Ratchford Conrad, Wang Jin
University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA.
Math Biosci Eng. 2019 Nov 7;17(2):948-974. doi: 10.3934/mbe.2020051.
We propose a multi-group, multi-scale mathematical model to investigate the betweenhost and within-host dynamics of cholera. At the between-host level, we divide the total population into a number of host groups with different characteristics representing spatial heterogeneity. Our model incorporates the dual transmission pathways that include both the environment-to-human and human-to-human transmission routes. At the within-host level, our model describes the interaction among the pathogenic bacteria, viruses, and host immune response. For each host group, we couple the between-host disease transmission and within-host pathogen dynamics at different time scales. Our study thus integrates multi-scale modeling and multi-group modeling into one single framework. We describe the general modeling framework and demonstrate it through two specific and biologically important cases. We conduct detailed analysis for each case and obtain threshold results regarding the multi-scale dynamics of cholera in a spatially heterogeneous environment. In particular, we find that the between-host reproduction number is shaped by the collection of the disease risk factors from all the individual host groups. Our findings highlight the importance of a whole-population approach for cholera prevention and intervention.
我们提出了一个多群体、多尺度数学模型，以研究霍乱在宿主间和宿主体内的动态变化。在宿主间层面，我们将总人口划分为若干具有不同特征的宿主群体，以体现空间异质性。我们的模型纳入了包括环境到人类以及人类到人类传播途径的双重传播路径。在宿主体内层面，我们的模型描述了病原菌、病毒和宿主免疫反应之间的相互作用。对于每个宿主群体，我们在不同时间尺度上耦合了宿主间疾病传播和宿主体内病原体动态变化。因此，我们的研究将多尺度建模和多群体建模整合到了一个单一框架中。我们描述了一般建模框架，并通过两个具体且具有生物学重要性的案例进行了演示。我们对每个案例进行了详细分析，并获得了关于霍乱在空间异质环境中多尺度动态变化的阈值结果。特别是，我们发现宿主间繁殖数是由所有个体宿主群体的疾病风险因素集合所塑造的。我们的研究结果凸显了采用全人群方法进行霍乱预防和干预的重要性。
