In this paper, a mathematical ordinary differential tumor-immune model is proposed based on an immune checkpoint inhibitor, which is an innovative method for tumor immunotherapies. Two important factors in tumor-immune response are the programmed cell death protein 1 (PD-1) and its ligand PD-L1. The model consists of three populations: tumor cells, activated T cells and anti-PD-1. By analyzing the dynamics of the model, it is found that there is always a unique tumor-free equilibrium and at most two tumor interior equilibria. The nonexistence of nontrivial positive periodic orbits is established by using the new Dulac function, and then a global dynamics of the model is obtained. The conclusions of our analysis show that increasing the possibility of T cells killing tumor cells ([Formula: see text]), early detection of tumor cells, or the use of PD-1 inhibitors to activate T cells are effective in eliminating tumor cells.

新冠肺炎疫情的突发,对我国高校教育教学质量是一次"大考".南华大学积极响应教育部号召开展线上教学,"停课不停学";校院两级教学督导督学体系高速运转,采用多种措施确保教学质量和强化课程监控,取得了卓有成效的成绩.文章在介绍线上教学督导巡查及作用的基础上,阐述了线上课程教学现状与督导的工作内容,分析了线上教学存在的主要问题,并有针对性地提出了线上教学质量监控与督导模式的探索及思考.

研究了具Holling-IV型发生率的时滞SEIR传染病模型.首先定义了模型基本再生数,然后研究了模型平衡点的存在性,证明了无病平衡点局部稳定性与Hopf分支存在性条件,给出了地方病平衡点局部稳定性条件与Hopf分支存在性条件,通过构造Lyapunov泛函以及运用Lasalle不变集原理得到无病平衡点全局稳定性结论.最后通过数值模拟验证了理论分析结果.

对一类具抗原性和简化Holling-IV型肿瘤与免疫系统的动力学模型进行了研究,得到了模型有瘤平衡点的存在性,并分析了各平衡点的局部动力学性质.研究表明,该模型在一定条件下会出现双稳定现象,即肿瘤增长的最终结果依赖于其初始状态.

利用常微分方程定性与稳定性分析理论研究了一类具Holling-III型治疗函数的SEIR传染病模型,给出了基本再生数的定义,分析了模型的正定性,有界性以及无病平衡点的局部渐近稳定性,并判断了地方病平衡点局部渐近稳定需满足的条件.最后通过数值模拟验证了理论分析结果.

高校教学督导在教学活动中既具有咨询与参谋的作用,也是保障学校教学质量的重要抓手,不但是高校建设一流大学的关键助推力,而且对教师尤其是青年教师教学能力提升具有积极的引领作用.然而由于我国高校教学督导仍处于摸索阶段,在助推青年教师教学能力的提升方面存在亟待解决的问题.为此,需要进一步创新督导理念,丰富督导形式,强化督导作用,为青年教师教学水平提升保驾护航,为国家教育事业培养高素质人才注入新的活力.

针对新时期地方高校在实施教学质量监控中出现的主要问题,给出了教学质量监控体系实效提升的对策,着重介绍了南华大学本科教学质量监控体系实效提升的实践成效.

一流高校是顶尖人才培育和产出的主要阵地,也是国家高素质人才发展战略的重要抓手.地方高校教学督导在助推一流本科教育建设中的地位不可或缺,作用日趋凸显.本文通过解读地方高校教学督导与一流本科教育建设的关系,分析地方高校一流本科教育建设中教学督导存在的问题,有针对性地提出地方高校教学督导助推一流本科教育建设的优化路径,即要强化督导的智能与作用,提高督导评价的科学性,推进督导理念的不断创新.

建立一类具媒体影响的时滞HIV传染动力学模型来研究媒体等对HIV传染的影响.通过运用时滞微分方程相关理论证明了模型解的正性;运用常微分方程比较定理和时滞微分方程解的指数有界定义等证明了模型解的有界性.研究模型解的正性与有界性是研究此类模型其它动力学性质的前提基础.

目的 研究ARIMA乘积季节模型对湖南省HIV感染的适用性,并进行预测. 方法 本文以湖南省2005-2014年HIV月感染数据建立模型,以2015年月数据进行模拟.首先采用差分的方法对序列进行平稳化,然后进行模型识别、定阶,再对模型进行检验并预测未来3年的发病情况. 结果 对时间序列进行自然对数转换,一阶差分和一阶季节差分得到ARIMA乘积季节模型,结果显示ARIMA(1,1,1)(0,1,1)12很好地拟合了HIV的感染情况(R2=0.894).残差序列经Ljung-Box 检验为白噪声序列,P=0.472.预测结果显示未来3年全省HIV感染人数仍有增长趋势. 结论 利用乘积季节ARIMA模型对湖南省HIV感染拟合效果较好,可以为卫生工作者采取控制措施提供依据.

在文章中,我们提出了一类具有意识分类和带有干预措施的分数阶HIV/AIDS传染病模型.讨论了模型无病平衡点和地方病平衡点的存在性,并且证明了地方病平衡点的依赖分数阶导数的阶数的稳定性.

In this paper,a class of HIV/AIDS epidemic fractional differential models was studied.Human awareness as a factor of the transmission of the epidemic was included in the model.Stability results of the rest points of the model were obtained and numerical sim￣ulations were carried out to illustrate the results.

A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of the impulsive differential equation, the boundedness of the model solution, the existence and stability of the free-tumor periodic solution are given. Furthermore, the persistence of the system is analyzed. Numerical simulations are carried to confirm the main theorems.

This paper presents a fractional-order differential equation model of HIV by in-troducing Caputo derivative and cell immune delay.The uniqueness of the equilibrium point of the model is analyzed and some sufficient conditions of the stability of the solution are obtained.

专业认证、持续改进内部质量监控,是通过对教学环节、教学过程的持续监控,定期收集有关教学运行和效果方面的信息,通过对信息的处理,对课程体系设置和教学质量进行评价,发现可能存在的问题,对教学进行调节,促使改进沿着课程体系达成毕业要求、毕业要求达成培养目标的方向进行.本文结合南华大学卓越工程师计划试点专业校内专业认证工作实际,构建了以教学督导监控为主导,以教学运行监控、教师教学信息监控、学生教学信息监控为辅助系统的多主体持续改进内部质量监控体系.

A type of HIV Infection Model characterized by distributed delay with CTL immune response is discussed.The global asymptotic stability of uninfected equilibrium and infected equilibrium with no immunity is analyzed,and the sufficient condition of the local asymptotic stability of infected equilibrium with immunity is given.

持续改进是工程教育专业认证的三大核心理念之一，而内部质量监控是持续改进的重要环节。本文介绍了南华大学教学督导在学校工程教育专业认证持续改进之内部质量监控的制度保障及过程实施情况，阐述了其所发挥的督教、督学、督管理作用及其产生的效果。

The hemivariational inequality is one of important research subjects in nonlinear partial differential equations. The main aim of this theory is the treatment of nonconvex and nonsmooth energy problems in mechanics. In this paper,we consider the existence results for a class of parabolic hemivariational inequalities with nonlocal conditions.

A periodic pulse differential equation model of tumor immunotherapy is estab-lished by considering the periodic and transient behavior of infusing immune cells. Using the comparison theorem and Floquet multiplier theory of the impulsive differential equa-tion,the existence and asymptotic stability of the free-tumor periodic solution are given. Numerical simulations are carried to confirm the main theorems.

In this paper,we consider a class of HIV treatment model with uninfected CD4+T cells,infected CD4+T cells in the eclipse phase and productively infected cells. Then we get the sufficient condition of locally asymptotic stability of uninfected and infected e-quilibriums in the treament model without impulsive infusing immune factors. By using the comparison theorem of impulsive differential equation and Floquent multiplier theory, we obtain the sufficient conditions for the global asymptotic stability of the disease-free period-ic solution in this system with impulsive infusing immune factors and healthy cell survival. Finally,some numerical simulation are carried on to verify the effectiveness of the theoreti-cal results obtained.