<p>The COVID-19 pandemic underscored the necessity of including human behavioral change in disease dynamics models. As a result, diverse models that integrate human behavior were proposed. In this study, we analyze the dynamics of a network-based epidemic model that incorporates two social groups with distinct susceptibilities. The model is based on a susceptible-infected-susceptible (SIS) framework, incorporating two susceptible compartments to stand for normal and educated states. First, we establish the condition for the existence of an endemic equilibrium and derive two critical threshold parameters, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1823_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathscr {R}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1823_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$\hat{\mathscr {R}}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mi mathvariant="script">R</mi> <mo stretchy="false">^</mo> </mover> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. Next, we prove the global asymptotic stability of the disease-free equilibrium and demonstrate the condition for disease persistence. Moreover, we investigate the bifurcation behavior at <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1823_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathscr {R}_0 = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, providing a necessary and sufficient condition for the occurrence of a backward bifurcation when <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1823_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathscr {R}_0 < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Our findings highlight that variations in social behavior can play a significant role in the emergence of this bifurcation type. Finally, we validate the theoretical results through numerical simulations, offering further insights into the model dynamics.</p>

Dynamics and bifurcation analysis of a network-based SIS epidemic model with different susceptibilities

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发表日期：

2025年8月25日

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A. A. Elsadany,
Chun-Hsien Li,
A. M. Yousef

摘要

The COVID-19 pandemic underscored the necessity of including human behavioral change in disease dynamics models. As a result, diverse models that integrate human behavior were proposed. In this study, we analyze the dynamics of a network-based epidemic model that incorporates two social groups with distinct susceptibilities. The model is based on a susceptible-infected-susceptible (SIS) framework, incorporating two susceptible compartments to stand for normal and educated states. First, we establish the condition for the existence of an endemic equilibrium and derive two critical threshold parameters, $\mathscr {R}_0$ $R_{0}$ and $\hat{\mathscr {R}}_0$ ${\hat{R}}_{0}$ . Next, we prove the global asymptotic stability of the disease-free equilibrium and demonstrate the condition for disease persistence. Moreover, we investigate the bifurcation behavior at $\mathscr {R}_0 = 1$ $R_{0} = 1$ , providing a necessary and sufficient condition for the occurrence of a backward bifurcation when $\mathscr {R}_0 < 1$ $R_{0} < 1$ . Our findings highlight that variations in social behavior can play a significant role in the emergence of this bifurcation type. Finally, we validate the theoretical results through numerical simulations, offering further insights into the model dynamics.