School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China.
Virus Res. 2020 Feb;277:197841. doi: 10.1016/j.virusres.2019.197841. Epub 2019 Dec 27.
In this paper, a fractional-order delayed model with Holling II functional response and CTL immune response is constructed to describe the transmission of hepatitis B virus. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of three equilibriums are obtained. Thirdly, the stability of three equilibriums are investigated. In addition, some sufficient conditions for the occurrence of Hopf bifurcation near the endemic equilibrium are demonstrated by using time delay as the bifurcation parameter. After that, some numerical simulations are performed to verify the theoretical prediction. At last, a brief discussion is presented to end this paper.
本文构建了一个具有 Holling II 功能反应和 CTL 免疫反应的分数阶时滞模型，用以描述乙型肝炎病毒的传播。首先，证明了正解的存在唯一性。其次，得到了基本再生数和三个平衡点存在的充分条件。再次，研究了三个平衡点的稳定性。此外，通过时滞作为分岔参数，证明了地方病平衡点附近发生 Hopf 分岔的一些充分条件。之后，进行了一些数值模拟来验证理论预测。最后，对本文进行了简要讨论。
