<p>Hepatitis B Virus (HBV) remains a global health challenge, with re-infection adding complexity to control efforts. This article introduces a novel epidemiological model that incorporates re-infection dynamics with a Crowley–Martin incidence rate, along with the effects of constant vaccination and preventive measures. The model is structured into susceptible, infected, and recovered compartments, and its dynamic properties are rigorously analyzed. Key aspects such as the basic reproduction number <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2431_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">$(R_n)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, stability conditions, boundedness, non-negativity, and bifurcation behavior are explored. Using Lyapunov function, we establish the globally asymptotic stability of Hepatitis B Virus-free equilibrium for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2431_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$R_n < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mi>n</mi> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and identify a transcritical bifurcation at <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2431_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">$R_n = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mi>n</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Additionally, we demonstrate that the endemic equilibrium is globally asymptotic stable for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2431_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$R_n>1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mi>n</mi> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. The results of our numerical simulations, which employ NSFD scheme, validate our findings and demonstrate its superior efficiency when compared to RK4 and Euler methods. Specifically, NSFD produces faster and more accurate results. Our findings emphasize the critical role of vaccination, re-infection and preventive measures in HBV transmission dynamics, offering valuable perspective for public health strategies aimed at controlling HBV spread.</p>

Dynamics of re-infection in a Hepatitis B Virus epidemic model with constant vaccination and preventive measures

期刊论文
发表日期：

2025年3月25日

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Thangavel Megala,
Thangaraj Nandha Gopal,
Manickasundaram Siva Pradeep,
Muthurathinam Sivabalan,
Arunachalam Yasotha

摘要

Hepatitis B Virus (HBV) remains a global health challenge, with re-infection adding complexity to control efforts. This article introduces a novel epidemiological model that incorporates re-infection dynamics with a Crowley–Martin incidence rate, along with the effects of constant vaccination and preventive measures. The model is structured into susceptible, infected, and recovered compartments, and its dynamic properties are rigorously analyzed. Key aspects such as the basic reproduction number $(R_n)$ $(R_{n})$ , stability conditions, boundedness, non-negativity, and bifurcation behavior are explored. Using Lyapunov function, we establish the globally asymptotic stability of Hepatitis B Virus-free equilibrium for $R_n < 1$ $R_{n} < 1$ and identify a transcritical bifurcation at $R_n = 1$ $R_{n} = 1$ . Additionally, we demonstrate that the endemic equilibrium is globally asymptotic stable for $R_n>1$ $R_{n} > 1$ . The results of our numerical simulations, which employ NSFD scheme, validate our findings and demonstrate its superior efficiency when compared to RK4 and Euler methods. Specifically, NSFD produces faster and more accurate results. Our findings emphasize the critical role of vaccination, re-infection and preventive measures in HBV transmission dynamics, offering valuable perspective for public health strategies aimed at controlling HBV spread.