具有Hattaf-Yousfi功能反应的丙型肝炎病毒时空细胞传播模型的全局分析
Global analysis of a spatiotemporal cellular model for the transmission of hepatitis C virus with Hattaf-Yousfi functional response
摘要：
本文对一个偏微分方程病毒感染细胞模型的全局动力学进行了数学分析。我们研究了丙型肝炎病毒（HCV）模型的动力学，在治疗下，考虑了吸收现象和扩散的病毒粒子，感染和未感染的细胞在肝脏中。首先，我们证明了所得到的初值和边值问题的势解的有界性、整体解的存在唯一性和正性。然后，该模型的动力学行为完全由一个门限参数称为基本再生数$\mathcal{R}_{0}$。利用直接李雅普诺夫方法证明了当$\mathcal{R}_{0} \leq 1 $满足时，该模型的未感染空间齐次平衡点是全局渐近稳定的。这意味着HCV被清除，疾病消失。通过构造适当的李雅普诺夫泛函，研究了该模型空间齐次平衡点的全局渐近稳定性。这意味着HCV在宿主体内持续存在，感染成为慢性。最后，进行了数值模拟，以支持所获得的理论结果。
英文摘要：
In this paper, a mathematical analysis of the global dynamics of a partial differential equation viral infection cellular model is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both absorption phenomenon and diffusion of virions, infected and uninfected cells in liver. Firstly, we prove boundedness of the potential solutions, global existence, uniqueness and positivity of the solutions to the obtained initial value and boundary problem. Then, the dynamical behavior of the model is completely determined by a threshold parameter called the basic reproduction number $\mathcal{R}_{0}$. We show that the uninfected spatially homogeneous equilibrium of the model is globally asymptotically stable if $\mathcal{R}_{0} \leq 1 $ by using the direct Lyapunov method. This means that the HCV is cleared and the disease dies out. Also, the global asymptotically properties stability of the infected spatially homogeneous equilibrium of the model are studied via a skilful construction of a suitable Lyapunov functional. It means that the HCV persists in the host and the infection becomes chronic. Finally, numerical simulations are performed to support the theoretical results obtained.
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