In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of const...In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.展开更多
This paper investigates the stochastic HTLV-I infection model with CTL immune response,and the corresponding deterministic model has two basic reproduction numbers.We consider the nonlinear CTL immune response for the...This paper investigates the stochastic HTLV-I infection model with CTL immune response,and the corresponding deterministic model has two basic reproduction numbers.We consider the nonlinear CTL immune response for the interaction between the virus and the CTL immune cells.Firstly,for the theoretical needs of system dynamical behavior,we prove that the stochastic model solution is positive and global.In atldition,we obtain the existence of ergodic stationary distribution by stochastic Lyapunov functions.Meanwhile,sufficient condition for the extinction of the stochastic system is acquired.Reasonably,the dynamical behavior of deterministic model is included in our result of stochastic model when the white noise disappears.展开更多
In this paper,we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise.First,we prove the existence of the unique global positive solution.Second,by constructing an appr...In this paper,we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise.First,we prove the existence of the unique global positive solution.Second,by constructing an appropriate Lyapunov function,we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model.Then we establish sufficient conditions for the extinction of diseases.Finally,numerical simulations are introduced to illustrate our theoretical results.展开更多
In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also s...In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.展开更多
In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by t...In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.展开更多
In this paper,we investigate the stochastic avian influenza model with human-to-human transmission,which is disturbed by both white and telegraph noises.First,we show that the solution of the stochastic system is posi...In this paper,we investigate the stochastic avian influenza model with human-to-human transmission,which is disturbed by both white and telegraph noises.First,we show that the solution of the stochastic system is positive and global.Furthermore,by using stochastic Lyapunov functions,we establish sufficient conditions for the existence of a unique ergodic stationary distribution.Then we obtain the conditions for extinction.Finally,numerical simulations are employed to demonstrate the analytical results.展开更多
基金supported by the Natural Science Foundation of Shandong Province,China(Nos.ZR2021MA028 and ZR2021MA025).
文摘In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.
基金The work was supported by the National Nature Science Foundation of China (No. 11871473).
文摘This paper investigates the stochastic HTLV-I infection model with CTL immune response,and the corresponding deterministic model has two basic reproduction numbers.We consider the nonlinear CTL immune response for the interaction between the virus and the CTL immune cells.Firstly,for the theoretical needs of system dynamical behavior,we prove that the stochastic model solution is positive and global.In atldition,we obtain the existence of ergodic stationary distribution by stochastic Lyapunov functions.Meanwhile,sufficient condition for the extinction of the stochastic system is acquired.Reasonably,the dynamical behavior of deterministic model is included in our result of stochastic model when the white noise disappears.
基金the National Natural Science Foundation of China(Grant Nos.11801566,11871473)the Fundamental Research Funds for the Central Universities of China(No.19CX02059A)for their financial support.
文摘In this paper,we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise.First,we prove the existence of the unique global positive solution.Second,by constructing an appropriate Lyapunov function,we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model.Then we establish sufficient conditions for the extinction of diseases.Finally,numerical simulations are introduced to illustrate our theoretical results.
基金The authors are grateflfl to tile anonymous referees for carefully reading the manuscript and for important snggestions and comments, which led to the improvement of their manuscript. This research is supported by NSFC grant 11601043, China Postdoctoral Science Foundation (Grant No. 2016M590243), Jiangsu Province "333 High-Level Personnel Training Project" (Grant No. BRA2017468) and Qing Lan Project of Jiangsu Province of 2016 and 2017.
文摘In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.
文摘In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.
文摘In this paper,we investigate the stochastic avian influenza model with human-to-human transmission,which is disturbed by both white and telegraph noises.First,we show that the solution of the stochastic system is positive and global.Furthermore,by using stochastic Lyapunov functions,we establish sufficient conditions for the existence of a unique ergodic stationary distribution.Then we obtain the conditions for extinction.Finally,numerical simulations are employed to demonstrate the analytical results.