前沿论坛与短期课程

前沿论坛与短期课程

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2019生物数学最新进展学术研讨会
日期:2019-04-23 点击:

本次研讨会的目的为交流生物数学相关领域的最新研究成果和学术发展动态,促进学术交流与合作,围绕生命科学、生态学、生物医学等领域的实际问题,深入探讨数学与大数据科学在生物、生态和医学等系统理论研究中的重要作用,通过问题驱动的理论研究促进生物数学和大数据科学的理论发展。会议议题包括传染病学、生态学、动力系统与微分方程等。

专业组织委员会:肖燕妮(西安交通大学)、唐三一(陕西师范大学)、舒洪英(陕西师范大学)、吴事良(西安电子科技大学)、聂华(陕西师范大学)、梁菊花(陕西师范大学)、王霞(陕西师范大学)

会议时间:4月26日—28日

会议地点:陕西师范大学长安校区教育博物馆主楼学术报告厅

日程安排:



报告摘要:


我国MSM人群HIV耐药毒株流行的传播动力学模型

韩丽涛,中国人民大学

本文利用传染病动力学模型研究HIV在MSM人群中的流行模式,尤其是耐药毒株的流行与传播。所得结果表明:未来几年MSM人群中的HIV感染率和HIV耐药率都会持续走高;HIV野生毒株感染人数会在达到一个高峰后下降,而HIV耐药毒株感染人数会持续走高,其中传播耐药每年新增人数持续走高后趋于平稳而略有下降,治疗耐药每年新增人数在后期会下降。


Multistrain edge-based compartmental model on networks

靳祯,山西大学

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this tak, we build competitive and mutative two-strain edge-based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two-strain models.


Propagation dynamics of asymmetric nonlocal dispersal equations

李万同,兰州大学

This talk is concerned with entire solutions of the asymmetric nonlocal dispersal equation u_t=J*u-u+f(u) with monostable, bistable and ignition nonlinearity, respectively, where the kernel function J is asymmetric. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more different types of entire solutions since it can affect the range and sign of the wave speeds, which further leads to no symmetry between the corresponding nonincreasing and nondecreasing waves. For the KPP, bistable and ignition nonlinearities, We establish respectively some new entire solutions and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds. In particular, if f is the KPP nonlinear term and the kernel J is symmetric, then the entire solutions are proved to be 5-dimensional, 4-dimensional, and 3-dimensional manifolds, respectively. This is the joint work with Yu-Juan Sun, Zhi-Cheng Wang and Li Zhang.

Dynamics of an age-structured heroin transmission model with vaccination and treatment

李学志, 河南师范大学

Based on the development of heroin vaccine, in this paper, we propose an age structured heroin transmission model with treatment and vaccination. The model allows the drug reuse rate of the individuals in treatment to depend on a treatment-age and the vaccine waning rate of the vaccinated to depend on a vaccination age. Meanwhile, the model allows that the heroin vaccine provides an imperfect protection (i.e., the vaccinated individuals can also become drug addicted). We derive the basic reproduction number which dependents on vaccination. The basic reproduction number completely determines the persistence and extinction of heroin spread, i.e., if the basic reproduction number is less than one the drug-free steady state is globally asymptotically stable (i.e., the heroin spread dies out), if the basic reproduction number is larger than one, there exists an unique positive steady state and it is locally and globally stable in some special cases. Finally, some numerical simulations are carried out to illustrate the stability of the positive steady state.


气候变暖和空间异质性对西尼罗河病毒扩散的影响

林支桂, 扬州大学

我们用反应扩散方程组描述西尼罗河病毒的空间扩散,用自由边界表示病毒扩散的边沿。为了检查空间特征对病毒扩散的影响,我们定义了四个基本再生数,分别对应于常微分方程组问题、具齐次Neumann问题,齐次Dirichlet问题和自由边界问题。结果表明,在高风险区域,如果感染区域范围大或者扩散慢,病毒将蔓延;在低风险区域,小的初始感染病例,小的感染范围和大的扩散速率有利于病毒的消退。当病毒蔓延时我们证明了其空间扩散速度接近于一个常数。另外我们重点考察了全球气候变暖和空间异质性对西尼罗河病毒扩散的影响。


Population models with stage structures and state-dependent delays

刘贤宁,西南大学

Time-delays widely exist in natural ecosystems. And delay differential equations with constant delays have been extensively studied. Due to the influence of circumstances such as resources and interaction, howeverthe constant time delays may not be reasonable. In this talk, population models with stage structures and state-dependent delays will be introduced and discussed.


HIV-1 model with infection age and drug-resistance

刘胜强,哈尔滨工业大学

We propose a hybrid two-strain HIV dynamic model with mutation which describes the interactions of the healthy CD4+ T cells, infected CD4+ T cells and viruses, where two transmission modes, virus-to-cell and cell-to-cell, age structure and drug resistance are considered. We obtain the basic reproductive number for each strain. We conducted qualitative analyses of the model such as the asymptotic smoothness, uniform persistence and steady states stability. By subtle construction and estimates of Lyapunov functionals, we show that there exists the principle of competitive exclusion if there is no mutation, the disease-free and drug-resistant steady states are globally asymptotically stable if there is mutation. Furthermore, mutation, which from the drug-sensitive to drug-resistant strain, play a critical role in the existence and stability of steady states. Numerical simulations are also performed in order to illustrate the global dynamical behavior, and analyze the mutation impacts on dynamics of system.


Optimal pest regulation tactics for a stochastic process model

with impulsive controls using regression analysis

裴永珍,天津工业大学

Aphids, the sap-sucking insects, often feeding in clusters on new plant growth, have resulted in large amounts of resources and efforts being spent attempting to control their activities. Taking cotton aphids as an example, this paper presents optimal control problems governed by stochastic models with impulsive interferences. Differing from the moment closure equation methods which are computationally intractable when the model contains excessive species, a new computational approach is employed to solve this problem. The key of the approach is to establish a functional relationship between the control variables involving the releasing rates of sterile insects and the spraying rates of pesticide and corresponding states on aphids and sterile aphids. Then the log-linear regression model is proposed to link the control variables with the moments (including the mean and variance) of states. Using training sample simulated from Gillespie algorithm, the regression coefficients for constraints and the objective function are estimated by least squares method. Simulation shows the error of the prediction of this model is relatively low and control results based on regression model are superior to the method based on the moment closure equations in terms of the control cost. Finally, the relative impacts of the prices and area of the field on optimal tactics are explored.


Stability and spatiotemporal dynamics in a diffusive predator-prey model

with nonlocal prey competition

宋永利,杭州师范大学

In this paper, we investigate the influence of the nonlocal intraspecific competition of the prey on the dynamics of the diffusive Rosenzweig-MacArthur model with Holling type II functional response. Using the linear stability analysis, the conditions for the positive constant steady state to remain stable and to undergo Turing-Hopf bifurcation have been studied under the Neumann boundary conditions. We find that the introduction to the nonlocal term can produce Turing patterns, which cannot occur in the original model. Furthermore, we are interested in the interaction of Turing bifurcation and Hopf bifurcation. We also develop the algorithm of the normal form of the Turing-Hopf bifurcation for the model with nonlocality. By applying the developed normal form, the dynamical classification near the Turing-Hopf bifurcation point can be analytically determined. The stable spatially inhomogeneous steady states, stable spatially inhomogeneous periodic solutions and unstable spatially inhomogeneous periodic solutions are found. Especially, we find that two stable spatially inhomogeneous steady states and one stable spatially inhomogeneous periodic solution can coexist for appropriate parameters and that there are transitions from one unstable solution to another stable one.


非局部扩散SIR模型的行波解的存在性

滕志东, 新疆大学

In this paper for a class of nonlocal dispersal SIR epidemic models with general nonlinear incidence we investigate the existence of traveling wave solutions connecting the disease-free equilibrium with endemic equilibrium. We obtain that the existence of traveling waves depends on the minimal wave speed c* and basic reproduction number R_0. That is, if R_0>1 and c> c* then the model has a traveling wave solution connecting the disease-free equilibrium with endemic equilibrium. The numerical simulations verify the obtained theoretical results, and through the numerical simulations we find that the traveling wave solution connecting the disease-free equilibrium and endemic equilibrium may be unique.

Our results improve and generalize some known results.


Mathematical analysis of disease evolution within host

王稳地,西南大学

I will first review relevant advances in mathematical modeling of disease evolution under treatments. Then I will introduce our studies of mathematical analysis for the dynamical behaviors of mathematical models of HIV, bacteria and tumors. Our aims are to understand how to control the rebounds of diseases.


Epidemics and underlying factors of multiple-peak pattern on hand,

foot and mouth disease in Wenzhou, China

王开发,西南大学

Background: Several outbreaks of severe hand-foot-mouth disease (HFMD) in East Asia and Southwest Asia in recent years have had a serious impact on the countries. However, the factors that contribute to annual multiple-peak pattern of HFMD outbreaks, and how and when do these factors play the decisive role in the HFMD transmission is still unclear.

Methods: Based on the surveillance data of HFMD between 1 January 2010 to 31 December 2015 in Wenzhou, China, the daily model-free basic reproduction number and its annual average were first estimated by incorporating incubation and infection information, then the annual model-based basic reproduction number was computed by the proposed kinetic model, and finally the potential impact factors of multiple-peak pattern are assessed through the global and time-varying sensitivity analyses.

Results: All annual model-based and model-free basic reproduction numbers were significantly higher than one. The school opening both in the spring and fall semester, meteorological effect in the spring semester, and the interactions among them were strongly correlated with the annual model-based basic reproduction number, which were the main underlying factors on the annual multiple-peak pattern of HFMD outbreaks.

Conclusions: School opening was primarily responsible for peaks of HFMD outbreaks and meteorological factors in the spring semester should also be highly concerned. The optimum timing for social distance implementation is at the beginning of every school semester and health education focusing on personal hygiene and good sanitation should be highlighted in the spring semester.


Diffusive Predator-Prey System with non-random motion

王治安,香港理工大学

In this talk, we discuss the global boundedness, asymptotic stability and pattern formation of predator-prey systems with non-random motion in a two-dimensional bounded domain with Neumann boundary conditions, where the motility of the predator depends on the distribution of the prey. We first establish the existence of classical solution with uniform-in time bound. Then by constructing Lyapunov functionals, we establish the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on parameters. We also use the numerical simulations to demonstrate that spatially homogeneous time-periodic patterns, stationary spatially inhomogeneous patterns and chaotic spatio-temporal patterns are all possible for the parameters outside the stability regime. From the numerical simulations, we also find that the temporal dynamics between linear and nonlinear systems is quite different, and the random motion and non-random motion also generate different spatial patterns (i.e. the population distribution in space).


非均匀环境下的对流时滞反应扩散logistic方程的分支分析

魏俊杰,哈尔滨工业大学

本报告将介绍在非均匀环境下的对流时滞反应扩散的logistic方程的分支分析,包括非常值稳态解的存在性,Hopf分支的存在性,以及分支方向和分支周期解的稳定性的确定。


Global dynamics of an age-structured cholera model with multiple transmissions,

saturation incidence and imperfect vaccination

徐瑞,山西大学

In this work, an age-structured cholera model with multiple transmissions, saturation incidence and imperfect vaccination is proposed. In the model, we consider both the infection age of infected individuals and the biological age of Vibrio cholerae in the aquatic environment. Asymptotic smoothness is verified as a necessary argument. By analyzing the characteristic equations, the local stability of disease-free and endemic steady states is established. By using Lyapunov functionals and LaSalle’s invariance principle, it is proved that the global dynamics of the model can be completely determined by basic reproduction number. The study of optimal control helps us seek cost-effective solutions of time-dependent vaccination strategy against cholera outbreaks. Numerical simulations are carried out to illustrate the corresponding theoretical results.


Dynamics of interactive wild and sterile mosquitoes with time delay

庾建设,广州大学

To prevent and control the spread of mosquito-borne diseases, such as malaria, dengue fever and Zika, people try to suppress mosquito population density by releasing sterile mosquitoes into the wild field. To investigate the impact of such releases, we develop a delay differential equation model for the interactive wild and sterile mosquitoes in this paper. Different from the existing modeling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics.We consider either the number of releases of the useful sterile mosquitoes stays at a constant level or varies as a presumed given function, and give complete analysis on the model dynamics. We establish a threshold of the releases with which the wild mosquito suppression either succeeds or fails provided the number of releases of sterile mosquitoes is above or below the threshold. The model exhibits rich dynamics including bistable, semi-stable, and global stable equilibria. We obtain conditions for the existence and stability of these equilibria, and particularly the necessary and sufficient conditions for the trivial equilibrium to be globally uniformly asymptotically stable. We also consider the case where the releases of sterile mosquitoes are periodic and impulsive. Using numerical examples we illustrate the dynamical features of the model. Brief discussions are provided as well.


About the optimal harvesting of a fuzzy predator-prey system: A bioeconomic model

incorporating prey refuge and predator mutual interference

原三领,上海理工大学

To understand roles of fuzzy biological parameters, in this paper, we propose a fuzzy predator-prey harvesting model that incorporates both the effects of prey refuge and predator mutual interference. Using the triangular fuzzy numbers for the imprecise parameters, we first study the existence of the feasible equilibria and their global stability. Then discuss the bionomic equilibrium and the possible optimal harvesting policy. Numerical simulations are carried out to illustrate our analytical results, based on which discussions and conclusions are made. They show that the fuzziness of biological parameters can greatly affect the dynamics of the ecological system.


Dynamics analysis of a Zika-dengue co-infection model

赵洪涌,南京航空航天大学

In this talk, we will formulate a Zika-dengue co-infection model that focuses on investigating the effect of the antibody-dependent enhancement(ADE) and dengue vaccine programs on the control and prevention of infectious disease. We derive the basic and invasion reproduction numbers, which are threshold values to identify the existence and stability of a disease-free state and a boundary state where only one strain (Zika or dengue) is present, and to identify the persistence of disease. Our analysis and numerical simulations suggest that although vaccination against dengue has a positive effect on the control of dengue, it has a negative effect on the control of Zika, and the increasing level of ADE induces a large number of accumulated Zika cases.


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