Isolation in the control of epidemic

Yong Zhou; Minrui Guo; Yong Zhou; Minrui Guo

doi:10.3934/mbe.2022507

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 10846-10863. doi: 10.3934/mbe.2022507

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Research article

Isolation in the control of epidemic

Yong Zhou ^{1
,
,},
Minrui Guo ²

1.
College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
2.
College of Energy Engineering, Huanghuai University, Zhumadian 463000, China

Received: 25 May 2022 Revised: 26 July 2022 Accepted: 27 July 2022 Published: 29 July 2022

Among many epidemic prevention measures, isolation is an important method to control the spread of infectious disease. Scholars rarely study the impact of isolation on disease dissemination from a quantitative perspective. In this paper, we introduce an isolation ratio and establish the corresponding model. The basic reproductive number and its biological explanation are given. The stability conditions of the disease-free and endemic equilibria are obtained by analyzing its distribution of characteristic values. It is shown that the isolation ratio has an important influence on the basic reproductive number and the stability conditions. Taking the COVID-19 in Wuhan as an example, isolating more than 68% of the population can control the spread of the epidemic. This method can provide precise epidemic prevention strategies for government departments. Numerical simulations verify the effectiveness of the results.
- epidemic,
- isolation ratio,
- basic reproductive number,
- stability of equilibrium
Citation: Yong Zhou, Minrui Guo. Isolation in the control of epidemic[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 10846-10863. doi: 10.3934/mbe.2022507

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Abstract

Among many epidemic prevention measures, isolation is an important method to control the spread of infectious disease. Scholars rarely study the impact of isolation on disease dissemination from a quantitative perspective. In this paper, we introduce an isolation ratio and establish the corresponding model. The basic reproductive number and its biological explanation are given. The stability conditions of the disease-free and endemic equilibria are obtained by analyzing its distribution of characteristic values. It is shown that the isolation ratio has an important influence on the basic reproductive number and the stability conditions. Taking the COVID-19 in Wuhan as an example, isolating more than 68% of the population can control the spread of the epidemic. This method can provide precise epidemic prevention strategies for government departments. Numerical simulations verify the effectiveness of the results.

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