This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises an...This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises and color noises on TB control in random environments.We first investigate the existence and uniqueness of ergodic stationary distribution(EUESD)for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions,and suficient conditions on the extinction of disease are acquired.Next,sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established.Eventually,some numerical examples validate the theoretical findings.What's more,it has been observed that higher amplitude noises may lead to the eradication of TB,which is conducive to TB control.展开更多
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
文摘This contribution probes into ergodic stationary distribution for two stochastic SVELIT(susceptible-vaccinated-early latent-late latent-infective-treated)tuberculosis(TB)models to observe the impact of white noises and color noises on TB control in random environments.We first investigate the existence and uniqueness of ergodic stationary distribution(EUESD)for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions,and suficient conditions on the extinction of disease are acquired.Next,sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established.Eventually,some numerical examples validate the theoretical findings.What's more,it has been observed that higher amplitude noises may lead to the eradication of TB,which is conducive to TB control.
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.
