Xue Yuyi, Xiao Yanni
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China.
Math Biosci Eng. 2020 Sep 30;17(6):6720-6736. doi: 10.3934/mbe.2020350.
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.
构建从宏观尺度到微观尺度的联系并分析多尺度模型存在诸多挑战。我们提出了一个具有标准发病率的双向耦合模型，该模型包括宿主间传播动力学和宿主体内病毒动力学之间的相互作用，并研究了多尺度系统在两个时间尺度上的动态行为。我们发现多尺度系统表现出更复杂的动力学，包括反向分岔，这意味着从流行病学模型或病毒动力学模型中获得的通常的感染控制或病毒消除阈值在一定条件下可能不作为阈值参数。可能存在多个流行平衡点，其中一个是稳定的，尽管基本再生数小于1。我们通过数值研究了宏观和微观动力学之间的协同影响。特别是，提高药物疗效可以降低疾病的流行率。接触率可能通过诱导反向分岔的发生来影响病毒动力学模型平衡点的数量和大小。这一发现表明，有效的控制措施可能包括在人群层面降低接触率或传播率以及在个体层面提高药物疗效，并且同时使用这些控制措施可以有效地控制疾病。
