治疗下具有细胞间传播和吸收效应的广义病毒感染时间模型的全局分析

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2022-05-15 DOI:10.5206/mase/14663
Alexis Nangue, Paulin Tiomo Lemofouet, Simon Ndouvatama, Kengne Emmanuel
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引用次数: 1

摘要

在病毒动力学中,当一个细胞被感染时,细胞外的病毒粒子数量减少一个:这种现象被称为吸收效应。大多数体内数学模型都忽略了这一现象。病毒-细胞感染和直接细胞-细胞传播是病毒繁殖和传播的两种基本方式。在这项工作中,我们提出了一个新的病毒动力学模型,它结合了这两种模式,并考虑了吸收效应和治疗。首先,我们从数学和生物学上证明了模型的适定性,然后给出了解的存在性和唯一性。并给出了模型基本再现数R0的显式公式。通过对特征方程的分析,建立了以R0表示的未感染平衡点和感染平衡点的局部稳定性。通过构造一个适当的Lyapunov泛函来研究模型的全局行为,并应用几何方法来研究感染平衡。通过数值模拟验证了所得到的理论结果。
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Global Analysis of a generalized viral infection temporal model with cell-to-cell transmission and absorption effect under therapy
In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in vivo models neglect this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted.  In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case.
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来源期刊
CiteScore
1.40
自引率
0.00%
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0
审稿时长
21 weeks
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