Mathematical analysis of a tuberculosis transmission model with vaccination in an age structured population

Abstract

This article presents a mathematical model of Tuberculosis (TB) transmission considering BCG vaccination in an age- structured population. We used several strategies to simulate the TB dynamic and evaluate the potential impact on active TB. We developed a deterministic compartmental model where the population was distributed into seven compartments, i.e., susceptible individuals that can be vaccinated (S 1 ) and can't be vaccinated (S 2 ), vaccinated (V), slow (L) and fast (E) exposed, infectious (I), and recovery (R). The mathematical model analysis was done by determining the equilibrium points, the Basic Reproduction Number (R 0 ) of the model, and analysing the stability of the equilibrium point. Some numeric interpretations were given by sensitivity vaccination parameters and percentage vaccine protection to the value of R 0 and autonomous model simulations. We find that to reach TB free condition is not enough by maximising one of the vaccination parameters for newborn, adults or percentage vaccine protection. We also find that vaccination into the adult population is more effective to suppress TB spread rather than newborn.