Fractional-order analysis of covid-19 and tuberculosis co-infection incorporating hospitalization via Caputo derivatives and Laplace Adomian

Abstract This paper presents a fractional-order model using Caputo derivatives to analyze the co-infection dynamics of COVID-19 and tuberculosis (TB), incorporating hospitalization effects. The model comprises eight compartments: susceptible, latent TB, active TB, COVID-19 exposed, COVID-19 infectious, co-infected, hospitalized, and recovered individuals. Memory-dependent dynamics enhance the biological realism compared to classical models. Mathematical analysis confirms the model’s positivity, boundedness, and the existence and uniqueness of solutions. The basic reproduction number R0 is derived, and sensitivity analysis identifies critical transmission parameters. The Laplace Adomian Decomposition Method (LADM) provides semi-analytical solutions, capturing the interaction between co-infections and healthcare interventions. Numerical simulations demonstrate that increased hospitalization and fractional-order effects significantly lower infection levels. The study underscores the utility of fractional calculus in epidemiological modeling and highlights hospitalization as a key control strategy against co-infection.