一类具有HollingⅡ反应的害虫治理的Filippov模型的研究

首先,在不采取综合害虫治理策略的情况下,本文给出一个具有HollingⅡ反应的害虫模型的正平衡点的存在条件和正平衡点的全局稳定性条件;其次,把害虫种群数量作为害虫综合控制的指标,利用阈值控制策略建立了一个具有HollingⅡ反应的害虫治理的Filippov模型,并系统地对该模型的动力学性质进行分析,其中包括模型的滑线区域,真、假平衡点及伪平衡点的存在性和稳定性.     

一类潜伏期和染病期均传染且具非线性传染率的流行病模型

研究了一类潜伏期和染病期都传染的具非线性传染率的SEIS流行病模型,确定了各类平衡点存在的条件阈值,讨论了各平衡点的稳定性,揭示了潜伏期传染和染病期传染对流行病发展趋势的共同影响．     

一类分数阶SIR流行病模型的稳定性研究

本文讨论了一类分数阶SIR流行病模型的稳定性问题.对不考虑疾病治疗的情形,利用特征值分析的方法分析了其平衡点的稳定性,并在一定条件下证明了模型一致稳态正解的存在唯一性;在此基础上,进一步考虑了具有治疗的分数阶SIR流行病模型的平衡点的稳定性,得到了其后向分支发生的条件.最后通过数值仿真验证了所得结论的正确性.     

甘蔗瞑的综合控制策略（英文）

提出了一个针对甘蔗瞑的综合害虫治理策略.该控制策略不仅保证解达到一个不引起经济损失的平衡点,还保证了平衡点的渐近稳定性.最后给出数值模拟验证控制策略的有效性.     

捕食者有病的生态-流行病模型的分析

建立并分析了捕食者具有疾病且有功能反应的生态-流行病(SI)模型,讨论了解的有界性．应用特征根法得到了平衡点局部渐近稳定的充分条件,进一步分析了平衡点的全局稳定性,得到了边界平衡点和正平衡点全局稳定的充分条件。     

具有感染周期和垂直传播的阶段结构SIS流行病模型的无害时滞

本文提出并研究了一个具有感染期和垂直传播的阶段结构SIS流行病模型,分别讨论了模型在无时滞和有时滞两种情况下平衡点的稳定性.结果表明,在添加时滞后平衡点的稳定性不发生变化,即这个时滞是无害的.     

一类具时滞和非线性发生率的生态流行病模型的稳定性和Hopf分支

研究一类具有时滞和非线性发生率的生态流行病模型.以滞量为参数,通过分析特征方程,得到了正平衡点局部稳定和Hopf分支存在的条件.同时,应用中心流形定理和规范型理论,得到了分支方向和分支周期解的稳定性计算公式.最后对所得理论结果进行了数值模拟.     

一类含分布时滞的流行病模型的研究

提出了一类含分布时滞的流行病模型,利用构造李亚普诺夫泛函的方法,得到了无病平衡点和地方病平衡点全局稳定性的结论,揭示了平均时滞对各类平衡点稳定性的影响。     

害虫治理的病毒感染模型

研究了一类食饵受病毒感染的生态流行病模型,考虑脉冲释放病毒颗粒和自然天敌来进行害虫治理.利用Floquet乘子理论、小振幅扰动技巧和比较定理证明了害虫灭绝周期解的全局渐近稳定性以及系统持续生存的充分条件.结果为现实的害虫管理提供了科学依据.     

具有非线性接触率的SILI流行病模型

本文研究了具有一般非线性接触率的SILI流行病模型的平衡点的存在性、稳定性以及Hopf分支现象,并且分析了潜伏期的时滞效应．     

具有经济临界值的非光滑捕食与被捕食系统的全局稳定性分析(英文)

只要害虫种群数量在经济临界值水平之上就连续的实施综合控制策略,基于此本文提出了具有经济临界值的非光滑捕食与被捕食系统.我们给出了系统真平衡态、假平衡态和伪平衡态的存在性和稳定性,以及这些平衡态全局稳定或系统存在全局吸引子的条件,同时借助数值方法验证了所得结论.得到的主要结果说明通过采用临界控制策略能让害虫稳定在一个给定的临界值水平上,而达到害虫控制的目的.     

A Theoretical Approach on Controlling Agricultural Pest by Biological Controls

In this paper we propose and analyze a prey-predator type dynamical system for pest control where prey population is treated as the pest. We consider two classes for the pest namely susceptible pest and infected pest and the predator population is the natural enemy of the pest. We also consider average delay for both the predation rate i.e. predation to the susceptible pest and infected pest. Considering a subsystem of original system in the absence of infection, we analyze the existence of all possible non-negative equilibria and their stability criteria for both the subsystem as well as the original system. We present the conditions for transcritical bifurcation and Hopf bifurcation in the disease free system. The theoretical evaluations are demonstrated through numerical simulations.     

Competitive exclusion and coexistence of pathogens in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373-390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable.     

一类具Holling Ⅲ型功能反应的捕食者-食饵模型的定性分析

研究一类具Holling Ⅲ型功能反应的捕食者一食饵模型．应用定性分析和Hopf分支理论,得到了一个正平衡点的全局稳定性、三个正平衡点的局部稳定性和极限环的存在性的充分条件,使用MATLAB软件。本文给出了三个例子来模拟这些结论。     

Mathematical analysis of a model for a plant-herbivore system

The apple twig borer (Amphicerus bicaudatus) is an insect pest of the grape vine, causing considerable damage to the grape vine in early spring. A simple difference equation model is formulated and analysed for this plant-herbivore system based on two control strategies, cane removal and pesticide application. The system has two equilibria, one where the pest is present and one where the pest is absent. Regions are found in parameter space for global stability of the equilibria and in the absence of global stability it is shown that there exist periodic or quasiperiodic solutions.     

A State Dependent Pulse Control Strategy for a SIRS Epidemic System

With the consideration of mechanism of prevention and control for the spread of infectious diseases, we propose, in this paper, a state dependent pulse vaccination and medication control strategy for a SIRS type epidemic dynamic system. The sufficient conditions on the existence and orbital stability of positive order-1 or order-2 periodic solution are presented. Numerical simulations are carried out to illustrate the main results and compare numerically the state dependent vaccination strategy and the fixed time pulse vaccination strategy.     

Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity

We derive and analyse a deterministic model for the transmission of malaria disease with mass action form of infection. Firstly, we calculate the basic reproduction number, R(0), and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation. The implication of this occurrence is that the classical epidemiological requirement for effective eradication of malaria, R(0)<1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory we derive the conditions under which it is optimal to eradicate the disease and examine the impact of a possible combined vaccination and treatment strategy on the disease transmission. When eradication is impossible, we derive the necessary conditions for optimal control of the disease using Pontryagin's Maximum Principle. The results obtained from the numerical simulations of the model show that a possible vaccination combined with effective treatment regime would reduce the spread of the disease appreciably.     

Global stability of single-species diffusion volterra models with continuous time delays

In this paper we consider the stability property of single-species patches connected by diffusion with a within-patch dynamics of Volterra type and with continuous time delays. We prove that this system can only have two kinds of equilibria: the positive and the trivial one. By the assumption that the delay kernels are convex combinations of suitable non-negative and normalized functions, the linear chain trick gives an expanded system of O.D.E. with the same stability properties as the original integro-differential system. Homotopy function techniques provide sufficient conditions for the existence of the positive equilibrium and for its global stability. We also prove the local stability of any positive equilibrium and the local instability both of positive and trivial equilibria. The biological meanings of the results obtained are compared with known results from the literature. This work was performed under the auspices of G.N.F.M., C.N.R. (Italy) and within the activity of the Evolution Equations and Applications group, M.P.I. (Italy). I thank the Department of Applied Mathematics, Shizuoka University, Japan, which enabled me to visit Urbino.     

Integrated pest management models and their dynamical behaviour

Two impulsive models of integrated pest management (IPM) strategies are proposed, one with fixed intervention times and the other with these unfixed. The first model allows natural enemies to survive but under some conditions may lead to extinction of the pest. We use a simple prey-dependent consumption model with fixed impulsive effects and show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than certain critical values. The effects of pest resistance to pesticides are also studied. The second model is constructed in the light of IPM practice such that when the pest population reaches the economic injury level (EIL), a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is invoked. Using analytical methods, we show that there exists an orbitally asymptotically stable periodic solution with a maximum value no larger than the given Economic Threshold (ET). The complete expression for this periodic solution is given and the ET is evaluated for given parameters.We also show that in some cases control costs can be reduced by replacing IPM interventions at unfixed times with periodic interventions. Further, we show that small perturbations of the system do not affect the existence and stability of the periodic solution. Thus, we provide the first demonstration using mathematical models that an IPM strategy is more effective than classical control methods.     

Maintenance of multilocus variability under strong stabilizing selection

We present exact conditions for stability of monomorphic equilibria in a general multilocus multiallele system and of specific polymorphic equilibria in general one- and two-locus multiallele systems. We show how these exact results on one- and two-locus systems can be used in approximate analysis of polymorphic equilibria in multilocus systems under selection strong relative to recombination. We determine conditions for existence and stability of polymorphic equilibria in specific models of quadratic stabilizing selection on additive polygenic traits.