具有细胞间传播和治愈率的病毒动力学模型的全局动力学
Global Dynamics of a Virus Dynamical Model with Cell-to-Cell Transmission and Cure Rate.
作者信息
Zhang Tongqian, Meng Xinzhu, Zhang Tonghua
机构信息
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China ; State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China.
Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, Australia.
出版信息
Comput Math Methods Med. 2015;2015:758362. doi: 10.1155/2015/758362. Epub 2015 Oct 1.
The cure effect of a virus model with both cell-to-cell transmission and cell-to-virus transmission is studied. By the method of next generation matrix, the basic reproduction number is obtained. The locally asymptotic stability of the virus-free equilibrium and the endemic equilibrium is considered by investigating the characteristic equation of the model. The globally asymptotic stability of the virus-free equilibrium is proved by constructing suitable Lyapunov function, and the sufficient condition for the globally asymptotic stability of the endemic equilibrium is obtained by constructing suitable Lyapunov function and using LaSalle invariance principal.
研究了具有细胞间传播和细胞与病毒间传播的病毒模型的治疗效果。通过下一代矩阵方法，得到了基本再生数。通过研究模型的特征方程，考虑了无病毒平衡点和地方病平衡点的局部渐近稳定性。通过构造合适的李雅普诺夫函数证明了无病毒平衡点的全局渐近稳定性，并通过构造合适的李雅普诺夫函数和使用拉萨尔不变性原理得到了地方病平衡点全局渐近稳定性的充分条件。
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