A caputo fractional-order model of tuberculosis incorporating enlightenment and therapy using the Laplace-Adomian decomposition method

Abstract

In this study, we used a deterministic model to investigate tuberculosis transmission dynamics while considering control measures. We analyzed four compartmental models representing susceptible, latent, infected, and recovered populations. To assess the potential spread of the disease, we calculated the basic reproduction number using the next-generation matrix after establishing a disease-free equilibrium. Additionally, we explored the endemic equilibrium, as well as local and global stabilities. To obtain numerical solutions, we employed the Laplace-Adomian decomposition method. For constructing the model, we utilized Maple 18 software and varied the order (0 < ψ < 1) to examine the impact of enlightenment and therapy. Graphical representations were used to analyze the effects of non-integer order Caputo derivative parameters on the susceptible, latent, infected, and recovered populations over time. Our detailed discussion highlights the crucial role of mathematical models based on Caputo fractional derivatives in effectively controlling and eradicating tuberculosis from society. These findings contribute valuable insights to inform strategies for combating the disease and promoting public health initiatives.