Caputo fractional-order model formulation of tuberculosis epidemics incorporating consciousness effects via the Laplace–Adomian decomposition method with adjusted initial condition

Abstract

Mycobacterium tuberculosis is the causative agent of tuberculosis (TB), a communicable infectious disease that mainly affects the lungs but can also affect other vital systems like the bones, joints, and nervous system. TB is still a major global health concern despite tremendous efforts to combat it. The current study examines and analyzes the tuberculosis epidemic under the consciousness effect using a Caputo-type fractional-order derivative operator. The impact of curative treatment on the infected population and preventive treatment on the latent population is described and examined by the developed model. The fractional-order tuberculosis epidemic is investigated using a variety of analytical techniques. By using positivity and boundedness theory, the generalized mean value theorem facilitates the investigation of the model's solutions. Additionally, the existence and uniqueness of solutions are established using the Banach fixed-point technique. The response of the fractional-order system to different model parameters is examined using the normalized forward sensitivity approach. This study presents the development of a novel fractional-order tuberculosis (TB) model that integrates public consciousness (awareness) effects and treatment dynamics within a population-level epidemic framework. The Laplace–Adomian decomposition method (LADM), employed with modified initial conditions, serves as a robust analytical technique for obtaining approximate solutions to the resulting fractional differential equations. The model quantitatively illustrates that synergistically combining public awareness campaigns with therapeutic interventions can substantially reduce the TB burden, particularly when memory-dependent processes, captured by the fractional-order dynamics are incorporated. This modeling framework offers valuable insights for policy formulation, highlighting the necessity of coupling behavioral sensitization programs with medical strategies to enhance the effectiveness of TB control measures.