In this article, we present a hepatitis B epidemic model with saturated incidence.The dynamic behaviors of the deterministic and stochastic system are studied. To thisend, we first establish the local and global stabi...In this article, we present a hepatitis B epidemic model with saturated incidence.The dynamic behaviors of the deterministic and stochastic system are studied. To thisend, we first establish the local and global stability conditions of the equilibrium of thedeterministic model. Second, by constructing suitable stochastic Lyapunov functions, thesufficient conditions for the existence of ergodic stationary distribution as well as extinctionof hepatitis B are obtained.展开更多
Observations imply that long ＂y-ray bursts （GRBs） originate from the explo- sions of massive stars, therefore they may occur in the molecular clouds where their progenitors were born. We show that the prompt optica...Observations imply that long ＂y-ray bursts （GRBs） originate from the explo- sions of massive stars, therefore they may occur in the molecular clouds where their progenitors were born. We show that the prompt optical-UV emission from GRBs may be delayed due to dust extinction, which can explain the observed optical delayed on- set and fast rise in GRB 080319B well. The density and the size of the molecular cloud around GRB 080319B are roughly constrained to be ~ 103 cm-z and ~ 8 pc, respectively. We also investigate other GRBs with prompt optical-UV data, and find similar values of the densities and sizes of the local molecular clouds. Future obser- vations of prompt optical-UV emission from GRBs on a timescale of subseconds, e.g. by UFFO-Pathfinder and SVOM-GWAC, will provide more evidence and probes of the local environments of GRBs.展开更多
The extinction phenomenon induced by multiplicative non-Gaussian L′evy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in term...The extinction phenomenon induced by multiplicative non-Gaussian L′evy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.展开更多
基金supported by NSFC(11371085)the Fundamental Research Funds for the Central Universities(15CX08011A)
文摘In this article, we present a hepatitis B epidemic model with saturated incidence.The dynamic behaviors of the deterministic and stochastic system are studied. To thisend, we first establish the local and global stability conditions of the equilibrium of thedeterministic model. Second, by constructing suitable stochastic Lyapunov functions, thesufficient conditions for the existence of ergodic stationary distribution as well as extinctionof hepatitis B are obtained.
基金Supported by the National Natural Science Foundation of Chinasupported by the National Basic Research Programof China (973 Program,2009CB824800)+2 种基金the China Postdoctoral Science Foundation funded project(No. 20110490590)the National Natural Science Foundation of China (Grant No. 111030262)the Foundation for the Authors of National Excellent Doctoral Dissertations of China
文摘Observations imply that long ＂y-ray bursts （GRBs） originate from the explo- sions of massive stars, therefore they may occur in the molecular clouds where their progenitors were born. We show that the prompt optical-UV emission from GRBs may be delayed due to dust extinction, which can explain the observed optical delayed on- set and fast rise in GRB 080319B well. The density and the size of the molecular cloud around GRB 080319B are roughly constrained to be ~ 103 cm-z and ~ 8 pc, respectively. We also investigate other GRBs with prompt optical-UV data, and find similar values of the densities and sizes of the local molecular clouds. Future obser- vations of prompt optical-UV emission from GRBs on a timescale of subseconds, e.g. by UFFO-Pathfinder and SVOM-GWAC, will provide more evidence and probes of the local environments of GRBs.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10932009,11172233,and 11302169
文摘The extinction phenomenon induced by multiplicative non-Gaussian L′evy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.
