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<p>Mathematical modeling is vital for understanding infectious disease dynamics and informing public health strategies. This study introduces a compartmental model that integrates age-structured vaccination dynamics, waning immunity, and multistage disease progression to analyze COVID-19 transmission in Italy and Portugal. Using differential equations, the model captures interactions among susceptible, exposed, vaccinated, infected, hospitalized, recovered, and deceased populations. We prove the existence and uniqueness of the solution, calculate the basic reproduction number (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11332_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathscr {R}_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>), and analyze steady-state stability. Parameters are estimated using weighted least squares using real-world data, validated with Portugal and Italy data to capture transmission dynamics. Simulations using finite difference methods across three stability scenarios guide booster shot strategies.</p>

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A Mathematical model for Epidemic dynamics with multiple vaccines, age-structured strategies, and parameter estimation

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • Abdellah Ouakka,
  • Abdelouahed Alla Hamou,
  • Abdelhai El Azzouzi

摘要

Mathematical modeling is vital for understanding infectious disease dynamics and informing public health strategies. This study introduces a compartmental model that integrates age-structured vaccination dynamics, waning immunity, and multistage disease progression to analyze COVID-19 transmission in Italy and Portugal. Using differential equations, the model captures interactions among susceptible, exposed, vaccinated, infected, hospitalized, recovered, and deceased populations. We prove the existence and uniqueness of the solution, calculate the basic reproduction number ( \(\mathscr {R}_0\) R 0 ), and analyze steady-state stability. Parameters are estimated using weighted least squares using real-world data, validated with Portugal and Italy data to capture transmission dynamics. Simulations using finite difference methods across three stability scenarios guide booster shot strategies.