Qualitative analysis of TB transmission dynamics considering both the age since latency and relapse

Abstract

Since the beginning of time, tuberculosis (TB) has been a fatal illness that predominantly affects the human lungs before spreading to other organs including the brain, spine, etc. The main elements of TB mitigation are age-dependent heterogeneity, identifying those who are latently infected, and treating them using the right diagnostic strategy. In this present work, the complex transmission mechanism of this disease in a population is described by a coupled system of integro-partial differential equations (IDE-PDE). The system’s well-posedness requirement is confirmed. The proposed system’s basic reproduction number () is obtained. This work provides a complete analysis of the qualitative properties of the model, including steady state existence, asymptotic smoothness of the solution semi-flow, uniform persistence of the endemic equilibrium, and the global asymptotic stability criterion. It is observed that in assessing the severity of the pandemic, the value of is crucial. Additionally, the stability results are visually illustrated by solving the model equations numerically while assuming two hypothetical cases. The current work also suggests several methods for reducing the value of the basic reproductive number () by manipulating a few parameter values, which may help to lessen the prevalence of TB in a community.