There are many challenges to constitute the linkage from the macroscale to the microscale and analyze the multiscale model. We proposed a bidirectional coupling model with standard incidence which includes the interaction of between-host transmission dynamics and within-host viral dynamics, and investigated the dynamic behaviors of the multiscale system on two time-scales. We found that the multiscale system exhibits more complex dynamics including backward bifurcation, which means that the usual thresholds for infection control or virus elimination obtained from the epidemiological model or virus dynamic model may not act as threshold parameter under a certain condition. There may be multiple epidemic equilibriums, one of which is stable, although the basic reproduction number is less than 1. We numerically examine the synergistic impact between the macro and micro dynamics. In particular, increasing the drug efficacy can decrease the prevalence of disease. The contact rate may affect the number and size of equilibria of viral dynamics model by inducing the occurrence of backward bifurcation. The finding suggests that the effective control measures may include both the reduction in contact rate or transmission rate at the population level and the increase in drug efficacy at the individual level, and using these control measures together can effectively control the diseases.

中文翻译：

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宿主内病毒动力学与宿主间传播动力学耦合的多尺度HIV-1模型分析

构成从宏观到微观的联系并分析多尺度模型存在许多挑战。我们提出了一种具有标准发病率的双向耦合模型，该模型包括宿主之间传播动力学和宿主内病毒动力学之间的相互作用，并研究了两个时间尺度上多尺度系统的动力学行为。我们发现多尺度系统表现出更复杂的动力学，包括向后分叉，这意味着从流行病学模型或病毒动力学模型获得的通常用于控制感染或消除病毒的阈值在特定条件下可能不会充当阈值参数。可能存在多种流行病平衡，尽管基本繁殖数小于1，但其中一个是稳定的。我们从数值上检查了宏观和微观动力学之间的协同影响。特别地，增加药物功效可以降低疾病的患病率。接触速率可能通过诱导反向分叉的发生而影响病毒动力学模型平衡的数量和大小。该发现表明，有效的控制措施可能既包括降低人群水平的接触率或传播率，又包括提高个人水平的药物疗效，并且一起使用这些控制措施可以有效地控制疾病。