A fractional order model for the dynamics of tuberculosis spread

Abstract

In this paper, we establish a mathematical model for Tuberculosis (TB) spread in a human population. The proposed mathematical model is in the form of a nonlinear fractional order differential equation system which is an extension of the SEIR epidemic model. The model is constructed based on grouping the population into five compartments, namely the susceptible sub-population compartment, the exposed sub-population compartment, the infected sub-population compartment, the quarantine sub-population compartment, and the recovered subpopulation compartment. It was shown that the stability of the equilibrium points of the model depends on the basic reproduction number, and the addition of the quarantine sub-population compartment decreases the number of basic reproduction. A numerical simulation is given to demonstrate the validity of the results. The analysis reveals that the convergence to the equilibrium points becomes faster as the fractional order increases.