Stability Analysis of SEIAR Model with Age Structure Under Media Effect

In this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected...

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Main Authors: Hongliang Gao, Fanli Zhang, Jiemei Li
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/6/412
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author Hongliang Gao
Fanli Zhang
Jiemei Li
author_facet Hongliang Gao
Fanli Zhang
Jiemei Li
author_sort Hongliang Gao
collection DOAJ
description In this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected individuals becoming dominant through contact with infectious individuals. Theoretical analysis yields the explicit expression for the basic reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>, which serves as a critical threshold for disease dynamics. Through comprehensive threshold analysis, we investigate the existence and stability of both disease-free and endemic equilibrium states. By applying characteristic equation analysis and the method of characteristics, we establish the following: (1) when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease-free equilibrium is globally asymptotically stable; (2) when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, a unique endemic equilibrium exists and maintains local asymptotic stability under specific conditions. This study shows that strengthening media promotion, raising awareness, and reducing the density of recessive infected individuals can effectively control the further spread of a disease. To validate our theoretical results, we present numerical simulations that quantitatively assess the impact of varying media reporting intensities on epidemic containment measures. These simulations provide practical insights for public health intervention strategies.
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spelling doaj-art-91b208bf8b3745dc82b3d4d5685e5b8d2025-08-20T03:26:15ZengMDPI AGAxioms2075-16802025-05-0114641210.3390/axioms14060412Stability Analysis of SEIAR Model with Age Structure Under Media EffectHongliang Gao0Fanli Zhang1Jiemei Li2School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaIn this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected individuals becoming dominant through contact with infectious individuals. Theoretical analysis yields the explicit expression for the basic reproduction number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>, which serves as a critical threshold for disease dynamics. Through comprehensive threshold analysis, we investigate the existence and stability of both disease-free and endemic equilibrium states. By applying characteristic equation analysis and the method of characteristics, we establish the following: (1) when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease-free equilibrium is globally asymptotically stable; (2) when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, a unique endemic equilibrium exists and maintains local asymptotic stability under specific conditions. This study shows that strengthening media promotion, raising awareness, and reducing the density of recessive infected individuals can effectively control the further spread of a disease. To validate our theoretical results, we present numerical simulations that quantitatively assess the impact of varying media reporting intensities on epidemic containment measures. These simulations provide practical insights for public health intervention strategies.https://www.mdpi.com/2075-1680/14/6/412media effectage structurerecessive infectionstabilitycharacteristic line method
spellingShingle Hongliang Gao
Fanli Zhang
Jiemei Li
Stability Analysis of SEIAR Model with Age Structure Under Media Effect
Axioms
media effect
age structure
recessive infection
stability
characteristic line method
title Stability Analysis of SEIAR Model with Age Structure Under Media Effect
title_full Stability Analysis of SEIAR Model with Age Structure Under Media Effect
title_fullStr Stability Analysis of SEIAR Model with Age Structure Under Media Effect
title_full_unstemmed Stability Analysis of SEIAR Model with Age Structure Under Media Effect
title_short Stability Analysis of SEIAR Model with Age Structure Under Media Effect
title_sort stability analysis of seiar model with age structure under media effect
topic media effect
age structure
recessive infection
stability
characteristic line method
url https://www.mdpi.com/2075-1680/14/6/412
work_keys_str_mv AT honglianggao stabilityanalysisofseiarmodelwithagestructureundermediaeffect
AT fanlizhang stabilityanalysisofseiarmodelwithagestructureundermediaeffect
AT jiemeili stabilityanalysisofseiarmodelwithagestructureundermediaeffect