Cai Liming, Li Zhaoqing, Yang Chayu, Wang Jin
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P.R. China.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA.
Appl Math Model. 2020 Oct;86:404-423. doi: 10.1016/j.apm.2020.05.022. Epub 2020 Jun 2.
In this paper, a multi-scale mathematical model for environmentally transmitted diseases is proposed which couples the pathogen-immune interaction inside the human body with the disease transmission at the population level. The model is based on the nested approach that incorporates the infection-age-structured immunological dynamics into an epidemiological system structured by the chronological time, the infection age and the vaccination age. We conduct detailed analysis for both the within-host and between-host disease dynamics. Particularly, we derive the basic reproduction number for the between-host model and prove the uniform persistence of the system. Furthermore, using carefully constructed Lyapunov functions, we establish threshold-type results regarding the global dynamics of the between-host system: the disease-free equilibrium is globally asymptotically stable when 1, and the endemic equilibrium is globally asymptotically stable when 1. We explore the connection between the within-host and between-host dynamics through both mathematical analysis and numerical simulation. We show that the pathogen load and immune strength at the individual level contribute to the disease transmission and spread at the population level. We also find that, although the between-host transmission risk correlates positively with the within-host pathogen load, there is no simple monotonic relationship between the disease prevalence and the individual pathogen load.
本文提出了一种针对环境传播疾病的多尺度数学模型，该模型将人体内病原体 - 免疫相互作用与人群层面的疾病传播相结合。该模型基于嵌套方法，将感染年龄结构的免疫动力学纳入由时间、感染年龄和接种年龄构成的流行病学系统。我们对宿主内和宿主间的疾病动态进行了详细分析。特别地，我们推导了宿主间模型的基本再生数，并证明了系统的一致持久性。此外，通过精心构造李雅普诺夫函数，我们建立了关于宿主间系统全局动态的阈值型结果：当(\mathcal{R}_0 < 1)时，无病平衡点全局渐近稳定；当(\mathcal{R}_0 > 1)时，地方病平衡点全局渐近稳定。我们通过数学分析和数值模拟探索了宿主内和宿主间动态之间的联系。我们表明，个体层面的病原体载量和免疫强度有助于疾病在人群层面的传播和扩散。我们还发现，尽管宿主间传播风险与宿主内病原体载量呈正相关，但疾病流行率与个体病原体载量之间不存在简单的单调关系。
