Mathematics Department, University of Louisiana at Lafayette, Lafayette, LA, USA.
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada.
J Math Biol. 2021 May 15;82(7):59. doi: 10.1007/s00285-021-01612-3.
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.
持续感染的病毒在不杀死细胞的情况下，在感染细胞内长时间存在并能通过出芽病毒颗粒或在分裂后传递给子细胞进行复制。受感染细胞群体的长寿能力和通过细胞分裂复制病毒后代的能力，对于 HIV 潜伏库、肿瘤溶瘤病毒治疗和微生物宿主中非毒性噬菌体等例子中的病毒存活可能至关重要。我们考虑了在感染细胞复制形式之前的潜伏期存在时间延迟的复制细胞群体中持续病毒感染的模型。我们获得了繁殖数，这些繁殖数为系统平衡点的存在和稳定性提供了标准，并提供了说明跨临界（向后和向前）、鞍结和 Hopf 分岔的分岔图，并提供了同宿分岔和 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，研究了感染（由慢性感染细胞和游离病毒表示）在细胞群体中长期存活的可能性。使用从噬菌体-微生物系统估计的参数值的数值连续软件，我们获得了两个参数分岔图，将参数空间划分为具有不同动力学结果的区域。因此，我们研究了如何改变不同的参数，包括在潜伏期内花费的时间，如何影响病毒是否存活。
