Mathematical Biosciences and Engineering
2021, Volume 18, Issue 1: 92-111.	doi: 10.3934/mbe.2021005
Asymptomatic transmission shifts epidemic dynamics
Jinlong Lv 1 ,
Songbai Guo 1 ,
Jing-An Cui 1 , , ,
Jianjun Paul Tian 2 , ,
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
Received: 12 August 2020 Accepted: 20 October 2020 Published: 19 November 2020
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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.
asymptomatic transmission,
basic reproduction number,
final size
Citation: Jinlong Lv, Songbai Guo, Jing-An Cui, Jianjun Paul Tian. Asymptomatic transmission shifts epidemic dynamics[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 92-111. doi: 10.3934/mbe.2021005
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© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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Jinlong Lv
Songbai Guo
Jing-An Cui
Jianjun Paul Tian
Jinlong Lv, Songbai Guo, Jing-An Cui, Jianjun Paul Tian. Asymptomatic transmission shifts epidemic dynamics[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 92-111. doi: 10.3934/mbe.2021005
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Figure 1. Flow chart of mathematical model
Figure 2. Basic reproduction number
Figure 6. Cumulative infections
Figure 8. Asymptomatic infections
Figure 10. Basic reproduction number
Figure 14. Cumulative infections
Figure 16. Asymptomatic infections