<p>Marburg virus disease, also known as Marburg hemorrhagic fever, is a rare yet severe and often fatal viral disease caused by the Marburg virus, a member of the Filoviridae family. The Marburg virus is zoonotic, meaning it can be transmitted from animals to humans. In this study, a mathematical model is formulated and analyzed to describe the transmission dynamics of the Marburg virus, incorporating quarantine measures and protective interventions within the population. The next-generation method is employed to calculate the effective reproduction number, <InlineEquation ID="IEq1101"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2264_Article_IEq1101.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal{R}_e$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mi>e</mi> </msub> </math></EquationSource> </InlineEquation>. By applying the Routh-Hurwitz criterion and constructing a Lyapunov function, results demonstrate that the Marburg virus-free equilibrium is both locally and globally asymptotically stable if the effective reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2264_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal{R}_e < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mi>e</mi> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> . Conversely, when <InlineEquation ID="IEq1102"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2264_Article_IEq1102.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal{R}_e > 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mi>e</mi> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the endemic equilibrium becomes globally asymptotically stable. Simulation results emphasize the importance of quarantining exposed individuals and enforcing protective measures in controlling the transmission of the Marburg virus within the population. Consequently, to effectively combat the disease, increased efforts should be directed toward implementing quarantine and protective measures.</p>

Modelling the effects of quarantine and protective interventions on the transmission dynamics of Marburg virus disease

期刊论文
发表日期：

2025年1月20日

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Jufren Zakayo Ndendya,
Eunice Mureithi,
Joshua A. Mwasunda,
Gibson Kagaruki,
Nyimvua Shaban,
Mary Mayige

摘要

Marburg virus disease, also known as Marburg hemorrhagic fever, is a rare yet severe and often fatal viral disease caused by the Marburg virus, a member of the Filoviridae family. The Marburg virus is zoonotic, meaning it can be transmitted from animals to humans. In this study, a mathematical model is formulated and analyzed to describe the transmission dynamics of the Marburg virus, incorporating quarantine measures and protective interventions within the population. The next-generation method is employed to calculate the effective reproduction number, $\mathcal{R}_e$ $R_{e}$ . By applying the Routh-Hurwitz criterion and constructing a Lyapunov function, results demonstrate that the Marburg virus-free equilibrium is both locally and globally asymptotically stable if the effective reproduction number $\mathcal{R}_e < 1$ $R_{e} < 1$ . Conversely, when $\mathcal{R}_e > 1$ $R_{e} > 1$ , the endemic equilibrium becomes globally asymptotically stable. Simulation results emphasize the importance of quarantining exposed individuals and enforcing protective measures in controlling the transmission of the Marburg virus within the population. Consequently, to effectively combat the disease, increased efforts should be directed toward implementing quarantine and protective measures.