<p>The highly infectious Marburg virus (MARV) spreads rapidly through contact with infected individuals and improperly handled deceased bodies. Although burial and cremation practices have been examined for other pathogens, their role in MARV transmission remains largely unquantified. This study introduces a novel fractional-order compartmental model that explicitly incorporates burial, cremation, and awareness-based interventions to assess their combined impact on MARV control. The model employs the Caputo fractional derivative to capture memory effects in disease progression, offering a more realistic representation of transmission dynamics compared to traditional integer-order models. The basic reproduction number is derived via the next-generation matrix (NGM) approach, and the local asymptotic stability of the Marburg-free equilibrium is established. The Marburg present equilibrium point is obtained, and its global stability is rigorously proved using a Lyapunov function framework. Furthermore, bifurcation analysis is conducted to explore qualitative changes in system dynamics and confirm the occurrence of a forward bifurcation at <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43088_2025_691_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">$\textrm{R}_0=1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>R</mtext> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Global sensitivity analysis identifies the most influential parameters affecting disease spread, highlighting that increasing awareness and reducing contact with infectious or deceased individuals markedly suppress transmission. Theoretical contributions include proofs of positivity, boundedness, existence, and uniqueness of solutions, and Ulam–Hyers stability. To validate the proposed approach, results from the generalized Euler method (GEM) are compared with those obtained using Runge–Kutta methods for integer-order models and the Adams-Bashforth-Moulton (ABM) scheme for fractional-order models, showing strong agreement. The findings underscore the novel application of fractional-order modeling to MARV, demonstrating its superior capability to capture long-term effects and guide culturally sensitive, evidence-based public health strategies for outbreak mitigation.</p>

Fractional-order model for marburg virus transmission: assessing the impact of awareness, burial and cremation practices

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2025年10月23日

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Kaushal Soni,
Shyamsunder Kumawat,
Arvind Kumar Sinha

摘要

The highly infectious Marburg virus (MARV) spreads rapidly through contact with infected individuals and improperly handled deceased bodies. Although burial and cremation practices have been examined for other pathogens, their role in MARV transmission remains largely unquantified. This study introduces a novel fractional-order compartmental model that explicitly incorporates burial, cremation, and awareness-based interventions to assess their combined impact on MARV control. The model employs the Caputo fractional derivative to capture memory effects in disease progression, offering a more realistic representation of transmission dynamics compared to traditional integer-order models. The basic reproduction number is derived via the next-generation matrix (NGM) approach, and the local asymptotic stability of the Marburg-free equilibrium is established. The Marburg present equilibrium point is obtained, and its global stability is rigorously proved using a Lyapunov function framework. Furthermore, bifurcation analysis is conducted to explore qualitative changes in system dynamics and confirm the occurrence of a forward bifurcation at $\textrm{R}_0=1$ $R_{0} = 1$ . Global sensitivity analysis identifies the most influential parameters affecting disease spread, highlighting that increasing awareness and reducing contact with infectious or deceased individuals markedly suppress transmission. Theoretical contributions include proofs of positivity, boundedness, existence, and uniqueness of solutions, and Ulam–Hyers stability. To validate the proposed approach, results from the generalized Euler method (GEM) are compared with those obtained using Runge–Kutta methods for integer-order models and the Adams-Bashforth-Moulton (ABM) scheme for fractional-order models, showing strong agreement. The findings underscore the novel application of fractional-order modeling to MARV, demonstrating its superior capability to capture long-term effects and guide culturally sensitive, evidence-based public health strategies for outbreak mitigation.