Dynamics of an SEIR model with media coverage mediated nonlinear infectious force

Jingli Xie; Hongli Guo; Meiyang Zhang; Jingli Xie; Hongli Guo; Meiyang Zhang

doi:10.3934/mbe.2023654

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14616-14633. doi: 10.3934/mbe.2023654

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Dynamics of an SEIR model with media coverage mediated nonlinear infectious force

College of Mathematics and Statistics, Jishou University, Jishou, Hunan 416000, China

Academic Editor: Xiang-Sheng Wang

Received: 10 April 2023 Revised: 04 June 2023 Accepted: 21 June 2023 Published: 05 July 2023

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.
- media influence,
- SEIR model,
- incubation period,
- sensitivity analysis,
- stability
Citation: Jingli Xie, Hongli Guo, Meiyang Zhang. Dynamics of an SEIR model with media coverage mediated nonlinear infectious force[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14616-14633. doi: 10.3934/mbe.2023654

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Abstract

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.

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