It is well known that, during replication, RNA viruses spontaneously generate defective viral genomes (DVGs). DVGs are unable to complete an infectious cycle autonomously and depend on coinfection with a wild-type helper virus (HV) for their replication and/or transmission. The study of the dynamics arising from a HV and its DVGs has been a longstanding question in virology. It has been shown that DVGs can modulate HV replication and, depending on the strength of interference, result in HV extinctions or self-sustained persistent fluctuations. Extensive experimental work has provided mechanistic explanations for DVG generation and compelling evidences of HV-DVGs virus coevolution. Some of these observations have been captured by mathematical models. Here, we develop and investigate an epidemiological-like mathematical model specifically designed to study the dynamics of betacoronavirus in cell culture experiments. The dynamics of the model is governed by several degenerate normally hyperbolic invariant manifolds given by quasineutral planes - i.e., filled by equilibrium points. Three different quasineutral planes have been identified depending on parameters and involving: (i) persistence of HV and DVGs; (ii) persistence of non-infected cells and DVG-infected cells; and (iii) persistence of DVG-infected cells and DVGs. Key parameters involved in these scenarios are the maximum burst size (B), the fraction of DVGs produced during HV replication (β), and the replication advantage of DVGs (δ). More precisely, in the case 0<B<1+β the system displays tristability, where all three scenarios are present. In the case 1+β<B<1+β+δ this tristability persists but attracting scenario (ii) is reduced to a well-defined half-plane. For B>1+β+δ, the scenario (i) becomes globally attractor. Scenarios (ii) and (iii) are compatible with the so-called self-curing since the HV is removed from the population. Sensitivity analyses indicate that model dynamics largely depend on DVGs production rate (β) and their replicative advantage (δ), and on both the infection rates and virus-induced cell deaths. Finally, the model has been fitted to single-passage experimental data using an artificial intelligence methodology based on genetic algorithms and key virological parameters have been estimated.

中文翻译：

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细胞培养物中缺陷辅助性 β 冠状病毒感染的流行病学样模型中的准中性多稳定性


众所周知，在复制过程中，RNA 病毒会自发产生有缺陷的病毒基因组 （DVG）。DVG 无法自主完成感染周期，并依赖于与野生型辅助病毒 （HV） 的共同感染进行复制和/或传播。研究 HV 及其 DVG 产生的动力学一直是病毒学中一个长期存在的问题。已经表明，DVG 可以调节 HV 复制，并且根据干扰的强度，导致 HV 消退或自我持续的持续波动。广泛的实验工作为 DVG 的产生提供了机制解释和 HV-DVGs 病毒协同进化的令人信服的证据。其中一些观察结果已被数学模型捕获。在这里，我们开发和研究了一种类似流行病学的数学模型，专门用于研究细胞培养实验中 β 冠状病毒的动力学。该模型的动力学由准中性平面给出的几个简并常曲不变流形控制 - 即，由平衡点填充。根据参数和涉及：（i） HV 和 DVG 的持久性;（ii） 未感染细胞和 DVG 感染细胞的持久性;（iii） DVG 感染的细胞和 DVG 的持久性。这些场景涉及的关键参数是最大突发大小 （B）、HV 复制过程中产生的 DVG 分数 （β） 以及 DVG 的复制优势 （δ）。更准确地说，在 0<B<1+ 的情况下β系统显示三稳态，其中所有三种情况都存在。在 1+β<B<1+β+δ 的情况下，这种三稳态仍然存在，但吸引情景 （ii） 被简化为一个明确定义的半平面。 对于 B>1+β+δ，情景 （i） 变为全局吸引子。情景 （ii） 和 （iii） 与所谓的自固化兼容，因为 HV 已从种群中去除。敏感性分析表明，模型动力学在很大程度上取决于 DVGs 产生率 （β） 及其复制优势 （δ），以及感染率和病毒诱导的细胞死亡。最后，使用基于遗传算法的人工智能方法将模型拟合到单代实验数据中，并估计了关键病毒学参数。