公共教育影响的SIR传染病斑块模型性态分析

建立了考虑公共卫生教育影响的SIR斑块模型.通过分析模型动力学性态,给出模型平衡点存在条件,并证明了无病平衡点和地方病平衡点的稳定性.通过数值模拟分析公共卫生教育和斑块间的传播对模型疾病传播的影响,发现媒体的传播和公众之间的交流可以促进疾病防护意识,进而降低传染及传播疾病的几率.当疾病爆发时,应尽量减少人口流通,当疾病爆发后,应加强疾病防护意识的传播,尤其是医疗水平较低的地区.     

一类具有垂直传染与接种的DS—I—R传染病模型研究

本文研究了-类具有垂直传染与接种的疾病在多个易感群体中传播的DS-I-R传染病模型,得到了疾病流行的阈值.运用微分方程定性与稳定性理论分析了无病平衡点的局部稳定与全局渐近稳定性及存在唯一地方病平衡点与其全局渐近稳定性.     

具有交通流量异质性的网络传染病模型研究

主要研究了异质集合种群网络上的移动和扩散行为对疾病传播的影响.针对现实社会中的网络所具有的异质性,分析了影响城市疾病传播的主要因素为网络拓扑结构以及城市交通流量异质性,建立了依赖于交通流量移出率的传染病动力学模型.通过分析模型的无病平衡点以及正平衡点的存在及其稳定性,发现人口流动会使交通较发达的城市拥有更多的染病者,更容易促使疾病的爆发.     

一类具有病毒变异的Logistic死亡率SEIR传染病模型研究分析

本文建立了一类具有病毒变异的Logistic死亡率SEIR传染病模型,借助Lyapunov函数和LaSalle''s不变原理,证明了无病平衡点全局稳定性.利用代数方法构造Lyapunov函数,证明了地方病平衡点全局稳定性.另外,通过数值模拟分析了参数对疾病传播的影响.     

带有脉冲药物治疗策略的SIA模型的全局稳定性

根据艾滋病的传播特点,建立了带有脉冲药物治疗策略的感染年龄结构SIA模型,得到了控制疾病传播的基本再生数R_O(p,T),并讨论了无病平衡态的全局稳定性.     

疾病在食饵中流行的捕食与被捕食模型的分析

分析并建立了疾病在食饵中传播的生态-传染病模型,同时考虑到两种群都受密度制约因素的影响,讨论了模型解的有界性和各平衡点的存在性,利用Routh-Hurwitz判据证明了各平衡点的局部渐进稳定性,通过构造Lyapunov函数分析了各平衡点的全局渐进稳定性,得到了疾病存在与否的充分性条件.     

疾病在食饵中传播的具有时滞的捕食被捕食模型的分析

研究了一个疾病在食饵中传播的捕食与被捕食模型.在未引入时滞时,利用Routh-Hurwitz定理证明了正平衡点的局部渐近稳定性.在引入时滞后,主要讨论了正平衡点的稳定性,得到了当经过一系列临界条件时发生Hopf分支.     

一类患病阶段服从非指数分布的SEITR传染病模型的潜在假设和稳定性分析

建立了一类SEITR传染病模型,推导出模型潜在的假设条件,并得到了一般分布下相应的积分微分方程.进而,通过在疾病传播的特定阶段引入Gamma分布和指数分布将积分微分方程化简成了ODE方程,证明了服从指数分布的ODE方程的无病平衡点的局部和全局稳定性.对两类模型的控制再生数进行敏感度分析的结果表明传染率β是影响疾病传播的最重要因素.     

基于存在基础病史易感者的SEIR模型对COVID-19传播的研究

该文基于经典的SEIR传染病模型建立了一类含有基础疾病历史人群的新冠肺炎传播模型,得到了其传播的基本再生数,确定了模型平衡点的存在性,并通过构造Lyapunov函数和利用LaSalle不变性原理论证了平衡点的全局稳定性,用数值模拟对所得理论研究结果进行了有效验证.同时,讨论了由无基础病向有基础病转化的速率系数对疾病传播...     

一类具有体液免疫的宿主内部和宿主之间的疾病传播耦合模型

讨论了一类具有体液免疫的宿主内部和宿主之间疾病传播耦合模型.首先使用极限系统思想,将模型分解成宿主内的快时间子模型和宿主间的慢时间子模型.对快时间子模型,得到了平衡点的存在性,并使用李雅普诺夫函数方法建立了平衡点全局稳定性的阈值条件.对慢时间子模型,当宿主内抗体不发生作用时,得到模型可能存在后向分支;而当宿主内抗体发生作用时,建立了平衡点全局稳定性的阈值条件.因此,宿主内抗体对控制宿主间疾病的传播具有非常重要的作用,特别地当宿主内抗体细胞达到一定水平时,可以使宿主之间的疾病灭绝.     

Chaotic effects on disease spread in simple eco-epidemiological system

In this paper, an eco-epidemiological model where prey disease is structured as a susceptible-infected model is investigated. Thresholds that control disease spread and population persistence are obtained. Existence, stability and instability of the system are studied. Hopf bifurcation is shown to occur where a periodic solution bifurcates from the coexistence equilibrium. Simulations show that the system exhibits chaotic phenomena when the transmission rate is varied.     

DOES WATER DISINFECTANT PLAY A SUPPORTIVE ROLE IN THE SPREAD OF INFECTIOUS DISEASE? A MATHEMATICAL STUDY

The waterborne diseases cause millions of deaths across the globe. It was a preconceived notion since years that ingestion of contaminated water is the only possible way for the spread of waterborne infectious diseases. But some recent studies have shown that waterborne disease can also spread as a result of human to human transmission. The use of disinfectants is a common practice to prevent a waterborne disease. We assume that the inclusion of the disinfectant, although helpful in prevention of disease, caused negative effect on individuals. In this paper, a nonlinear mathematical model has been proposed to analyze the negative effects caused by disinfectant of water on individuals. Our study shows that if the mixing of disinfectant has not been performed in a controlled manner, then it results in an increase in human to human transmission of disease. The equilibrium and stability analysis have been performed to study the nature of the model system. An extensive numerical experiment has been performed to support the analytical findings.     

Optimal control and basic reproduction numbers for a compartmental spatial multipatch dengue model

Dengue is a vector‐borne viral disease increasing dramatically over the past years due to improvement in human mobility. In this work, a multipatch model for dengue transmission dynamics is studied, and by that, the control efforts to minimize the disease spread by host and vector control are investigated. For this model, the basic reproduction number is derived, giving a choice for parameters in the endemic case. The multipatch system models the host movement within the patches, which coupled via a residence‐time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission effectively reduces the spread of the disease.     

Optimal control and sensitivity analysis of SIV→HIV dynamics with effects of infected immigrants in sub‐Saharan Africa

Regional migration has become an underlying factor in the spread of HIV transmission. In addition, immigrants with HIV status has contributed with high‐risk of sexually transmitted infection to its “destination” communities and promotes dissemination of HIV. Efforts to address HIV/AIDS among conflict‐affected populations should be properly addressed to eliminate potential role of the spread of the disease and risk of exposure to HIV. Motivated from this situation, HIV‐infected immigrants factor to HIV/SIV transmission link will be investigated in this research and examine its potential effect using optimal control method. Nonlinear deterministic mathematical model is used which is a multiple host model comprising of humans and chimpanzees. Some basic properties of the model such as invariant region and positivity of the solutions will be examined. The local stability of the disease‐free equilibrium was examined by computing the basic reproduction number, and it was found to be locally asymptotically stable when ?₀<1 and unstable otherwise. Sensitivity analysis was conducted to determine the parameters that help most in the spread of the virus. Pontryagin's maximum principle is used to obtain the optimality conditions for controlling the disease spread. Numerical simulation was conducted to obtain the analytical results. The results shows that combination of public health awareness, treatment, and culling help in controlling the HIV disease spread.     

Global dynamics and control of malicious signal transmission in wireless sensor networks

This paper studies the global dynamics of a discontinuous delayed model of malicious signal transmission in wireless sensor networks under the framework of differential inclusion. The local stability of two types of steady states are investigated for the discontinuous system by studying the corresponding characteristic equation. The sufficient conditions for the existence of two types of globally asymptotically stable steady states are obtained for the discontinuous system by using the comparison arguments method. Furthermore, the optimal control of the discontinuous system is investigated by using Pontryagin’s maximum principle. Numerical simulations of two examples are carried out to illustrate the main theoretical results. The obtained results can help us to better control and predict the spread of malicious signal transmission in wireless sensor networks.     

一类具有非线性发生率的时滞传染病模型的全局稳定性

充分考虑人口统计效应、疾病的潜伏期与传播规律的复杂性,研究了一类具有非线性发生率的时滞SIRS传染病模型的动力学行为.通过分析对应的线性化近似系统的特征方程,证明了无病平衡点的局部稳定性.利用Lyapunov-LaSalle不变集原理,当基本再生数R₀<1时,证明了无病平衡点是全局渐近稳定的;当R₀>1时,得到了地方病平衡点全局渐近稳定的充分条件.所得结论可为人们有效预防和控制传染病传播提供一定的理论依据.     

Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives

In this paper, we study the impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. Initially we consider constant controls and thereafter treat control measures as time dependent control parameters. In the constant controls case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit transcritical bifurcation. For the time dependent controls, we formulate the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of unaware infectives in the spread of HIV/AIDS. We observed that unawareness by infectives has a great cost impact on the community. We further investigate the impact of combinations of the strategies in the control of HIV/AIDS. Carrying out cost-effectiveness analysis, we found that the most cost-effective strategy is the combination of all the control strategies.     

Spread of a disease and its effect on population dynamics in an eco-epidemiological system

In this paper, an eco-epidemiological model with simple law of mass action and modified Holling type II functional response has been proposed and analyzed to understand how a disease may spread among natural populations. The proposed model is a modification of the model presented by Upadhyay et al. (2008) [1]. Existence of the equilibria and their stability analysis (linear and nonlinear) has been studied. The dynamical transitions in the model have been studied by identifying the existence of backward Hopf-bifurcations and demonstrated the period-doubling route to chaos when the death rate of predator (μ₁) and the growth rate of susceptible prey population (r) are treated as bifurcation parameters. Our studies show that the system exhibits deterministic chaos when some control parameters attain their critical values. Chaotic dynamics is depicted using the 2D parameter scans and bifurcation analysis. Possible implications of the results for disease eradication or its control are discussed.     

Modelling the Spread of HIV/AIDS Epidemic

In this paper, a deterministic mathematical model for the spread of HIV/AIDS in a variable size population through horizontal transmission is considered. The existence of a threshold parameter, the basic reproduction number, is established, and the stability of both the disease-free equilibrium and the endemic equilibrium is discussed in terms of $R_0$.     

The impact of Wolbachia on dengue transmission dynamics in an SEI–SIS model

Dengue has grown dramatically in recent decades globally. In order to investigate the spread of dengue with vector control, especially, the impact of Wolbachia on dengue transmission, a mathematical model is established and analyzed to study dengue transmission between humans and mosquitoes. Firstly, model qualitative analysis including the existence and local asymptotic stability of dengue-free equilibria and endemic equilibria is done. It is found that dengue will disappear when the basic reproduction number is less than one, and dengue will prevail when the basic reproduction number is larger than one. More important finding is that the persistence of Wolbachia is determined by its fitness effect on mosquitoes, and Wolbachia can drastically reduce dengue fever transmission. All the results are verified by numerical simulation. Secondly, sensitivity analysis is done to explore the relative importance of different parameters on the system. It is obtained that parameters with strong sensitivity and controllability are the biting rate, the probability of dengue infection between mosquitoes and humans and the recovery rate of infectious humans. Finally, the control methods are discussed.