The present study develops and analyses a system of partial differential equations that model a single population of dividing cells infected by lytic viruses in a closed system. This mean-field model stratifies cells by cell size (continuous) and number of virus particles per cell (discrete) to couple the cell cycle and the lytic cycle under mass conservation. We present numerical solutions to the mean-field model and an equivalent stochastic model for parameter values representative of Escherichia Coli and lytic bacteriophages such as Escherichia virus T4. This analysis suggests that dividing cells and lytic virus populations in isolation can coexist in the absence of evolutionary, ecological and biochemical processes. Coexistence emerges because viral load dilution via cell growth and viral load partitioning via cell division both counteract viral load growth via viral synthesis and hence cell death by lysis. Furthermore, we analytically determine the quasi-steady state solution of the mean-field model in the continuum limit with respect to viral loads. From this solution we derive a condition for cell-virus coexistence through viral load partitioning: that the product of the viral synthesis rate, cell lysis rate and the time between cell divisions must be less than the product of log(2) and the cell growth rate. Overall, the present study provides a theoretical argument for a stable relationship between cells and lytic viruses simply by virtue of cell growth and division.

中文翻译：

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分裂细胞的病毒结构模型通过细胞后代之间的病毒负荷分配显示细胞病毒共存

本研究开发和分析了偏微分方程组的系统，该系统对在封闭系统中被裂解病毒感染的单个分裂细胞进行建模。该平均场模型按细胞大小（连续）和每个细胞的病毒颗粒数量（离散）对细胞进行分层，以在质量守恒下耦合细胞周期和裂解周期。我们提出了均值场模型和等效随机模型的数值解，这些模型代表了大肠杆菌的参数值和裂解性噬菌体，例如大肠杆菌T4病毒。该分析表明，在没有进化，生态和生化过程的情况下，分离细胞和裂解病毒种群可以共存。共存之所以出现是因为通过细胞生长进行的病毒载量稀释和通过细胞分裂进行的病毒载量分配均抵消了通过病毒合成产生的病毒载量增长，从而抵消了细胞因裂解而死亡的趋势。此外，我们分析地确定了在连续极限中相对于病毒载量的平均场模型的准稳态解。从该解决方案中，我们得出了通过病毒载量分配实现细胞-病毒共存的条件：病毒合成速率，细胞裂解速率和细胞分裂时间之间的乘积必须小于log（2）与细胞生长的乘积率。总体，