Xu Jinhu, Zhou Yicang
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China. email:
Math Biosci Eng. 2016 Apr 1;13(2):343-67. doi: 10.3934/mbe.2015006.
A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory. Numerical simulations are done to explore the rich dynamics, including stability switches, Hopf bifurcations, and chaotic oscillations.
研究了一个具有病毒到细胞和细胞到细胞传播以及免疫反应时间延迟的宿主体内病毒感染模型。数学分析表明，延迟可能会使受感染的稳态不稳定并导致霍普夫分岔。此外，通过范式和中心流形理论研究了霍普夫分岔的方向和周期解的稳定性。进行了数值模拟以探索丰富的动力学，包括稳定性切换、霍普夫分岔和混沌振荡。
