共查询到16条相似文献,搜索用时 218 毫秒
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本文建立了一个吸毒人群具有吸毒年龄,治疗人群具有治疗年龄的海洛因传播模型.得到了基本再生数.通过波动引理和李雅普诺夫泛函,证明了当基本再生数小于1时无海洛因吸食平衡点是全局渐近稳定的,当基本再生数大于1时,海洛因传播平衡点是全局渐近稳定的. 相似文献
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:研究一类具有一般形式非线性饱和传染率染病年龄结构SIS流行病传播数学模型动力学性态,得到疾病绝灭和持续生存的阈值条件——基本再生数。当基本再生数小于或等于1时,仅存在无病平衡点,且在其小于1的情况下,无病平衡点全局渐遗稳定,疾病将逐渐消除;当基本再生数大于1时,存在不稳定的无病平衡点和唯一的局部渐近稳定的地方病平衡点,疾病将持续存在。已有的两类模型可视为本模型的特例,其相关结论可作为本文的推论。 相似文献
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基于重新感染情形,建立了一个具有接种、潜伏和染病年龄结构的流行病模型,目的在于讨论疫苗接种年龄、潜伏年龄和感染年龄对模型全局动力学的影响,得到了模型的全局动力学由基本再生数决定。首先,利用偏微分方程沿特征线积分理论,给出了模型解的存在唯一性、连续有界性和渐近光滑性;其次,利用微分方程解的理论,得到模型的平衡点和基本再生数。再次,结合引入的基本再生数和构造的Lyapunov函数,应用LaSalle不变性原理得到结论:若基本再生数小于1,则无病平衡点全局渐近稳定;若基本再生数大于1,则无病平衡点不稳定。最后,数值模拟验证了所讨论模型的解收敛于无病平衡点。 相似文献
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本文旨在利用非标准有限差分方法离散并求解一个包含预防接种的霍乱传染病模型.该离散模型具有和对应的原连续模型一致的平衡点,正性和有界性等性质.其次本文证明当基本再生数小于 1 时,无病平衡点是局部渐近稳定和全局渐近稳定的;当基本再生数大于 1 时,通过构造适当的 Lyapunov 函数,地方病平衡点也是全局渐近稳定的.最后利用离散模型可以成功模拟 2008 年津巴布韦霍乱,并可数值证明离散模型的稳定性,且与步长和初始条件等无关,再与其他离散方法比较验证 NSFD 方法的优势所在. 相似文献
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Jean M. Tchuenche Christinah Chiyaka 《Dynamical Systems: An International Journal》2012,27(2):145-160
A disease transmission model of susceptible-infective-recovered type with a constant latent period is analysed. The global dynamics of the disease-free equilibrium is investigated. If the basic reproduction number is greater than unity, a unique endemic equilibrium exists. Using Lyapunov functional approach, this endemic equilibrium is globally stable in the feasible region. The disease will persist (and is permanent) at the endemic equilibrium if it is initially present. The effects of loss of immunity on the dynamics of the model are analysed, and the parameters that drive the disease dynamics are obtained. Numerical simulations support our analytical results and illustrate possible behavioural scenarios of the model. 相似文献
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预防接种情况下非线性饱和接触率SIR流行病模型动力学性态研究 总被引:2,自引:1,他引:2
研究了一类预防接种情况下具有一般非线性饱和接触率SIR流行病模型动力学性态。得到决定疾病灭绝和持续生存的基本再生数。当基本再生数小于等于1时,仅存在无病平衡态:当基本再生数大于1时,除存在无病平衡态外,还存在惟一的地方病平衡态。利用Hurwitz判据、Liapunov-Lasalle不变集原理得到各个平衡态局部渐近稳定及无病平衡态全局渐近稳定的条件。特别地。当传染率为双线性时,无病平衡态及地方病平衡态全局渐近稳定。 相似文献
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本文主要研究了具有三个年龄阶段的离散SCIRS模型的动力学性态.首先,利用再生矩阵的方法定义了模型的基本再生数R0,证明了当R01时,模型存在唯一的无病平衡点并且是全局渐近稳定的,当R01时,除了无病平衡点,模型还存在唯一的地方病平衡点.其次,利用法定传染病报告的流脑数据,把模型应用到我国流脑的流行传播中.针对模型中很多参数的不确定性,对基本再生数中的参数进行了敏感性分析.最后,在模型的基础上考虑流脑发病的季节因素对模型加以改进,预测分析了我国流脑的发病情况,数值模拟的结果显示季节因素对疾病进展率的影响程度大于对疾病传染率的影响,为控制流脑在我国的流行传播提供建议. 相似文献
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In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model. 相似文献
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This study proposes a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection‐free equilibrium point and an endemic infection equilibrium point. Using Lyapunov functions and LaSalle’s invariance principle shows that if the model’s basic reproductive number R 0 < 1, the infection‐free equilibrium point is globally asymptotically stable, otherwise the endemic infection equilibrium point is globally asymptotically stable. It is shown that a forward bifurcation will occur when R 0 = 1. The basic reproductive number R 0 of the modified model is independent of plasma total CD4+ T cell counts and thus the modified model is more reasonable than the original model proposed by Buonomo and Vargas‐De‐León. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of two group patients’ anti‐HIV infection treatments. The simulation results have shown that the first 4 weeks’ treatments made the two group patients’ R′ 0 < 1, respectively. After the period, drug resistance made the two group patients’ R′ 0 > 1. The results explain why the two group patients’ mean CD4+ T cell counts raised and mean HIV RNA levels declined in the first period, but contrary in the following weeks.Inspec keywords: microorganisms, cellular biophysics, differential equations, Lyapunov methods, blood, drugs, patient treatment, RNAOther keywords: global stability, infection‐free state, endemic infection state, modified human immunodeficiency virus infection model, HIV, differential equation model, saturated infection rate, infection‐free equilibrium point, endemic infection equilibrium point, Lyapunov functions, LaSalle invariance principle, forward bifurcation, plasma total CD4+ T cell counts, HIV drug resistance database, mean HIV RNA levels 相似文献