<p>The age-structured approach plays a crucial role in epidemiological modelling as it accounts for age-specific variations in susceptibility, transmission and disease progressions, providing a more accurate description of disease dynamics. In this paper, we create an age-structured epidemic model that incorporates age-dependent susceptibility and latency, as well as a relapse phase, with the objective of investigating the global dynamics of this model under the impact of that combination. The very important threshold parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10440_2025_723_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{R}_{0}$</EquationSource> </InlineEquation> was introduced, and it has shown that it completely controls the stability of each equilibrium of the model. Based on the Lyapunov functional approach, we show that the disease-free equilibrium is globally asymptotically stable when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10440_2025_723_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{R}_{0}<1$</EquationSource> </InlineEquation>, while the positive endemic equilibrium is globally asymptotically stable whenever <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10440_2025_723_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\mathcal{R}_{0}>1$</EquationSource> </InlineEquation>. Our results suggest that early diagnostic of latency individuals, reduction in transmission rate and improvements in treatment and heath-care of infected individuals may effectively control the spread of the disease.</p>

Dynamics of a Double Age-Structured SEIRI Epidemic Model

期刊论文
发表日期：

2025年3月13日

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Abderrazak Nabti,
Salih Djilali,
Malek Belghit

摘要

The age-structured approach plays a crucial role in epidemiological modelling as it accounts for age-specific variations in susceptibility, transmission and disease progressions, providing a more accurate description of disease dynamics. In this paper, we create an age-structured epidemic model that incorporates age-dependent susceptibility and latency, as well as a relapse phase, with the objective of investigating the global dynamics of this model under the impact of that combination. The very important threshold parameter $R_{0}$ $\mathcal{R}_{0}$ was introduced, and it has shown that it completely controls the stability of each equilibrium of the model. Based on the Lyapunov functional approach, we show that the disease-free equilibrium is globally asymptotically stable when $R_{0} < 1$ $\mathcal{R}_{0}<1$ , while the positive endemic equilibrium is globally asymptotically stable whenever $R_{0} > 1$ $\mathcal{R}_{0}>1$ . Our results suggest that early diagnostic of latency individuals, reduction in transmission rate and improvements in treatment and heath-care of infected individuals may effectively control the spread of the disease.