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Global Transmission Dynamics of a Schistosomiasis Model and Its Optimal Control 预览
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作者 Mouhamadou Diaby Mariama Sène Abdou Sène 《应用数学(英文)》 2019年第6期397-418,共22页
Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model f... Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model for schistosomiasis transmission dynamics in order to explore the role of the several control strategies. The global stability of a schistosomiasis infection model that involves mating structure including male schistosomes, female schistosomes, paired schistosomes and snails is studied by constructing appropriate Lyapunov functions. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We show that the disease can be eradicated when R0?&le;1;otherwise, the system is persistent. In the case where ?R0?>1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. Sensitivity analysis and simulations are carried out in order to determine the relative importance of different control strategies for disease transmission and prevalence. Next, optimal control theory is applied to investigate the control strategies for eliminating schistosomiasis using time dependent controls. The characterization of the optimal control is carried out via the Pontryagins Maximum Principle. The simulation results demonstrate that the insecticide is important in the control of schistosomiasis. 展开更多
关键词 SCHISTOSOMIASIS Models Nonlinear Dynamical Systems GLOBAL Stability REPRODUCTION Number Optimal Control Sensitivity Analysis
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Stability and Optimal Control of Tuberculosis Spread with an Imperfect Vaccine in the Case of Co-Infection with HIV 预览
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作者 Leontine Nkague Nkamba Thomas Timothee Manga Noboru Sakamoto 《建模与仿真(英文)》 2019年第2期97-114,共18页
This paper focuses on the study and control of a non-linear mathematical epidemic model ( SSvihVELI ) based on a system of ordinary differential equation modeling the spread of tuberculosis infectious with HIV/AIDS co... This paper focuses on the study and control of a non-linear mathematical epidemic model ( SSvihVELI ) based on a system of ordinary differential equation modeling the spread of tuberculosis infectious with HIV/AIDS coinfection. Existence of both disease free equilibrium and endemic equilibrium is discussed. Reproduction number R0 is determined. Using Lyapunov-Lasalle methods, we analyze the stability of epidemic system around the equilibriums (disease free and endemic equilibrium). The global asymptotic stability of the disease free equilibrium whenever Rvac is proved, where R0 is the reproduction number. We prove also that when R0 is less than one, tuberculosis can be eradicated. Numerical simulations are conducted to approve analytic results. To achieve control of the disease, seeking to reduce the infectious group by the minimum vaccine coverage, a control problem is formulated. The Pontryagin’s maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the Runge Kutta fourth procedure. 展开更多
关键词 TUBERCULOSIS Basic REPRODUCTION Number Global STABILITY Prevalence CD4 Cells Immune Deficiency Optimal Control OPTIMALITY HIV
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Global Dynamics of an SEIRS Compartmental Measles Model with Interrupted Vaccination 预览
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作者 Dominic Otoo Justice A. Kessie +2 位作者 Elvis K. Donkoh Eric Okyere Williams Kumi 《应用数学(英文)》 2019年第7期588-604,共17页
Measles is a reemerging disease that has a devastating impact, especially among children under 5. In this paper, an SEIRS model is developed to investigate a possible outbreak among the population of children under 5 ... Measles is a reemerging disease that has a devastating impact, especially among children under 5. In this paper, an SEIRS model is developed to investigate a possible outbreak among the population of children under 5 in the Sunyani Municipality. We consider waning immunity or loss of immunity among those who were vaccinated, which leads to secondary attacks among some in the population. Using Routh-Hurwitz criterion, Matrix Theoretic and Goh-Volterra Lyapunov functions, the stability of the model was investigated around the equilibria. We have computed the threshold parameter, R0, using the Next Generation Matrix method. The disease-free equilibrium is globally stable whenever R0 &le;1 and unstable otherwise. The endemic equilibrium is globally stable when R0?>1. 展开更多
关键词 Global Stability LYAPUNOV Function MATRIX Theoretic Method NEXT Generation MATRIX SEIRS
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A General Model of Zoonosis Where the Diseases Can Only Be Transmitted from Animals to Humans 预览
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作者 Xueying Liu 《理论数学进展(英文)》 2019年第2期67-77,共11页
Zoonosis is an important factor affecting human economic development and population mortality. This paper introduces a general model of zoonosis, in which the diseases can only be transmitted from animals to humans, s... Zoonosis is an important factor affecting human economic development and population mortality. This paper introduces a general model of zoonosis, in which the diseases can only be transmitted from animals to humans, such as rabies, brucellosis and so on. The basic reproduction number R0 is derived. And then the global stability of the disease-free equilibrium and endemic equilibrium models is analyzed by using the method of comparison principle and Lyapunov function. Next, a numerical analysis is performed to elaborate the consistency of theoretical and numerical results and to prove the practical significance of zoonosis research. The numerical results show that our models are applicable to zoonosis with animal size larger than or smaller than population size. Finally, in order to see the most important factor for the epidemic of zoonosis a sensitive analysis is analyzed. 展开更多
关键词 ZOONOSIS Global Stability EQUILIBRIUM Sensitive Analysis
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Global Analysis of an SEIR Epidemic Model with Infectious Force under Intervention Strategies 预览
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作者 Minmin Zhou Tiansi Zhang 《应用数学与应用物理(英文)》 2019年第8期1706-1717,共12页
In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic re... In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic reproduction number R0 plays an essential role in determining whether the disease extincts or persists. If , there is a unique disease-free equilibrium point of the model which is globally asymptotically stable and the disease dies out, and if , there exists a unique endemic equilibrium point which is globally asymptotically stable and the disease persists. 展开更多
关键词 SEIR EPIDEMIC Model INTERVENTION Strategies Basic REPRODUCTION NUMBER Global Stability
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Global dynamics of a cholera model with age structures and multiple transmission modes
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作者 Xia Wang Yuming Chen Xinyu Song 《生物数学学报:英文版》 2019年第5期63-96,共34页
In this paper,we propose and analyze a cholera model.The model incorporates both direct transmission (person-to-person transmission) and indirect transmission (contaminated environment-to-person transmission: hyper-in... In this paper,we propose and analyze a cholera model.The model incorporates both direct transmission (person-to-person transmission) and indirect transmission (contaminated environment-to-person transmission: hyper-infectivity and lower-infcctivity).Moreover,we employ general nonlinear incidences and introduce infection age of infectious individuals and biological ages of pathogens in the environment.After considering the well-posedness of the system,we study the existence and local stability of steady states,which is determined by the basic reproduction number.To establish the attractivity of the infection steady state,we also get the uniform persistence and existence of compact global attractors.The main result is a threshold dynamics obtained by applying the Fluctuation Lemma and the approach of Lyapunov functionals.When the basic reproduction number is less than one,the infection-free steady state is globally asymptotically stable while when the basic reproduction number is larger than one,the infection steady state attracts each solution with nonzero infection force at some time point.The effect of multiple transmission modes on the disease dynamics is also discussed. 展开更多
关键词 MULTIPLE transmission MODES age of infection GLOBAL stability UNIFORM per-sistence compact GLOBAL ATTRACTOR
欠驱动水面机器人变周期全局渐近镇定控制 预览
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作者 张鹏飞 郭戈 《控制理论与应用》 EI CAS CSCD 北大核心 2019年第5期746-752,共7页
为了实现欠驱动水面机器人的全局渐近镇定,首先借助微分同胚变换,将欠驱动水面机器人的镇定问题转化成对由两个串级子系统构成的二阶欠驱动系统的镇定问题.针对转换后的系统,本文提出一种光滑的变周期控制方法,以实现对该系统的全局渐... 为了实现欠驱动水面机器人的全局渐近镇定,首先借助微分同胚变换,将欠驱动水面机器人的镇定问题转化成对由两个串级子系统构成的二阶欠驱动系统的镇定问题.针对转换后的系统,本文提出一种光滑的变周期控制方法,以实现对该系统的全局渐近镇定.与已有文献中控制律使用常数周期的方法相比,本文方法根据系统状态实时调整控制律周期,从而提高系统在原点附近的收敛速率.随后,基于上述方法,给出了水面机器人变周期控制算法,实现原系统的全局渐近镇定.最后,仿真对比结果验证所提变周期控制方法的有效性. 展开更多
关键词 欠驱动水面机器人 变周期控制 全局稳定 渐近稳定
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一类具有媒体报道的传染病模型 预览
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作者 陈娟 戴斌祥 李文秀 《集美大学学报:自然科学版》 CAS 2019年第1期64-67,共4页
将媒体报道量M视为时间t的函数,利用非连续函数β/(1+εMI)来刻画媒体报道对传染率的影响,建立了一个分段光滑的SIM传染病模型,给出了模型的非负平衡点的存在性。利用微分方程线性化稳定性理论分析,得到了系统的各平衡点局部稳定的阈值... 将媒体报道量M视为时间t的函数,利用非连续函数β/(1+εMI)来刻画媒体报道对传染率的影响,建立了一个分段光滑的SIM传染病模型,给出了模型的非负平衡点的存在性。利用微分方程线性化稳定性理论分析,得到了系统的各平衡点局部稳定的阈值条件,并进一步利用Poincare-Bendixon定理给出了正平衡点全局渐近稳定的充分条件。 展开更多
关键词 媒体报道 传染病模型 局部稳定性 全局稳定性
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具有阶段进程的SLI艾滋病模型的全局稳定性
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作者 王晓红 刘桂荣 《数学的实践与认识》 北大核心 2019年第10期286-291,共6页
艾滋病的潜伏期很长,一般会经历几个潜伏阶段才会发病,故将其看作常数是不合理的.建立了一个具有现实分布的数学模型,即将潜伏期划分为n个阶段.对于一个一般的具有双线性发生率的n-阶段的阶段进程模型,研究了其动力学行为.首先给出了模... 艾滋病的潜伏期很长,一般会经历几个潜伏阶段才会发病,故将其看作常数是不合理的.建立了一个具有现实分布的数学模型,即将潜伏期划分为n个阶段.对于一个一般的具有双线性发生率的n-阶段的阶段进程模型,研究了其动力学行为.首先给出了模型的基本再生数.进一步得到,当基本再生数小于1时,无病平衡点是全局渐近稳定的且疾病最终会消失;当基本再生数大于1时,唯一的地方病平衡点是全局渐近稳定的且疾病最终会成为一种地方病. 展开更多
关键词 艾滋病 阶段进程 李雅普诺夫函数 全局稳定性
偏好情景应变式冲突分析模型 预览
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作者 陶良彦 刘思峰 +1 位作者 方志耕 胡骞 《运筹与管理》 CSSCI CSCD 北大核心 2019年第1期108-115,共8页
针对决策者偏好信息随未来潜在发展情景变化的情况,构建了偏好情景应变式冲突分析模型。首先利用情景分析技术生成了影响冲突分析的若干潜在情景,不同潜在情景下的冲突子系统共同构成偏好情景应变式冲突系统。进而将所有潜在情景下冲突... 针对决策者偏好信息随未来潜在发展情景变化的情况,构建了偏好情景应变式冲突分析模型。首先利用情景分析技术生成了影响冲突分析的若干潜在情景,不同潜在情景下的冲突子系统共同构成偏好情景应变式冲突系统。进而将所有潜在情景下冲突子系统稳定的交集定义为情景应变式冲突模型的全局稳定。由于全局稳定条件较为苛刻,交集可能为空集,进一步从集结不同情景下偏好信息角度定义了偏好集结型稳定。具体方法是依据策略优先权法对状态打分,接着利用决策者对不同情景的重视程度集结打分值,获得集结的偏好信息,并定义相应的稳定。最后以某大型客机立项论证阶段研制周期冲突决策为例比较了这两种稳定。 展开更多
关键词 冲突分析 情景 偏好 全局稳定 偏好集结 策略优先权排序法
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具有合作行为且捕食者患病的生态流行病模型分析 预览
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作者 张攀 王稳地 向茜 《西南师范大学学报:自然科学版》 CAS 北大核心 2019年第5期7-12,共6页
研究了一类捕食者患病的捕食-食饵模型,且考虑捕食者种群存在合作捕食行为.首先讨论了无病子模型的动力学性质,通过构造合适的Lyapunov函数,证明了边界平衡点的全局稳定性,利用Dulac函数讨论了仅一个正平衡点时的全局稳定性以及Hopf分... 研究了一类捕食者患病的捕食-食饵模型,且考虑捕食者种群存在合作捕食行为.首先讨论了无病子模型的动力学性质,通过构造合适的Lyapunov函数,证明了边界平衡点的全局稳定性,利用Dulac函数讨论了仅一个正平衡点时的全局稳定性以及Hopf分支产生的情况.其次讨论了有病系统中三者共存的平衡点的情况,利用Hurwitz判据得到共存平衡点的稳定条件. 展开更多
关键词 LYAPUNOV函数 DULAC函数 全局稳定性 HOPF分支
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Analysis on an SEIR Epidemic Model with Logistic Death Rate of Virus Mutation
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作者 Jianzhong GAO Tailei ZHANG 《数学研究及应用:英文版》 CSCD 2019年第3期259-268,共10页
In this paper, we propose an SEIR epidemic model with Logistic death rate of virus mutation. By means of the direct Lyapunov method and the LaSalle’s Invariance Principle, the global stability of the disease-free equ... In this paper, we propose an SEIR epidemic model with Logistic death rate of virus mutation. By means of the direct Lyapunov method and the LaSalle’s Invariance Principle, the global stability of the disease-free equilibrium is proved. Using algebraic method to construct Lyapunov function, the global stability of the endemic equilibrium is proved. In addition, numerical simulations are done and the influence of parameters in the model on disease transmission is analyzed. 展开更多
关键词 VIRUS MUTATION LOGISTIC DEATH RATE global stability ALGEBRAIC method
基于传播能力差异的IWSR垃圾信息传播模型 预览
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作者 冉茂洁 刘超 +2 位作者 黄贤英 刘小洋 曹琼 《计算机应用研究》 CSCD 北大核心 2019年第7期2169-2173,共5页
为研究用户传播能力差异性对垃圾信息传播的影响,根据仓室建模思想,将传播网络中的人群划分为I(ignorant)、W(weakly spreader)、S(strongly spreader)、R(removal)四个仓室并提出状态转换规则,运用微分动力系统理论建立一个具有传播能... 为研究用户传播能力差异性对垃圾信息传播的影响,根据仓室建模思想,将传播网络中的人群划分为I(ignorant)、W(weakly spreader)、S(strongly spreader)、R(removal)四个仓室并提出状态转换规则,运用微分动力系统理论建立一个具有传播能力差异的IWSR垃圾信息传播模型。通过计算模型的基本再生数,利用Hurwitz判据、Lyapunov稳定性定理和LaSalle不变性原理,得出垃圾信息传播平衡点的局部稳定和全局稳定条件。最后通过数值仿真与新浪微博真实数据集的对比实验证明所得结论的合理性和有效性。 展开更多
关键词 数学模型 全局稳定性 基本再生数 垃圾信息传播 传播能力差异
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Allee效应对单种群模型动力学行为影响研究
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作者 关心宇 谢向东 +1 位作者 刘羽 陈凤德 《生物数学学报》 2019年第1期140-144,共5页
提出具有Allee效应的抽象的单种群模型,证得如果原系统有唯一的全局稳定的正平衡点,则具有Allee效应的单种群模型仍然具有唯一的全局稳定的正平衡点.Allee效应并不改变种群的平衡位置和稳定性;其后,针对具有Allee效应的对数种群模型,食... 提出具有Allee效应的抽象的单种群模型,证得如果原系统有唯一的全局稳定的正平衡点,则具有Allee效应的单种群模型仍然具有唯一的全局稳定的正平衡点.Allee效应并不改变种群的平衡位置和稳定性;其后,针对具有Allee效应的对数种群模型,食物有限的单种群模型,Ayala型单种群模型分别进行了数值模拟,数值模拟表明随着Allee效应增大,系统的解需要更久的时间才能趋于正平衡点,从这一角度讲,Allee效应不利于系统的稳定,种群在受到外界干扰时,可能种群密度更容易出现剧烈波动. 展开更多
关键词 单种群 ALLEE效应 全局稳定
具有饱和发生率的血吸虫病动力学分析
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作者 王晓红 薛亚奎 《数学的实践与认识》 北大核心 2019年第8期249-257,共9页
血吸虫病是我国一种严重的寄生虫病,并且在湖北、安徽、湖南、江苏、四川和云南成地方病.结合中国血吸虫病的现状及特点,考虑人群、牛群以及水环境中的钉螺、尾蚴和毛蚴之间的相互传染,建立了具有饱和发生率的血吸虫病动力学模型,给出... 血吸虫病是我国一种严重的寄生虫病,并且在湖北、安徽、湖南、江苏、四川和云南成地方病.结合中国血吸虫病的现状及特点,考虑人群、牛群以及水环境中的钉螺、尾蚴和毛蚴之间的相互传染,建立了具有饱和发生率的血吸虫病动力学模型,给出了模型的基本再生数.通过构造Lyapunov函数证明了当基本再生数小于1时,模型的无病平衡点全局渐近稳定;当基本再生数大于1时,模型的地方病平衡点也是全局渐近稳定的.最后,利用数值模拟验证了理论结果. 展开更多
关键词 血吸虫病 基本再生数 平衡点 全局稳定性
一类带标准发病率的传染病模型的动力学分析 预览
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作者 谯婷 《兰州文理学院学报:自然科学版》 2019年第6期1-6,48共7页
对一类新的带有标准发病率的传染病模型进行了研究.首先,讨论了正平衡点的存在性和局部稳定性;最后,利用第二加性复合矩阵证明了正平衡点的全局稳定性.
关键词 传染病模型 第二加性复合矩阵 全局稳定性 数学流行病学
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Global stability analysis of fractional-order gene regulatory networks with time delay
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作者 Zhaohua Wu Zhiining Wang Tiejun Zhou 《生物数学学报:英文版》 2019年第6期99-118,共20页
Fractional-order gene regulatory networks with time delay(DFCIRNs)have proven that they are more suitable to model gene regulation mechanism than integer-order.In this paper,a novel DFGRN is proposed.The existence and... Fractional-order gene regulatory networks with time delay(DFCIRNs)have proven that they are more suitable to model gene regulation mechanism than integer-order.In this paper,a novel DFGRN is proposed.The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions.On this basis,the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN,and the stability conditions are dependent on the fractional-order q.Finally,numerical simulations show that the obtained results arc reasonable. 展开更多
关键词 FRACTIONAL-ORDER gene regulatory networks time delay global stability.
Global dynamics in a heroin epidemic model with different conscious stages and two distributed delays
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作者 Xamxinur Abdurahman Zhidong Teng Ling Zhang 《生物数学学报:英文版》 2019年第3期249-268,共20页
A heroin epidemic model with different conscious stages and distributed delays is constructed. The model allows for conscious drug users and unconscious drug users. The threshold dynamics of the model is established. ... A heroin epidemic model with different conscious stages and distributed delays is constructed. The model allows for conscious drug users and unconscious drug users. The threshold dynamics of the model is established. It is shown that drug-free equilibrium is globally asymptotically stable when basic reproduction number R0<1;when R0>1, the uniform persistence of the model is proved, and it is proved that the endemic equilibrium is globally asymptotically stable. 展开更多
关键词 HEROIN EPIDEMIC model distributed delay global stability STABLE
Vaccination of a multi-group model of zoonotic diseases with direct and indirect transmission
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作者 Wei Lv Xue-Ying Liu +1 位作者 Xin-Jian Xu Jie Lou 《生物数学学报:英文版》 2019年第6期119-146,共28页
Vaccination plays an important role in preventing or reducing the spread of zoonotic diseases.In this paper,we develop a susceptible-vaecinated-exposed-infectious-pathogen multi-group epidemic model of zoonotic diseas... Vaccination plays an important role in preventing or reducing the spread of zoonotic diseases.In this paper,we develop a susceptible-vaecinated-exposed-infectious-pathogen multi-group epidemic model of zoonotic diseases incorporating nonlinear direct and indi­rect incidence rates,nonlinear pathogen shedding rates,and common environmental contamination.Under certain assumptions,we first obtained the basic reproduction number of the model.Then,we utilized the comparison principle and global Lyapunov function method to prove global stability of dynamical equilibria.Finally,we analyzed optimal vaccination strategy.All the theoretical predictions were verified by numerical simulations. 展开更多
关键词 VACCINATION global stability optimal control zoonotic diseases.
一维非等温可压缩Navier-Stokes-Korteweg方程组稀疏波的整体稳定性 预览
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作者 郭起东 陈正争 《应用数学》 CSCD 北大核心 2019年第3期682-698,共17页
可压缩Navier-Stokes-Korteweg方程组可用来描述具有内部毛细作用的粘性可压缩流体的运动.本文研究了毛细系数依赖于密度、粘性系数和热传导系数依赖于温度的一维非等温的可压缩Navier-Stokes-Korteweg方程组Cauchy问题解的大时间行为.... 可压缩Navier-Stokes-Korteweg方程组可用来描述具有内部毛细作用的粘性可压缩流体的运动.本文研究了毛细系数依赖于密度、粘性系数和热传导系数依赖于温度的一维非等温的可压缩Navier-Stokes-Korteweg方程组Cauchy问题解的大时间行为.利用基本的L2能量方法,我们证明如果相应的Euler方程组的黎曼问题存在稀疏波解,那么所考虑的一维可压缩Navier-Stokes-Korteweg方程组存在唯一的整体强解,并且当时间趋于无穷大时,此强解趋向于稀疏波.这里初始扰动和稀疏波的强度都可以任意大. 展开更多
关键词 可压缩Navier-Stokes-Korteweg方程组 稀疏波 整体稳定性
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