Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

Boli Xie; Maoxing Liu; Lei Zhang; Boli Xie; Maoxing Liu; Lei Zhang

doi:10.3934/mbe.2022079

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 2: 1677-1696. doi: 10.3934/mbe.2022079

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Research article Special Issues

Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

School of Science, North University of China, Taiyuan 030051, China

Received: 05 October 2021 Accepted: 09 November 2021 Published: 14 December 2021

In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} < 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.
- network,
- bifurcation analysis,
- SEIR epidemic model,
- optimal control
Citation: Boli Xie, Maoxing Liu, Lei Zhang. Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1677-1696. doi: 10.3934/mbe.2022079

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Abstract

In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} < 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.

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