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基于非 commensurate 分数阶非线性系统的HIV模型稳定性分析

Stability analysis of the hiv model through incommensurate fractional-order nonlinear system.

作者信息

DaŞbaŞi Bahatdin

机构信息

Kayseri University, Faculty of Applied Sciences, TR-38039, Kayseri, Turkey.

出版信息

Chaos Solitons Fractals. 2020 Aug;137:109870. doi: 10.1016/j.chaos.2020.109870. Epub 2020 May 11.

DOI:10.1016/j.chaos.2020.109870
PMID:32395039
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7211765/
Abstract

In this study, it is employed a new model of infection in the form of incommensurate fractional differential equations systems involving the Caputo fractional derivative. Existence of the model's equilibrium points has been investigated. According to some special cases of the derivative-orders in the proposed model, the asymptotic stability of the infection-free equilibrium and endemic equilibrium has been proved under certain conditions. These stability conditions related to the derivative-orders depend on not only the basic reproduction rate frequently emphasized in the literature but also the newly obtained conditions in this study. Qualitative analysis results were complemented by numerical simulations in Matlab, illustrating the obtained stability result.

摘要

在本研究中，采用了一种以包含卡普托分数阶导数的非 commensurate 分数阶微分方程组形式的新型感染模型。研究了该模型平衡点的存在性。根据所提出模型中导数阶数的一些特殊情况，在一定条件下证明了无感染平衡点和地方病平衡点的渐近稳定性。这些与导数阶数相关的稳定性条件不仅取决于文献中经常强调的基本繁殖率，还取决于本研究中新得到的条件。通过 Matlab 中的数值模拟对定性分析结果进行了补充，说明了所得到的稳定性结果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/777136c26c76/gr9_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/05d1b676a6f6/gr1_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/47ed15d95be8/gr2_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/721666402839/gr3_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/b5560fda0409/gr4_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/54d9e8b6855d/gr5_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/ab7dc98712fd/gr6_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/fb5ec86638d3/gr7_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/9e5d3bc5d6f2/gr8_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/777136c26c76/gr9_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/05d1b676a6f6/gr1_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/47ed15d95be8/gr2_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/721666402839/gr3_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/b5560fda0409/gr4_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/54d9e8b6855d/gr5_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/ab7dc98712fd/gr6_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/fb5ec86638d3/gr7_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/9e5d3bc5d6f2/gr8_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/17bd/7211765/777136c26c76/gr9_lrg.jpg

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8
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9
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