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<p>In this study, a&#xa0;mathematical model for the transmission dynamics of HIV/AIDS and TB co-infection is developed and analyzed using a&#xa0;Caputo fractional operator. The model integrates several critical interventions: TB preventative therapy, TB vaccine, and antiretroviral treatment for HIV patients to assess their collective effectiveness. The basic reproduction number is derived using the next generation matrix method. The mathematical study of the model shows that the diseases free equilibrium points for HIV/AIDS, TB, and their co-infection are asymptotically stable both locally and globally if the corresponding basic reproductive numbers are less than unity, and unstable if they exceed unity. The result of sensitivity analysis shows that higher rates of TB preventive and antiretroviral therapies, together with lower vaccine fading rates and effective contact rates, significantly lower the prevalence of HIV/AIDS, TB and their co-infections. The simulation findings also show how a&#xa0;Caputo fractional operator helps to design effective preventative and control strategies by managing memory effects and enhancing a&#xa0;deeper understanding of the co-infection dynamics. These findings provide invaluable insights for healthcare policymakers and practitioners, aiding in the development of integrated approaches to manage HIV/AIDS and TB co-infection.</p>

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Fractional Order Modeling of HIV/AIDS and TB Co-infection with Vaccination and Treatment Therapies

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Abdurkadir Edeo Gemeda,
  • Legesse Lemecha Obsu,
  • Eshetu Dadi Gurmu,
  • Shambel Tadesse Degefa

摘要

In this study, a mathematical model for the transmission dynamics of HIV/AIDS and TB co-infection is developed and analyzed using a Caputo fractional operator. The model integrates several critical interventions: TB preventative therapy, TB vaccine, and antiretroviral treatment for HIV patients to assess their collective effectiveness. The basic reproduction number is derived using the next generation matrix method. The mathematical study of the model shows that the diseases free equilibrium points for HIV/AIDS, TB, and their co-infection are asymptotically stable both locally and globally if the corresponding basic reproductive numbers are less than unity, and unstable if they exceed unity. The result of sensitivity analysis shows that higher rates of TB preventive and antiretroviral therapies, together with lower vaccine fading rates and effective contact rates, significantly lower the prevalence of HIV/AIDS, TB and their co-infections. The simulation findings also show how a Caputo fractional operator helps to design effective preventative and control strategies by managing memory effects and enhancing a deeper understanding of the co-infection dynamics. These findings provide invaluable insights for healthcare policymakers and practitioners, aiding in the development of integrated approaches to manage HIV/AIDS and TB co-infection.