In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netiz...In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.展开更多
In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
In this study, we investigate a pine wilt transmission model with general nonlinear incidence rates and time-varying pulse roguing. Using the stroboscopic map and comparison theorem, we proved that the disease-free eq...In this study, we investigate a pine wilt transmission model with general nonlinear incidence rates and time-varying pulse roguing. Using the stroboscopic map and comparison theorem, we proved that the disease-free equilibrium is global attractive determined by the basic reproduction number <em>R</em><sub>1</sub> < 1, and in such a case, the endemic equilibrium does not exist. The disease uniformly persists only if <em>R</em><sub>2</sub> > 1.展开更多
Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence ...Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.展开更多
基金supported by the Funding for Outstanding Doctoral Dissertation in NUAA(Grant No.BCXJ18-09)the National Natural Science Foundation of China(Grant No.72071106)Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX180234)。
文摘In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
文摘In this study, we investigate a pine wilt transmission model with general nonlinear incidence rates and time-varying pulse roguing. Using the stroboscopic map and comparison theorem, we proved that the disease-free equilibrium is global attractive determined by the basic reproduction number <em>R</em><sub>1</sub> < 1, and in such a case, the endemic equilibrium does not exist. The disease uniformly persists only if <em>R</em><sub>2</sub> > 1.
基金Supported by the Natural Science Foundation of Shanxi Province(202303021211003)the National Natural Science Foundation of China(12126349,11601293,12361102)the Scientific Plan of Guizhou Province(No.Qian Ke He Jichu-ZK[2021]YiBan002).
文摘Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.