer. Simul..

[30]  Hai-Feng Huo,et al.  The threshold of a stochastic SIQS epidemic model , 2017 .

[31]  Omar Abu Arqub,et al.  Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions , 2017, Comput. Math. Appl..

[32]  K. Hattaf,et al.  Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity , 2018 .

[33]  Qimin Zhang,et al.  The effect of Lévy noise on the survival of a stochastic competitive model in an impulsive polluted environment , 2016 .

[34]  Hai-Feng Huo,et al.  Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species , 2018, Journal of biological dynamics.

[35]  Yanan Zhao,et al.  The threshold of a stochastic SIRS epidemic model with saturated incidence , 2014, Appl. Math. Lett..

[37]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[38]  Tasawar Hayat,et al.  Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps , 2017 .

[39]  Omar Abu Arqub,et al.  Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm , 2018 .

[40]  Ke Wang,et al.  Stochastic SIR model with jumps , 2013, Appl. Math. Lett..

[41]  Omar Abu Arqub,et al.  Solution of the fractional epidemic model by homotopy analysis method , 2013 .

[42]  Daqing Jiang,et al.  The threshold of a stochastic delayed SIR epidemic model with temporary immunity , 2016 .