具有非线性发生率和CTL免疫应答的病毒感染模型离散时间模拟的全局动力学。

IF 4.1 3区数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2016-01-01 Epub Date: 2016-05-23 DOI:10.1186/s13662-016-0862-y

Jianpeng Wang, Zhidong Teng, Hui Miao

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引用次数: 31

摘要

本文利用Micken非标准有限差分格式建立了具有非线性发生率和CTL免疫应答的病毒感染模型的离散时间模拟。定义了两个基本复制数r0和r1。建立了解的正有界性和无病毒平衡点、无免疫平衡点和感染平衡点存在性的基本性质。利用Lyapunov函数和线性化方法，建立了模型平衡点的全局稳定性。即当r0≤1时，无病毒平衡是全局渐近稳定的;在附加假设(4a)下，当r0 > 1且r1≤1时，无免疫平衡是全局渐近稳定的;当r0 > 1且r1 > 1时，感染平衡是全局渐近稳定的。此外，数值模拟表明，即使假设(4a)不成立，无免疫均衡和感染均衡也可能是全局渐近稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response.

In this paper, a discrete-time analog of a viral infection model with nonlinear incidence and CTL immune response is established by using the Micken non-standard finite difference scheme. The two basic reproduction numbers $R_{0}$ and $R_{1}$ are defined. The basic properties on the positivity and boundedness of solutions and the existence of the virus-free, the no-immune, and the infected equilibria are established. By using the Lyapunov functions and linearization methods, the global stability of the equilibria for the model is established. That is, when $R_{0} \leq 1$ then the virus-free equilibrium is globally asymptotically stable, and under the additional assumption $(A_{4})$ when $R_{0} > 1$ and $R_{1} \leq 1$ then the no-immune equilibrium is globally asymptotically stable and when $R_{0} > 1$ and $R_{1} > 1$ then the infected equilibrium is globally asymptotically stable. Furthermore, the numerical simulations show that even if assumption $(A_{4})$ does not hold, the no-immune equilibrium and the infected equilibrium also may be globally asymptotically stable.

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来源期刊

Advances in Difference Equations 数学-数学

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0.00%

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审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.