构建一类具有VCT(voluntary counseling and testing)意识及媒体报道影响的HIV/AIDS感染动力学模型.首先得到模型解的适定性,并给出模型的基本再生数.其次,借助Hurwitz判别法及Lyapunov函数分析模型的阈值动力学,当R_(0)<1时无病平...构建一类具有VCT(voluntary counseling and testing)意识及媒体报道影响的HIV/AIDS感染动力学模型.首先得到模型解的适定性,并给出模型的基本再生数.其次,借助Hurwitz判别法及Lyapunov函数分析模型的阈值动力学,当R_(0)<1时无病平衡点局部渐近稳定且当R_(0)≤1时全局渐近稳定;当R_(0)>1时,地方病平衡点局部渐近稳定.进一步,结合持续生存理论给出疾病的一致持续性.最后,数值模拟表明随着VCT意识比例的提高,艾滋病患者人数的峰值逐渐降低,而随着信息失效率的增大,艾滋病患者人数的峰值将有所提高.展开更多
In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belon...In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.展开更多
文摘构建一类具有VCT(voluntary counseling and testing)意识及媒体报道影响的HIV/AIDS感染动力学模型.首先得到模型解的适定性,并给出模型的基本再生数.其次,借助Hurwitz判别法及Lyapunov函数分析模型的阈值动力学,当R_(0)<1时无病平衡点局部渐近稳定且当R_(0)≤1时全局渐近稳定;当R_(0)>1时,地方病平衡点局部渐近稳定.进一步,结合持续生存理论给出疾病的一致持续性.最后,数值模拟表明随着VCT意识比例的提高,艾滋病患者人数的峰值逐渐降低,而随着信息失效率的增大,艾滋病患者人数的峰值将有所提高.
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
文摘In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.
