# On the Distributed Order Fractional Multi-Strain Tuberculosis Model: a Numerical Study

• Nasser Sweilam Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
• S. M. AL-Mekhlafi Department of Mathematics, Faculty of Education, Sana’a University, Yemen
• A. O. Albalawi Department of Mathematics, Faculty of Science, Shaqra University, Riyadh, KSA
Keywords: Tuberculosis, Distributed order fractional calculus, Grünwald-Letnikov definition, Nonstandard finite difference method

### Abstract

In this paper, a novel mathematical distributed order fractional model of multistrain Tuberculosis is presented. The proposed model is governed by a system of distributed order fractional differential equations, where the distributed order fractional derivative is defined in the sense of the Grünwald-Letinkov definition. A nonstandard finite difference method is proposed to study the resulting system. The stability analysis of the proposed model is discussed. Numerical simulations show that the nonstandard finite difference method can be applied to solve such distributed order fractional differential equations simply and eectively.

### Author Biographies

Nasser Sweilam, Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
S. M. AL-Mekhlafi, Department of Mathematics, Faculty of Education, Sana’a University, Yemen
Department of Mathematics, Faculty of Education, Sana’a University, Yemen
A. O. Albalawi, Department of Mathematics, Faculty of Science, Shaqra University, Riyadh, KSA
Department of Mathematics, Faculty of Science, Shaqra University, Riyadh, KSA

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Published
2020-02-18
How to Cite
Sweilam, N., M. AL-Mekhlafi, S., & O. Albalawi, A. (2020). On the Distributed Order Fractional Multi-Strain Tuberculosis Model: a Numerical Study. Statistics, Optimization & Information Computing, 8(1), 175-186. https://doi.org/10.19139/soic-2310-5070-621
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Research Articles