Open Access

ARTICLE

Modeling the Spread of Tuberculosis with Piecewise Differential Operators

Abdon Atangana^1,2, Ilknur Koca^3,*
1 Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, 9301, South Africa
2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 008864, Taiwan
3 Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sitki Kocman University, Mugla, 48300, Turkey
* Corresponding Author: Ilknur Koca. Email:
(This article belongs to this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 131(2), 787-814. https://doi.org/10.32604/cmes.2022.019221

Received 09 September 2021; Accepted 09 November 2021; Issue published 14 March 2022

Abstract

Very recently, a new concept was introduced to capture crossover behaviors that exhibit changes in patterns. The aim was to model real-world problems exhibiting crossover from one process to another, for example, randomness to a power law. The concept was called piecewise calculus, as differential and integral operators are defined piece wisely. These behaviors have been observed in the spread of several infectious diseases, for example, tuberculosis. Therefore, in this paper, we aim at modeling the spread of tuberculosis using the concept of piecewise modeling. Several cases are considered, conditions under which the unique system solution is obtained are presented in detail. Numerical simulations are performed with different values of fractional orders and density of randomness.

---

Keywords

Spread of tuberculosis; piecewise differentiation; numerical simulation

---