A fractional model for the dynamics of TB virus. (November 2018) - Ullah, Saif; Altaf Khan, Muhammad; Farooq, Muhammad
Highlights: A fractional TB model with Caputo derivative is presented. The real data of TB since 2002–2017 of Khyber Pakhtunkhwa, is considered. The model is locally and globally stable with fractional Lyapunov function. Numerical results with long term behavior of the infected individuals is presented. Abstract: In this paper, we present a nonlinear fractional order model in the Caputo sense to explore and simulate the TB dynamics. Using the TB confirmed notified cases from the year 2002 to 2017 in Khyber Pakhtunkhwa, Pakistan, we estimate the model parameters and demonstrate that the proposed fractional model provides a good fit to the real data. Initially, we compute the basic reproduction number and the model equilibria. Then, the existence and uniqueness of the model are shown via generalized mean value theorem. Further, we explore the local and global stability of the disease free equilibria in fractional environment. Finally, numerical results are obtained in order to validate the importance of the arbitrary order derivative and theoretical results. We conclude that the fractional epidemic model is more generalized than the classical model, which give more information about the disease dynamics and give a good agreement to the real data of TB infection.