Stability and Hopf bifurcation of TB-COVID-19 coinfection model with impact of time delay

Abstract

In this work, a compartmental approach used for modelling and surveillance of dynamics of Tuberculosis and COVID-19 coinfection by considering the post-infection and molecular variants compartments in addition to existing compartments. We have tried to explain how variants can affect the infection rate and its severity. Also, the post-infection compartment is studied to understand the impact after recovery from the disease and the consequences of the post-infection period. We highlight the conceptual idea and mathematical tools and techniques needed for such co-infection disease modelling. We investigate the basic properties of the co-infectious disease model, including the local and global stability of the equilibria for the delayed and non-delayed systems, and calculate the points of equilibria and the basic reproduction number of the suggested model. It is proved that when the time delay caused by the latent phase of tuberculosis exceeds the threshold value, the constructed model undergoes a Hopf bifurcation around the tuberculosis existence. The center manifold theory is used to study the direction and stability of the Hopf bifurcation which is essential to study the delayed system. Both delayed and non-delayed systems differ significantly and we have conducted numerical analyses to verify the efficacy of the deduced outcomes. © The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada 2024.