A mathematical model of TB control with vaccination in an age-structured susceptible population

Abstract

A new mathematical model for the transmission dynamics of tuberculosis (TB) with the intervention of vaccination in an age-structured susceptible population is designed and analyzed in this article. The model is constructed as an SEIR-based system of ten-dimensional ordinary differential equation. Each population is then further classified according to its age-class; children (<15 years old) and adult (15-65 years old). In the susceptible population, the classification goes even further by taking vaccination criteria into account. Mathematical analysis of the equilibrium points and its local stability is performed, both analytically and numerically, to help understand the possibility of the situation in the field for long-term behavior. We also show the form of the basic reproduction number as the spectral radius of the next- generation matrix. The basic reproduction number will become the threshold parameter to handle the existence of equilibrium points. Numerical simulations of the model are done for various scenarios to provide a better understanding of the analytical results. We can conclude that the vaccination strategy is successful in suppressing the spread of TB among the human population.