A kind of stochastic susceptible-exposed but not infectiousinfectious-removed (SEIR) model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of paramet...A kind of stochastic susceptible-exposed but not infectiousinfectious-removed (SEIR) model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of parameter perturbation which is standard in stochastic population modeling. The influence of the environmental noise as a standard Gaussian white noise on the epidemics' transmission is studied. Furthermore,the condition for the epidemics' persistence is obtained by formulating the corresponding function and using It 's formula. And the asymptotic behavior of the model near the endemic disease equilibrium is also studied. In this way, the decision support is provided in the application of this kind of stochastic SEIR model on the epidemics' prevention and control.展开更多
We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic multi-group SIR mode. Then, we define the basic reproduction number R0^S and show that it is a sharp th...We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic multi-group SIR mode. Then, we define the basic reproduction number R0^S and show that it is a sharp threshold for the dynamic of the stochastic multi-group SIR model. More specially, if R0^S 〈 1, then the disease-free equilibrium will be asymptotically stable which means the disease will die out, if R0^S 〉 1, the disease-free equilibrium will unstable, and our model will positively recurrence to a positive domain which implies the persistence of our model. Numerical simulation examples are carried out to substantiate the analytical results.展开更多
In this paper,stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are considered.We first show the existence of the global positive s...In this paper,stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are considered.We first show the existence of the global positive solution,then discuss the effects of noises on the extinction of the species and the stochastic persistence of the species.In the meanwhile,numerical simulations are carried to support results.Finally,we show the existence of the stationary distribution for a special case.展开更多
基金Humanities and Social Science Research Planning Fund of the Education Ministry of China(No.15YJCZH2010)the Research Innovation Program of Shanghai Municipal Education Commission,China(No.14YZ134)Shanghai 085 Project for Municipal Universities,China
文摘A kind of stochastic susceptible-exposed but not infectiousinfectious-removed (SEIR) model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of parameter perturbation which is standard in stochastic population modeling. The influence of the environmental noise as a standard Gaussian white noise on the epidemics' transmission is studied. Furthermore,the condition for the epidemics' persistence is obtained by formulating the corresponding function and using It 's formula. And the asymptotic behavior of the model near the endemic disease equilibrium is also studied. In this way, the decision support is provided in the application of this kind of stochastic SEIR model on the epidemics' prevention and control.
基金Acknowledgments This work was supported by the National Natural Science Foundation of China Grant 61273126, and the Natural Science Foundation of Guangdong Province Under Grants 10251064101000008 and S201210009675, the Fundamental Research Funds for the Central Universities 2012ZM0059, and Research Fund for the Doctoral Program of Higher Education of China under grant 20130172110027.
文摘We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic multi-group SIR mode. Then, we define the basic reproduction number R0^S and show that it is a sharp threshold for the dynamic of the stochastic multi-group SIR model. More specially, if R0^S 〈 1, then the disease-free equilibrium will be asymptotically stable which means the disease will die out, if R0^S 〉 1, the disease-free equilibrium will unstable, and our model will positively recurrence to a positive domain which implies the persistence of our model. Numerical simulation examples are carried out to substantiate the analytical results.
文摘In this paper,stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are considered.We first show the existence of the global positive solution,then discuss the effects of noises on the extinction of the species and the stochastic persistence of the species.In the meanwhile,numerical simulations are carried to support results.Finally,we show the existence of the stationary distribution for a special case.
