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 as...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.展开更多
In this paper,we focus on asymptotic speeds of spread for a reaction-diffusion two-group SIR epidemic model with constant recruitment,which lacks the comparison principle.More precisely,if R_(0)<1,then the solution...In this paper,we focus on asymptotic speeds of spread for a reaction-diffusion two-group SIR epidemic model with constant recruitment,which lacks the comparison principle.More precisely,if R_(0)<1,then the solution of the system converges to the disease-free equilibrium as t→∞ and if R_(0)>1,there exists a critical speed c^(*)such that the solution of the system is uniformly persistent with|x|≤ct,■c ∈[O,c^(*))and the infection dies out with|x|≥ct for any c>c^(*).Finally,some numerical experiments are presented to modeling the propagation dynamics of the system.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10971021)the Ministry of Education of China (Grant No. 109051)+1 种基金the Ph.D. Programs Foundation of Ministry of China (Grant No. 200918)the Graduate Innovative Research Project of NENU (Grant No. 09SSXT117)
文摘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.
基金L.Zhao was supported by the National Natural Science Foundation of China(12161052)Natural Science Foundation of Gansu,China(21JR7RA240).
文摘In this paper,we focus on asymptotic speeds of spread for a reaction-diffusion two-group SIR epidemic model with constant recruitment,which lacks the comparison principle.More precisely,if R_(0)<1,then the solution of the system converges to the disease-free equilibrium as t→∞ and if R_(0)>1,there exists a critical speed c^(*)such that the solution of the system is uniformly persistent with|x|≤ct,■c ∈[O,c^(*))and the infection dies out with|x|≥ct for any c>c^(*).Finally,some numerical experiments are presented to modeling the propagation dynamics of the system.
