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Modeling of Anthrax Disease via Efficient Computing Techniques

Ali Raza1,2, Dumitru Baleanu3,4, Muhammad Yousaf2, Naeem Akhter2, Syed Kashif Mahmood2, Muhammad Rafiq5,*
1 Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, 52000, Punjab Higher Education Department (PHED), Lahore, 54000, Pakistan
2 Department of Mathematics, National College of Business Administration and Economics, Lahore, 54660, Pakistan
3 Department of Mathematics, Cankaya University, Ankara, 06530, Turkey
4 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan
5 Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, 54000, Pakistan
* Corresponding Author: Muhammad Rafiq. Email:

Intelligent Automation & Soft Computing 2022, 32(2), 1109-1124.

Received 13 August 2021; Accepted 14 September 2021; Issue published 17 November 2021


Computer methods have a significant role in the scientific literature. Nowadays, development in computational methods for solving highly complex and nonlinear systems is a hot issue in different disciplines like engineering, physics, biology, and many more. Anthrax is primarily a zoonotic disease in herbivores caused by a bacterium called Bacillus anthracis. Humans generally acquire the disease directly or indirectly from infected animals, or through occupational exposure to infected or contaminated animal products. The outbreak of human anthrax is reported in the Eastern Mediterranean regions like Pakistan, Iran, Iraq, Afghanistan, Morocco, and Sudan. Almost ninety-five percent chances are the transmission of the bacteria from forming spores by the World Health Organization (WHO). The modeling of an anthrax disease is based on the four compartments along with two humans (susceptible and infected) and others are dead bodies and sporing agents. The mathematical analysis is studied along with the fundamental properties of deterministic modeling. The stability of the model along with equilibria is studied rigorously. The authentication of analytical results is examined through well-known computer methods like Euler, Runge Kutta, and Non-standard finite difference (NSFD) along with the feasible properties (positivity, boundedness, and dynamical consistency) of the model. In the end, comparison analysis of algorithms shows the effectiveness of the methods.


Anthrax disease; deterministic modeling; stability analysis; computer methods

Cite This Article

A. Raza, D. Baleanu, M. Yousaf, N. Akhter, S. Kashif Mahmood et al., "Modeling of anthrax disease via efficient computing techniques," Intelligent Automation & Soft Computing, vol. 32, no.2, pp. 1109–1124, 2022.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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