具有脉冲出生和脉冲接种的SIR传染病模型

考虑了脉冲出生、脉冲接种、垂直传染、因病死亡等因素,建立了脉冲出生和脉冲接种同时进行的SIR传染病模型,通过分析无病周期解的存在性以及稳定性,得出疾病灭绝的条件.     

一类具有饱和反应率的脉冲免疫接种的SIS模型

研究了具饱和传染率的脉冲免疫接种SIS模型,得到了无病周期解全局渐近稳定的充分条件和系统持续生存的充分条件．     

具有比例和脉冲接种的乙肝流行病模型

研究具有连续预防接种和脉冲预防接种的SIR乙肝传染病模型,获得了再生数σ0和σ1.在连续模型中,当σ0<1时仅有无病平衡点存在,全局渐近稳定;σ0>1时无病平衡点不稳定,地方病平衡点存在,全局渐近稳定.在脉冲模型中,当σ1<1时无病周期解存在稳定;σ1>1时无病周期解不稳定,且在接种率充分小时,地方病周期解存在稳定.     

一类疫苗预防接种具有效期性的SIRS模型稳定性分析

研究了一类预防接种下疫苗具有有效期的SIRS传染病模型,得到了决定疾病绝灭与否的闽值,给出了无病平衡点和地方病平衡点的全局稳定性的充分条件,最后借助Matlab软件进行了数值模拟．     

Stability of a Stochastic Model of an SIR Epidemic with Vaccination

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue \(\mathcal{R}_\sigma\) of the basic reproduction number \(\mathcal{R}_0\) of the underlying deterministic model, with \(\mathcal{R}_\sigma \le \mathcal{R}_0\). We prove that the disease-free equilibrium is almost sure exponentially stable if \(\mathcal{R}_\sigma <1\).     

具有时变接触率与接种率的脉冲传染病模型研究

讨论了时变接触率和时变接种率的传染病模型,模型中考虑对易感者和染病者同时接种.通过计算得到了判别疾病流行与否的阈值.证明了当基本再生数小于1时,疾病是流行的;当基本再生数大于1时,疾病将成为地方病.     

一类带有脉冲出生和垂直传染的时滞SEIS传染病模型

建立并分析了一个带有脉冲出生、垂直传染和时滞的SEIS传染病模型.利用频闪映射得到了无病周期解的存在性,并得到了两个临界值R~*和R_*,当R~*<1时,无病周期解全局吸引,疾病消失;当R_*>1时,疾病持续.     

Optimal Vaccination in a Stochastic Epidemic Model of Two Non-Interacting Populations

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that enables us to calculate the complete probability distribution for the final epidemic size in a stochastic Susceptible-Infected-Recovered (SIR) model. Based on these results, we determine the optimal allocations of a limited quantity of vaccine between two non-interacting populations. We compare the stochastic solution to results obtained for the traditional, deterministic SIR model. For intermediate quantities of vaccine, the deterministic model is a poor estimate of the optimal strategy for the more realistic, stochastic case.     

一类具有垂直传染和预防接种的传染病模型的稳定性

考虑了垂直传染和预防接种因素对传染病流行影响的SEIRS模型,主要研究了系统的平衡点及其稳定性,得出当预防接种水平超过某一个阈值时疾病可以根除,若接种水平低于阈值时疾病将流行.     

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.     

A Mathematical Model of the Tuberculosis Epidemic

Acta Biotheoretica - Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single...     

一类具有阶段结构的传染病模型的全局分析

通过建立一类具有阶段结构的传染病模型,得到了系统解的永久持续性,并通过构造Liapunov函数和定性分析得到了各类平衡点的全局稳定性的充分条件.     

具有年龄结构的接种流行病模型正平衡解的全局稳定性

研究一个具有年龄结构的接种SIS流行病模型正平衡解的稳定性,先利用等价积分方程给出了正平衡解存在的充分条件,再利用迭代方法及函数的单调性,得到了零平衡解与正平衡解全局稳定的充分条件。     

Bimodal Epidemic Size Distributions for Near-Critical SIR with Vaccination

We introduce a recursive algorithm which enables the computation of the distribution of epidemic size in a stochastic SIR model for very large population sizes. In the important parameter region where the model is just slightly supercritical, the distribution of epidemic size is decidedly bimodal. We find close agreement between the distribution for large populations and the limiting case where the distribution is that of the time a Brownian motion hits a quadratic curve. The model includes the possibility of vaccination during the epidemic. The effects of the parameters, including vaccination level, on the form of the epidemic size distribution are explored.     

一类具常数接触率传染病模型的稳定性分析

本文研究了一类具常数接触率的传染病模型,用上下解方法和Liapnuov泛函讨论了地方病平衡点及无病平衡点的渐近行为,得到了各自全局稳定的充分条件.     

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。     

具脉冲出生单种群模型的脉冲收获阈值分析

讨论了与生物资源管理相关的具脉冲出生与脉冲收获的单种群动力学模型,利用离散动力系统频闪映射理论,得到了生物资源管理控制阈值的充分条件.结论为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲微分方程理论.     

一类病毒自身发生变异的传染病模型的全局分析

针对病毒变异前和变异后传染病患者具有不同的传染率情形,建立了一类分阶段传播的SIS模型,通过构造Liapunov函数和定性分析,得到病毒变异前和变异后传染病患者平衡点的存在条件以及它们的全局渐近稳定性。     

一类具有非单调发生率SIS流行病模型的分析

该文讨论了具有非单调发生率SIS流行病模型,分别建立了带有分布时滞和离散时滞形式的感染个体的恢复时滞模型,同时分析了系统平衡态的稳定性．