Li Michael Y, Shu Hongying
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China.
J Math Biol. 2012 May;64(6):1005-20. doi: 10.1007/s00285-011-0436-2. Epub 2011 Jun 14.
To understand joint effects of logistic growth in target cells and intracellular delay on viral dynamics in vivo, we carry out two-parameter bifurcation analysis of an in-host model that describes infections of many viruses including HIV-I, HBV and HTLV-I. The bifurcation parameters are the mitosis rate r of the target cells and an intracellular delay τ in the incidence of viral infection. We describe the stability region of the chronic-infection equilibrium E* in the two-dimensional (r, τ) parameter space, as well as the global Hopf bifurcation curves as each of τ and r varies. Our analysis shows that, while both τ and r can destabilize E* and cause Hopf bifurcations, they do behave differently. The intracellular delay τ can cause Hopf bifurcations only when r is positive and sufficiently large, while r can cause Hopf bifurcations even when τ = 0. Intracellular delay τ can cause stability switches in E* while r does not.
为了理解靶细胞中逻辑斯蒂增长和细胞内延迟对体内病毒动力学的联合影响，我们对一个宿主内模型进行了双参数分岔分析，该模型描述了包括HIV-I、HBV和HTLV-I在内的多种病毒的感染情况。分岔参数是靶细胞的有丝分裂率r和病毒感染发生率中的细胞内延迟τ。我们描述了二维（r，τ）参数空间中慢性感染平衡点E的稳定区域，以及随着τ和r各自变化的全局霍普夫分岔曲线。我们的分析表明，虽然τ和r都可以使E不稳定并导致霍普夫分岔，但它们的表现有所不同。细胞内延迟τ只有在r为正且足够大时才会导致霍普夫分岔，而r即使在τ = 0时也会导致霍普夫分岔。细胞内延迟τ可以导致E*中的稳定性切换，而r则不会。
