School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China.
Department of Mathematical Sciences, New Mexico State University, NM 88001, Las Cruces, USA.
Math Biosci Eng. 2020 Nov 19;18(1):92-111. doi: 10.3934/mbe.2021005.
Asymptomatic transmission of infectious diseases has been recognized recently in several epidemics or pandemics. There is a great need to incorporate asymptomatic transmissions into traditional modeling of infectious diseases and to study how asymptomatic transmissions shift epidemic dynamics. In this work, we propose a compartmental model with asymptomatic transmissions for waterborne infectious diseases. We conduct a detailed analysis and numerical study with shigellosis data. Two parameters, the proportion $p$ of asymptomatic infected individuals and the proportion $k$ of asymptomatic infectious individuals who can asymptomatically transmit diseases, play major rules in the epidemic dynamics. The basic reproduction number $\mathscr{R}{0}$ is a decreasing function of parameter $p$ when parameter $k$ is smaller than a critical value while $\mathscr{R}{0}$ is an increasing function of $p$ when $k$ is greater than the critical value. $\mathscr{R}{0}$ is an increasing function of $k$ for any value of $p$. When $\mathscr{R}{0}$ passes through 1 as $p$ or $k$ varies, the dynamics of epidemics is shifted. If asymptomatic transmissions are not counted, $\mathscr{R}_{0}$ will be underestimated while the final size may be overestimated or underestimated. Our study provides a theoretical example for investigating other asymptomatic transmissions and useful information for public health measurements in waterborne infectious diseases.
最近，在几次传染病疫情或大流行中，人们已经认识到了传染病的无症状传播。因此，非常有必要将无症状传播纳入传染病的传统建模中，并研究无症状传播如何改变传染病的动态。在这项工作中，我们提出了一个带有无症状传播的水传播传染病的房室模型。我们利用志贺氏菌病的数据进行了详细的分析和数值研究。两个参数，无症状感染者的比例 $p$ 和无症状传染性个体的比例 $k$ ，在传染病动态中起着重要作用。当参数 $k$ 小于一个临界值时，基本再生数 $\mathscr{R}{0}$ 是参数 $p$ 的递减函数，而当 $k$ 大于临界值时，$\mathscr{R}{0}$ 是参数 $p$ 的递增函数。对于任何值的 $p$ ，$\mathscr{R}{0}$ 都是参数 $k$ 的递增函数。当 $\mathscr{R}{0}$ 随着 $p$ 或 $k$ 的变化而通过 1 时，传染病的动态就会发生变化。如果不计算无症状传播，$\mathscr{R}_{0}$ 将被低估，而最终规模可能被高估或低估。我们的研究为研究其他无症状传播提供了一个理论范例，并为水传播传染病的公共卫生措施提供了有用的信息。
