A nonlinear epidemic model for tuberculosis with Caputo operator and fixed point theory

Tuberculosis (TB) is one of the most dangerous infectious diseases which spreads from one person to another through the air and often attacks the lungs. A mathematical model of TB with control measures is considered in this paper. The integer order time derivative is modeled via the Caputo fractional order operator. A reliable numerical technique was applied to discretize the fractional derivative. The existence and uniqueness of solutions are examined. The effect of the control parameters was investigated through some numerical experiments. The effect of variation of the fractional-order parameters on the susceptible, early latent, infected, persistent latent, and recovered population with respect to time are given via figures and discussed. It was observed that a model with a fractional order parameter could serve as a good control measure to the spread of TB.