Asymptotic behaviour of the solutions to a virus dynamics model with diffusion
Asymptotic behaviour of the solutions to a virus dynamics model with diffusion
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DOI：
10.3934/dcdsb.2017206
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发表时间：
2017-12
影响因子：
1.2
通讯作者：
Toru Sasaki;Takashi Suzuki
中科院分区：
文献类型：
--
作者：
Toru Sasaki;Takashi Suzuki
讨论了一类基本病毒动力学模型解的渐近性态。我们考虑未感染细胞、感染细胞和病毒颗粒的群体。扩散效应被纳入其中。首先，对空间齐次部分（无扩散的ODE模型）有效的李雅普诺夫函数允许轨道的\开始{document} L^1\end {document}有界性。然后利用半群估计得到了该轨道在连续函数空间中的预紧性。因此，根据不变原理，如果基本再生数\开始{document}$R_0$\end{document}小于或等于1，则每个轨道收敛到无病空间齐次平衡点，并且如果\开始{document}$R_0> 1 $\end {document}，则每个轨道收敛到有病空间齐次平衡点，这意味着简单扩散不影响解的渐近行为。
Asymptotic behaviour of the solutions to a basic virus dynamics model is discussed. We consider the population of uninfected cells, infected cells, and virus particles. Diffusion effect is incorporated there. First, the Lyapunov function effective to the spatially homogeneous part (ODE model without diffusion) admits the \begin{document}$L^1$\end{document} boundedness of the orbit. Then the pre-compactness of this orbit in the space of continuous functions is derived by the semigroup estimates. Consequently, from the invariant principle, if the basic reproductive number \begin{document}$R_0$\end{document} is less than or equal to 1, each orbit converges to the disease free spatially homogeneous equilibrium, and if \begin{document}$R_0>1$\end{document} , each orbit converges to the infected spatially homogeneous equilibrium, which means that the simple diffusion does not affect the asymptotic behaviour of the solutions.