 A new fractional model for tuberculosis with relapse via Atangana–Baleanu derivativeMuhammad Altaf Khan, Saif Ullah and Muhammad Farooq Chaos, Solitons & Fractals, 2018, vol. 116, issue C, 227-238 Abstract: 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 τ 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. Keywords: Tuberculosis model; Atangana–Baleanu fractional derivative; Model fitting; Numerical results; Fixed point theorem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:116:y:2018:i:c:p:227-238 DOI: 10.1016/j.chaos.2018.09.039 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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