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<p>This paper explores tuberculosis (TB), a highly infectious disease primarily targeting the lungs but also capable of affecting other parts of the body, including the nervous system, bones, and joints. Despite extensive prevention efforts, TB remains a significant public health challenge. This study investigates the dynamics of TB through vaccination, awareness campaigns, and intervention strategies, employing a deterministic modeling approach. The analysis focuses on six compartmental models to represent different population groups: vaccinated, susceptible, latent, infected, isolated, and recovered individuals. It was discovered that the model is Ulam-Hyers stable and has a unique solution. After achieving the equilibrium of the disease-free, we used the next generation matrix to determine the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> in order to evaluate the possible Transmission of the ailment. Additionally, we investigate the endemic equilibrium and sensitivity analysis. We use Laplace-Adomian decomposition method to produce numerical solutions, and the convergence of the solution is verified using conventional mathematical approaches. The outcomes of the Caputo fractional-order numerical simulations show that the current state is strongly influenced by the host’s prior medical history.</p>

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Modeling Tuberculosis Dynamics with Awareness and Vaccination Using Laplace-Adomian and Fractional Calculus

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Morufu Oyedunsi Olayiwola,
  • Ezekiel Abiodun Oluwafemi

摘要

This paper explores tuberculosis (TB), a highly infectious disease primarily targeting the lungs but also capable of affecting other parts of the body, including the nervous system, bones, and joints. Despite extensive prevention efforts, TB remains a significant public health challenge. This study investigates the dynamics of TB through vaccination, awareness campaigns, and intervention strategies, employing a deterministic modeling approach. The analysis focuses on six compartmental models to represent different population groups: vaccinated, susceptible, latent, infected, isolated, and recovered individuals. It was discovered that the model is Ulam-Hyers stable and has a unique solution. After achieving the equilibrium of the disease-free, we used the next generation matrix to determine the \(R_{0}\) R 0 in order to evaluate the possible Transmission of the ailment. Additionally, we investigate the endemic equilibrium and sensitivity analysis. We use Laplace-Adomian decomposition method to produce numerical solutions, and the convergence of the solution is verified using conventional mathematical approaches. The outcomes of the Caputo fractional-order numerical simulations show that the current state is strongly influenced by the host’s prior medical history.