Mathematical modeling of tuberculosis transmission dynamics with vaccination and two lines of treatments: a caputo fractional approach

In this paper, we develop and examine a mathematical model for the transmission dynamics of tuberculosis (TB) using the Caputo fractional approach that takes into account vaccination and two treatment modalities: the first-line TB therapy and the second-line TB treatment. The purpose of this study is to investigate the impact of vaccination and these treatment modalities on the transmission dynamics of the disease. The next generation matrix technique is used to calculate the model’s fundamental reproduction number. According to a mathematical examination of the model, the TB-free equilibrium point is both locally and globally asymptotically stable if the basic reproduction number is less than unity and unstable if it exceeds unity. Sensitivity analysis highlights parameters most influential to the basic reproduction number, showing that higher vaccination rate and treatment rates, along with reduced effective contact and infection rates significantly decrease TB prevalence. The simulation results further demonstrate that by taking memory effects into account, a Caputo fractional order derivative enhances a deeper understanding of TB dynamics, aiding the design of effective prevention and control strategies. All things considered, these results provide insightful information for government officials, policymakers, and health professionals.