Dynamics of virus infection models with density-dependent diffusion
Dynamics of virus infection models with density-dependent diffusion
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具有密度依赖性扩散的病毒感染模型的动力学
DOI：
10.1016/j.camwa.2017.07.019
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发表时间：
2017
影响因子：
2.9
通讯作者：
Song Xinyu
中科院分区：
文献类型：
--
作者：
Wang Shaoli;Zhang Jiafang;Xu Fei;Song Xinyu
密度依赖性扩散在病毒感染过程中起着重要作用。在本文中，我们构建了数学模型来研究病毒的动力学及其控制。这项工作同时考虑了单株和多株病毒感染。使用Pao和Ruan（2013）提出的方法，我们证明了模型的适定性。通过构造适当的Lyapunov函数，我们证明了模型的全局渐近稳定性。对于多毒株模型，我们表明，当每个毒株的基本繁殖数大于 1 时，所有病毒株共存。由于不同治疗方法的效果可能会导致竞争性排斥，因此必须采用联合治疗的方法。我们惊讶地发现，病毒的密度依赖性扩散不会影响具有均匀诺依曼边界条件的模型的全局稳定性。
Density-dependent diffusion plays an important role in the process of viral infection. In this paper, we construct mathematical models to investigate the dynamics of the viruses and their control. Single strain and multi-strain viral infections are both considered in this work. Using the method proposed by Pao and Ruan (2013), we prove the well-posedness of the models. By constructing appropriate Lyapunov functions, we proved the global asymptotical stabilities of the models. For the multi-strain model, we show that when the basic reproduction number for each strain is greater than one, all viral strains coexist. Since the effect of different treatments may result in competitive exclusion, it is essential to employ the treatment with combined therapy. We find with surprise that the density-dependent diffusion of the virus does not influence the global stabilities of the model with homogeneous Neumann boundary conditions.