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 ${\mathcal{R}}_0$ is less than unity, we show theoretically and numerically that bistability for ${\mathcal{R}}_C<{\mathcal{R}}_0<1$ 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, ${\mathcal{R}}_C$ 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 ${\mathcal{R}}_C$.

幼稚 CD4 T 细胞的激活和增殖产生辅助 T 细胞，并在 HIV 存在时增加易感人群。这可能会导致向后分叉。为了验证这一点，我们构建了一个简单的宿主内 HIV 模型，其中包括关键变量，即健康的幼稚 CD4 T 细胞、辅助 T 细胞、受感染的 CD4 T 细胞和病毒。当病毒基本繁殖数${\mathcal{电阻}}_0$ 小于统一，我们在理论上和数值上证明了双稳态 ${\mathcal{电阻}}_C<{\mathcal{电阻}}_0<1$可能是由于健康幼稚 CD4 T 细胞激活成为辅助 T 细胞而产生的新易感群体导致的向后分叉造成的。包括 CTL 动力学的扩展模型也可能显示这种向后分叉。在健康幼稚 CD4 T 细胞的稳态来源很大的情况下，${\mathcal{电阻}}_C$大约是 HIV 独立于初始条件而持续存在的阈值。即使我们考虑到幼稚 CD4 T 细胞的潜在感染，后向分叉仍然可能发生。因此，为了控制宿主内 HIV 的传播，可能有必要进行治疗以减少以下繁殖数${\mathcal{电阻}}_C$.