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<p><?tk 3?>This study investigates a fractional-order SCIRV model, which is linear in nature, focusing on obtaining its exact solution. The model comprises Susceptible (<i>S</i>), Carrier (<i>C</i>), Infected (<i>I</i>), Recovered (<i>R</i>), and Vaccinated (<i>V</i>) populations, with fractional derivatives capturing memory effects in disease transmission. Fundamental mathematical properties, including positivity, boundedness, and the existence and uniqueness of solutions, are rigorously analyzed to ensure the model’s validity. We solve the system of linear fractional order equations and obtain the analytic result. Numerical simulations illustrate the impact of varying vaccination rates <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> </InlineEquation> and recovered-to-vaccinated rates <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\psi \)</EquationSource> </InlineEquation> on disease spread, demonstrating the effectiveness of vaccination in controlling infections. The findings show the significance of fractional-order modeling and exact solutions in epidemiological studies.</p>

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Exact solution of a fractional-order model for pneumonia dynamics

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Isa Abdullahi Baba,
  • Evren Hincal,
  • Fathalla A. Riha

摘要

This study investigates a fractional-order SCIRV model, which is linear in nature, focusing on obtaining its exact solution. The model comprises Susceptible (S), Carrier (C), Infected (I), Recovered (R), and Vaccinated (V) populations, with fractional derivatives capturing memory effects in disease transmission. Fundamental mathematical properties, including positivity, boundedness, and the existence and uniqueness of solutions, are rigorously analyzed to ensure the model’s validity. We solve the system of linear fractional order equations and obtain the analytic result. Numerical simulations illustrate the impact of varying vaccination rates \(\gamma \) and recovered-to-vaccinated rates \(\psi \) on disease spread, demonstrating the effectiveness of vaccination in controlling infections. The findings show the significance of fractional-order modeling and exact solutions in epidemiological studies.