Mathematical modeling and dynamic analysis of SIQR model with delay for pandemic COVID-19

Hongfan Lu; Yuting Ding; Silin Gong; Shishi Wang; Hongfan Lu; Yuting Ding; Silin Gong; Shishi Wang

doi:10.3934/mbe.2021159

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3197-3214. doi: 10.3934/mbe.2021159

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Research article Special Issues

Mathematical modeling and dynamic analysis of SIQR model with delay for pandemic COVID-19

Department of Mathematics, Northeast Forestry University, Harbin, 150040, China

Academic Editor: Cristiana Silva

Received: 24 February 2021 Accepted: 02 April 2021 Published: 06 April 2021

On the basis of the SIQR epidemic model, we consider the impact of treatment time on the epidemic situation, and we present a differential equation model with time-delay according to the characteristics of COVID-19. Firstly, we analyze the existence and stability of the equilibria in the modified COVID-19 epidemic model. Secondly, we analyze the existence of Hopf bifurcation, and derive the normal form of Hopf bifurcation by using the multiple time scales method. Then, we determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, we carry out numerical simulations to verify the correctness of theoretical analysis with actual parameters, and show conclusions associated with the critical treatment time and the effect on epidemic for treatment time.
- COVID-19 model,
- Time-delay,
- Hopf bifurcation,
- Normal form,
- Multiple time scales method
Citation: Hongfan Lu, Yuting Ding, Silin Gong, Shishi Wang. Mathematical modeling and dynamic analysis of SIQR model with delay for pandemic COVID-19[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3197-3214. doi: 10.3934/mbe.2021159

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Abstract

On the basis of the SIQR epidemic model, we consider the impact of treatment time on the epidemic situation, and we present a differential equation model with time-delay according to the characteristics of COVID-19. Firstly, we analyze the existence and stability of the equilibria in the modified COVID-19 epidemic model. Secondly, we analyze the existence of Hopf bifurcation, and derive the normal form of Hopf bifurcation by using the multiple time scales method. Then, we determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, we carry out numerical simulations to verify the correctness of theoretical analysis with actual parameters, and show conclusions associated with the critical treatment time and the effect on epidemic for treatment time.

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