Xie Xinqi, Ma Junling, van den Driessche P
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada.
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada.
Math Biosci. 2021 May;335:108569. doi: 10.1016/j.mbs.2021.108569. Epub 2021 Feb 24.
The activation and proliferation of naive CD4 T cells produce helper T cells, and increase the susceptible population in the presence of HIV. This may cause backward bifurcation. To verify this, we construct a simple within-host HIV model that includes the key variables, namely healthy naive CD4 T cells, helper T cells, infected CD4 T cells and virus. When the viral basic reproduction number R is less than unity, we show theoretically and numerically that bistability for R<R<1 can be caused by a backward bifurcation due to a new susceptible population produced by activation of healthy naive CD4 T cells that become helper T cells. An extended model including the CTL dynamics may also show this backward bifurcation. In the case that the homeostatic source of healthy naive CD4 T cells is large, R is approximately the threshold for HIV to persist independent of initial conditions. The backward bifurcation may still occur even when we consider latent infections of naive CD4 T cells. Thus to control the spread of within-host HIV, it may be necessary for treatment to reduce the reproduction number below R.
初始CD4 T细胞的激活和增殖会产生辅助性T细胞，并在有HIV存在的情况下增加易感人群。这可能会导致反向分岔。为了验证这一点，我们构建了一个简单的宿主体内HIV模型，该模型包含关键变量，即健康初始CD4 T细胞、辅助性T细胞、受感染的CD4 T细胞和病毒。当病毒基本繁殖数R小于1时，我们从理论和数值上表明，对于R<R<1，双稳性可能由反向分岔引起，这是由于健康初始CD4 T细胞激活后产生的新易感人群变成了辅助性T细胞。一个包含CTL动态的扩展模型也可能显示这种反向分岔。在健康初始CD4 T细胞的稳态来源很大的情况下，R大约是HIV持续存在与初始条件无关的阈值。即使我们考虑初始CD4 T细胞的潜伏感染，反向分岔仍可能发生。因此，为了控制宿主体内HIV的传播，治疗可能有必要将繁殖数降低到R以下。
