Efficient Solutions with the LRPS Method for Non-Linear Fractional Order Tuberculosis Models

Abstract

In this research article, we present a novel Non-Linear Fractional Order Tuberculosis mathematical model (NLFOTB) and introduce an efficient technique to obtain its solution. Fractional Order Models (FOMs) have garnered significant attention in contemporary research due to their widespread applicability. We address the challenge of solving the coupled Initial Value Problems (IVPs) associated with NLFOTB models by utilizing the groundbreaking LRPS method, which combines the RPS approach with the Laplace transform operator. This innovative approach generates approximate solutions in rapidly converging series forms, offering enhanced efficiency and reduced computational effort compared to conventional methods. Through the implementation of the LRPS method, we successfully derive an approximate solution for the NLFOTB model, contributing significantly to the field. Furthermore, our proposed approach demonstrates its efficacy in accurately capturing the dynamics of Tuberculosis (TB) through extensive computations and graphical representations, contributing to a deeper understanding of TB dynamics within a mathematical framework. Additionally, the LRPS method shows promise in tackling real world problems involving differential equations of various orders. Future investigations can extend the application of the LRPS method to explore other Fractional Order Models, further validating its effectiveness in a wide range of epidemic scenarios. Consequently, our study not only provides valuable insights into Tuberculosis dynamics but also introduces a powerful computational tool applicable to various practical problems in diverse disciplines, making a substantial contribution to the field of mathematical modeling and computation. HIGHLIGHTS · The comprehensive study highlights the LRPS strategy’s efficiency and accuracy in approximating solutions for fractional order equations. The research demonstrates its capability to predict compartmental behavior accurately within the specified range · The discussions presented in the article significantly contribute to the field of epidemiology by introducing and showcasing the LRPS approach’s effectiveness. As a valuable tool for investigating and validating epidemic models, the LRPS method offers improved efficiency and convenience, thereby enhancing the understanding of disease dynamics · The researchers anticipate that their findings will inspire further exploration and utilization of the LRPS technique in solving nonlinear models. This, in turn, is expected to contribute to advancements in the broader field of epidemiology, fostering continued innovation and development GRAPHICAL ABSTRACT