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
针对传统评估方法难以量化不确定性、且因未能保留中立态度而引发决策偏差的问题,首先在语言q阶正交模糊Z数(LqROFZ)的框架下,引入中性运算法则,定义中性运算下加权算术(LqROFZNWA)与加权几何(LqROFZNWGA)聚合算子并论证其数学特性,规...针对传统评估方法难以量化不确定性、且因未能保留中立态度而引发决策偏差的问题,首先在语言q阶正交模糊Z数(LqROFZ)的框架下,引入中性运算法则,定义中性运算下加权算术(LqROFZNWA)与加权几何(LqROFZNWGA)聚合算子并论证其数学特性,规避传统运算对专家中立态度的破坏,确保信息聚合时完整保留原始中立判断。其次,提出基于排序结果与评价值二维相似度的属性偏好计算方法,并借助Jensen-Shannon散度优化模型,动态平衡主客观信息;最后,采用Co Co So排序方法,有效融合两种聚合路径,并以安徽省药企质量风险评估为实例,验证该模型的优越性与有效性。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.
文摘针对传统评估方法难以量化不确定性、且因未能保留中立态度而引发决策偏差的问题,首先在语言q阶正交模糊Z数(LqROFZ)的框架下,引入中性运算法则,定义中性运算下加权算术(LqROFZNWA)与加权几何(LqROFZNWGA)聚合算子并论证其数学特性,规避传统运算对专家中立态度的破坏,确保信息聚合时完整保留原始中立判断。其次,提出基于排序结果与评价值二维相似度的属性偏好计算方法,并借助Jensen-Shannon散度优化模型,动态平衡主客观信息;最后,采用Co Co So排序方法,有效融合两种聚合路径,并以安徽省药企质量风险评估为实例,验证该模型的优越性与有效性。
