标题： 一种嵌套多尺度模型用于 COVID-19 病毒感染 显示英文标题

标题： A Nested Multi-Scale Model for COVID-19 Viral Infection

摘要： 在本研究中，我们开发并分析了一个整合宿主体内尺度和宿主间尺度子模型的嵌套多尺度模型，用于冠状病毒-19疾病。首先讨论了多尺度模型的适定性，随后进行了平衡点的稳定性分析。当$R_0 < 1$超过1时，无病平衡点被证明是全局渐近稳定的。当$R_0$超过1时，存在一个唯一的感染平衡点，系统在$R_0=1$处发生前向（跨临界）分岔。还进行了两个参数热图以找到使平衡点稳定的参数组合。发现参数$\beta, \pi$和$\Lambda$对$R_0$最为敏感。宿主体内子模型参数对宿主间子模型变量的影响被数值地说明。 感染在社区中的传播被证明受到宿主内子模型参数的影响，例如被感染细胞产生的病毒颗粒数量$(\alpha)$，免疫系统清除被感染细胞的速率$(x)$，以及免疫系统清除病毒颗粒的速率$(y)$。 三种健康干预措施（抗病毒药物、免疫调节剂和普遍的社会隔离）对COVID-19感染的比较效果是通过有效繁殖数$R_E$作为干预措施效果的指标来研究的。 结果表明，抗病毒药物、免疫调节剂和普遍社会隔离的综合策略将是实施的最佳策略，以控制社区中的感染传播。 显示英文摘要

摘要： In this study, we develop and analyze a nested multi-scale model for COVID -19 disease that integrates within-host scale and between-host scale sub-models. First, the well-posedness of the multi-scale model is discussed, followed by the stability analysis of the equilibrium points. The disease-free equilibrium point is shown to be globally asymptotically stable for $R_0 < 1$. When $R_0$ exceeds unity, a unique infected equilibrium exists, and the system is found to undergo a forward (trans-critical) bifurcation at $R_0=1$. Two parameter heat plots are also done to find the parameter combinations for which the equilibrium points are stable. The parameters $\beta, \pi$ and $\Lambda$ are found to be most sensitive to $R_0$. The influence of within-host sub-model parameter on the between-host sub-model variables is numerically illustrated. The spread of infection in a community is shown to be influenced by within-host level sub-model parameters, such as the production of viral particles by infected cells $(\alpha)$, the clearance rate of infected cells by the immune system $(x)$, and the clearance rate of viral particles by the immune system $(y)$. The comparative effectiveness of the three health interventions (antiviral drugs, immunomodulators, and generalized social distancing) for COVID-19 infection was examined using the effective reproductive number $R_E$ as an indicator of the effectiveness of the interventions. The results suggest that a combined strategy of antiviral drugs, immunomodulators and generalized social distancing would be the best strategy to implement to contain the spread of infection in the community.