<p>The stochastic Ebola epidemic model with a combination of nonlinear incidence functions is analyzed to gain deeper insights into the complex dynamics of disease transmission. We incorporate the effects of media coverage through a saturated incidence function and consider the efficacy of protective equipment in the force of infection. Additionally, we include the impact of insufficient medication in the density-independent recovery rate to reflect its effect on treatment. Initially, we investigate the global existence and uniqueness of solutions, as well as the asymptotic behavior of solutions for both disease-free and endemic equilibrium, by constructing an appropriate Lyapunov function. We analyze the model’s long-term behavior, focusing on persistence and eradication by defining two new threshold values, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="332_2025_10127_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$R_0^s$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>R</mi> <mn>0</mn> <mi>s</mi> </msubsup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="332_2025_10127_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$R_0^e$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>R</mi> <mn>0</mn> <mi>e</mi> </msubsup> </math></EquationSource> </InlineEquation>. When <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="332_2025_10127_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$ R_0^s > 1 $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>R</mi> <mn>0</mn> <mi>s</mi> </msubsup> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the presence of a stationary distribution is confirmed. Conversely, when <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="332_2025_10127_Article_IEq4.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$R_0^e < 1 $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>R</mi> <mn>0</mn> <mi>e</mi> </msubsup> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the exponential extinction of disease is obtained. We derive the exact expression of the probability density function around the quasi-endemic equilibrium by solving the related Fokker–Planck equation. Finally, we perform numerical simulations to demonstrate the theoretical findings. Key results indicate that strong noise intensities can drive disease extinction, even in scenarios where deterministic models predict persistence. Additionally, the analysis highlights that media coverage, protective efficacy, safe burial practices, and recovery rate are crucial for significantly reducing the spread of infection.</p>

Dynamical Analysis of a Stochastic Ebola Model with Nonlinear Incidence Functions

期刊论文
发表日期：

2025年1月13日

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S. Fathima Nasrin,
C. Rajivganthi

摘要

The stochastic Ebola epidemic model with a combination of nonlinear incidence functions is analyzed to gain deeper insights into the complex dynamics of disease transmission. We incorporate the effects of media coverage through a saturated incidence function and consider the efficacy of protective equipment in the force of infection. Additionally, we include the impact of insufficient medication in the density-independent recovery rate to reflect its effect on treatment. Initially, we investigate the global existence and uniqueness of solutions, as well as the asymptotic behavior of solutions for both disease-free and endemic equilibrium, by constructing an appropriate Lyapunov function. We analyze the model’s long-term behavior, focusing on persistence and eradication by defining two new threshold values, $R_0^s$ $R_{0}^{s}$ and $R_0^e$ $R_{0}^{e}$ . When $ R_0^s > 1 $ $R_{0}^{s} > 1$ , the presence of a stationary distribution is confirmed. Conversely, when $R_0^e < 1 $ $R_{0}^{e} < 1$ , the exponential extinction of disease is obtained. We derive the exact expression of the probability density function around the quasi-endemic equilibrium by solving the related Fokker–Planck equation. Finally, we perform numerical simulations to demonstrate the theoretical findings. Key results indicate that strong noise intensities can drive disease extinction, even in scenarios where deterministic models predict persistence. Additionally, the analysis highlights that media coverage, protective efficacy, safe burial practices, and recovery rate are crucial for significantly reducing the spread of infection.