Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay in the eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system and provide bifurcation diagrams illustrating transcritical (backward and forward), saddle-node, and Hopf bifurcations, and provide evidence of homoclinic bifurcations and a Bogdanov–Takens bifurcation. We investigate the possibility of long term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of robust uniform persistence. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether or not the virus survives.

持续感染的病毒会在受感染的细胞内停留很长时间而不杀死细胞，并且可以通过出芽的病毒颗粒繁殖或在分裂后传递给子细胞。在诸如 HIV 潜伏储存库、肿瘤溶瘤病毒疗法和微生物宿主中的无毒噬菌体等例子中，受感染细胞群能够长寿并通过细胞分裂复制病毒后代的能力可能对病毒的存活至关重要。我们考虑了在受感染细胞复制形式之前的日蚀阶段具有时间延迟的复制细胞群中持续病毒感染的模型。我们获得了再生数，这些数为系统平衡的存在性和稳定性提供了标准，并提供了说明跨临界（向后和向前）、鞍形节点和 Hopf分岔，并提供同宿分岔和Bogdanov-Takens 分岔的证据。我们通过使用稳健一致持久性的数学概念来研究细胞群中感染（由慢性感染细胞和游离病毒表示）长期存活的可能性。使用具有从噬菌体-微生物系统估计的参数值的数值延续软件，我们获得了两个参数分叉图，将参数空间划分为具有不同动力学结果的区域。因此，我们研究了不同的参数（包括在日食阶段花费的时间）如何影响病毒是否存活。