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
In this paper we present some new existence results for singular boundary value problems by Arzela-Ascoli theorem. In particular our nonlinearity may be singular in its dependent variable.
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. Further- more, 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.
In this paper, we introduce the stochasticity into an HIV-1 infection model with cytotoxic T lymphocytes （CTLs） immune response via the technique of parameter perturbation. We show that there is a positive solution as desired in any population dynamics. Then we analyze the long time behavior of this model. We obtain a sufficient condition for the stochastic asymptotic stability in the large of the infection-free equilibrium and give the conditions for the solution fluctuating around the two infection equilibria （one without CTLs being activated and the other with）. Finally, we make sinmlations to conform to our analytical results.
