A new fractional model for tuberculosis with relapse via Atangana-Baleanu derivative. (English) Zbl 1442.92150

Summary: In this work, a new fractional order epidemic model for the tuberculosis (TB) disease with relapse using Atangana-Baleanu derivative is formulated. The basic reproduction number of the model is investigated using next generation technique. The fixed point theorem is applied to show the existence and uniqueness of solution for the model. A newly proposed numerical scheme in literature is implemented for the iterative solution of the proposed fractional model. The total new and relapse notified TB cases in Khyber Pakhtunkhwa Pakistan from 2002 to 2017 are used to parameterized the model parameters and provided a good fit to the real data. Finally, numerical results are obtained for different values of the fractional order \(\tau\) and the model parameters, in order to validate the importance of the arbitrary order derivative. It is noticed that the non-integer order derivative provides more realistic and deeper information about the complexity of the dynamics of TB model with relapse.


92D30 Epidemiology
34A08 Fractional ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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