Global dynamics of COVID-19 epidemic model with recessive infection and isolation

Rong Yuan; Yangjun Ma; Congcong Shen; Jinqing Zhao; Xiaofeng Luo; Maoxing Liu; Rong Yuan; Yangjun Ma; Congcong Shen; Jinqing Zhao; Xiaofeng Luo; Maoxing Liu

doi:10.3934/mbe.2021095

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 2: 1833-1844. doi: 10.3934/mbe.2021095

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Research article

Global dynamics of COVID-19 epidemic model with recessive infection and isolation

1.
School of Science, North University of China, Taiyuan 030051, China
2.
School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
3.
School of Information, Beijing Wuzi University, Beijing 101149, China
4.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Received: 20 October 2020 Accepted: 04 February 2021 Published: 22 February 2021

In this paper, we present an SEII$ { _\rm a} $HR epidemic model to study the influence of recessive infection and isolation in the spread of COVID-19. We first prove that the infection-free equilibrium is globally asymptotically stable with condition $ R_0 < 1 $ and the positive equilibrium is uniformly persistent when the condition $ R_0 > 1 $. By using the COVID-19 data in India, we then give numerical simulations to illustrate our results and carry out some sensitivity analysis. We know that asymptomatic infections will affect the spread of the disease when the quarantine rate is within the range of [0.3519, 0.5411]. Furthermore, isolating people with symptoms is important to control and eliminate the disease.
- COVID-19 epidemic model,
- recessive infection,
- isolation,
- asymptotically stable,
- basic reproduction number
Citation: Rong Yuan, Yangjun Ma, Congcong Shen, Jinqing Zhao, Xiaofeng Luo, Maoxing Liu. Global dynamics of COVID-19 epidemic model with recessive infection and isolation[J]. Mathematical Biosciences and Engineering, 2021, 18(2): 1833-1844. doi: 10.3934/mbe.2021095

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Abstract

In this paper, we present an SEII$ { _\rm a} $HR epidemic model to study the influence of recessive infection and isolation in the spread of COVID-19. We first prove that the infection-free equilibrium is globally asymptotically stable with condition $ R_0 < 1 $ and the positive equilibrium is uniformly persistent when the condition $ R_0 > 1 $. By using the COVID-19 data in India, we then give numerical simulations to illustrate our results and carry out some sensitivity analysis. We know that asymptomatic infections will affect the spread of the disease when the quarantine rate is within the range of [0.3519, 0.5411]. Furthermore, isolating people with symptoms is important to control and eliminate the disease.

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