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<p>This study introduces a mathematical model for disease dynamics, incorporating a non-linear incidence rate and time delay to analyze infectious disease transmission and recovery processes. Local stability is examined using the Routh-Hurwitz criterion, while global stability is established using Lyapunov functionals and the LaSalle invariance principle. The phase portraits and domain of attraction plots illustrate system dynamics, including equilibrium states, stability, intervention effects, and long-term predictions. The sensitivity analysis of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_333_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textbf{R}_0\)</EquationSource> </InlineEquation> with respect to the natural death rate (<i>d</i>) and disease-induced death rate (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_333_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(d_1\)</EquationSource> </InlineEquation>) provides a significant contribution to their relative impact on the transmission potential of the disease. Numerical simulations support the theoretical results, providing a comprehensive and robust mathematical framework for the analysis of epidemic dynamics, with valuable insights into the stability and control of infectious diseases.</p>

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Mathematical Analysis of an Infectious Disease Model: Stability, Persistence, and Equilibrium Analysis in a Non-Linear Epidemiological System

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月6日

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  • Sushil Pathak,
  • Venkata Ratnam Kota

摘要

This study introduces a mathematical model for disease dynamics, incorporating a non-linear incidence rate and time delay to analyze infectious disease transmission and recovery processes. Local stability is examined using the Routh-Hurwitz criterion, while global stability is established using Lyapunov functionals and the LaSalle invariance principle. The phase portraits and domain of attraction plots illustrate system dynamics, including equilibrium states, stability, intervention effects, and long-term predictions. The sensitivity analysis of \(\textbf{R}_0\) with respect to the natural death rate (d) and disease-induced death rate ( \(d_1\) ) provides a significant contribution to their relative impact on the transmission potential of the disease. Numerical simulations support the theoretical results, providing a comprehensive and robust mathematical framework for the analysis of epidemic dynamics, with valuable insights into the stability and control of infectious diseases.