Asymptomatic transmission shifts epidemic dynamics

Jinlong Lv; Songbai Guo; Jing-An Cui; Jianjun Paul Tian; Jinlong Lv; Songbai Guo; Jing-An Cui; Jianjun Paul Tian

doi:10.3934/mbe.2021005

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 92-111. doi: 10.3934/mbe.2021005

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Research article

Asymptomatic transmission shifts epidemic dynamics

1.
School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
2.
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

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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Abstract

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.

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