Dynamical analysis of an age-structured tuberculosis mathematical model with LTBI detectivity

Abstract

The age-dependent heterogeneity observed in tuberculosis (TB) epidemiology includes susceptibility, infectiousness, contact preferences of an individual. Also, the chance of finding a direct route to infectious pulmonary TB (PTB) of certain vulnerable risk-group and the diagnosis effort to detect latent TB individual (LTBI) are critical factors in TB epidemiology. The current investigation proposes a mathematical model based on a set of coupled partial differential equations (PDE) to encounter these vital characteristics of TB transmission. The analytical study mainly encompasses well-posedness of the PDE system, the asymptotic behavior of the model around the disease-free equilibrium point and existence criterion of endemic equilibrium point ⁎. A threshold quantity , called basic reproductive number provides the average size of infected population due to a single infectious individual introduced in the naive community. The current expression of offers a notable refinement in basic reproduction number compared to previous estimations. Also, theoretically we observe, detectivity of LTBI cases can both increase and decrease the size of depending upon a parametric condition.