会议委员会

程序委员会：

主  任：李永青

副主任：林伟川  李进金

委  员：谭  忠  谢向东  陈凤德  张金顺  周哲彦  李学鹏

李克典  温永仙  陈明玉  邱亚林  邱锦明  刘用麟

肖筱南  张国勇  陈水利

组织委员会：

主  任：常安

副主任：陈凤德  杨文生  魏凤英  李忠   

委  员：陈丽娟  陈晓星李婷婷林巧霞

会议日程安排

Recent work on stochastic epidemic model

淮阴师范学院王玮明

weimingwang2004@163.com

In this talk, I will give a review of our recent work on stochastic epidemic models. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number can be used to govern the stochastic dynamics of SDE model. If <1 , under mild extra conditions, the sde system has a disease-free absorbing set which means the extinction of disease with probability one. if >1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochasticpersistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.

Very singular solution and short time asymptotic behaviors of nonnegative singular solutions for heat equation with nonlinear convection

莆田学院   卢国富

gflu@vip.sina.com

若干具强局部空间异质性的反应-扩散方程的非线性波及其动力学

福建师范大学数学与计算机科学学院  沈建和

jhshen@fjnu.edu.cn

In this talk, the existence, stability and bifurcations of stationary single-pulse and multiple-pulse localized patterns in several one-dimensional (scalar) reaction-diffusion equations with strong spatially localized heterogeneity are introduced. By using the slow-fast separation technique from geometric singular perturbation theory, the possible singular homoclinic orbits with single-pulse/multiple-pulse are first geometrically constructed, and then the analytically conditions of the existence, stability and bifurcations of these localized structures are set up. Then by calculating the spectral equations associated with these pulse solutions, it is found that Hopf bifurcation of -pulse solutions can occur in one-component reaction-diffusion equation, where n>2, while it is impossible for one-pulse and two-pulse solutions to possess oscillations. Also, we find that it is more easier for multiple-component reaction-diffusion systems to give birth toHopf bifurcation. The theoretical results are illustrated in a series of examples. Numerical simulations are also carried out to verify the theoretical predictions.

基于多层次数据的可逆细胞谱系的推断研究

厦门大学数学科学学院  周达

zhouda@xmu.edu.cn

In this talk, I will present some model-based methods for detecting the de-dierentiation process.  For the time-course FACS data, a multi-type  branching  process is  applied  to  model  the cellular  dynamics.   For  the  single-cell genomic data, a coalescent-based statistical method is applied for inferring the de-dierentiation rate.

复杂网络SIRS传染病模型的最优控制

           bat365官网登录入口数学与计算机科学学院    陈丽娟

                  chenlijuan@fzu.edu.cn

探讨具有两类控制策略的的复杂网络SIRS 传染病模型的全局稳定性及其最优控制策略。首先，提出了具有疫苗注射和疾病治疗这两类控制策略的SIRS 传染病模型，求出疾病传播的阈值，并对该系统无病平衡点和疾病平衡点的稳定性进行分析。接着给出一性能指标，探讨最优控制策略。最后给出数值模拟说明所得结果的合理性。

      脉冲对Logistic模型动力学行为的影响

bat365官网登录入口数学与计算机科学学院    何梦昕

                     hemx_206@126.com

研究具有两种不同类型脉冲（线性和非线性脉冲）的Logistic模型。通过分析脉冲系统的通解，得到系统解的持久性、绝灭性及平衡点的全局吸引性。从而发现脉冲对Logistic模型动力学行为的影响。

Extinction and permanence in a Lotka-Volterra competitive system

         with the effect of toxic substances and single feedback control

               bat365官网登录入口数学与计算机科学学院    苗占帅

                  1017100503@qq.com

In this paper, a Lotka-Volterra competitive system with the effect of toxic substances and single feedback controls is studied. Firstly, we prove that one of the components will be driven to extinction while the other will be permanent under some conditions; Then, we establish sufficient conditions for the permanence of the system;Moreover, a very important fact is found in our results, that is,the single feedback control and toxic substances have no effect on the extinction and permanence of species;Finally, some numerical simulations show the feasibility of our main results.

Effects of a toxicant on a single-species population with partial

 pollution tolerance in a polluted environment

bat365官网登录入口数学与计算机科学学院    刘佳敏

    3126098316@qq.com

We study a model for the long-term behavior of a single-species population with some degree of pollution tolerance in a polluted environment. We derive sufficient conditions for the persistence and for the extinction of the population depending on the exogenous input rate of the toxicant into the environment and the level of pollution tolerance of the organisms. Numerical simulations are carried out to illustrate our main results.

Extinction in two species nonlinear discrete competitive system

            bat365官网登录入口数学与计算机科学学院   普丽琼

                   282930637@qq.com

In this paper, we proposed a nonlinear discrete system of two species with the effect of toxic substances.  By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components  will be driven to extinction while  the other will be globally attractive with any positive  solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.