In this paper,we propose a novel robust vehicle tracking method based on random sampling.Firstly,random sampli...
Lifang Li is with the Information Engineering Department,Jilin Police College,Changchun,130117,China Yang Lu and Xianliang Tong are with School of Computer Science and Information technology,Northeast Normal University,Changchun,130117,China.Man Liu is with Faculty of Mathematics,Dalian Nationalities University,Dalian,116600,China
A stochastic two-group SIR model is presented in this paper.The existence and uniqueness of its nonnegative solution is obtained,and the solution belongs to a positively invariant set.Furthermore,the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 ≤ 1,which means the disease will die out.While if R0 > 1,we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average.In addition,the intensity of the fluctuation is proportional to the intensity of the white noise.When the white noise is small,we consider the disease will prevail.At last,we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.
