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Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics

Muhammad Tariq Ali1, Dumitru Baleanu2,3,4, Muhammad Rafiq5, Jan Awrejcewicz6, Nauman Ahmed7, Ali Raza8,*, Muhammad Sajid Iqbal9, Muhammad Ozair Ahmad7

1 Department of Mathematics, Barani Institute of Sciences, Burewala, Pakistan
2 Department of Mathematics, Cankaya University, Balgat, Ankara, 06530, Turkey
3 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan
4 Institute of Space Sciences, Magurele-Bucharest, 077125, Romania
5 Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, 54000, Pakistan
6 Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland
7 Department of Mathematics and Statistics, University of Lahore, Lahore, 54590, Pakistan
8 Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore, 54000, Pakistan
9 H&BS, MCS, National University of Science and Technology (NUST), H-12, Islamabad, Humayun Road, Rawalpindi, 46000, Pakistan

* Corresponding Author: Ali Raza. Email: email

Intelligent Automation & Soft Computing 2023, 36(2), 1479-1496.


The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The Susceptible-Infected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes ‘ℎ’. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease.


Cite This Article

M. T. Ali, D. Baleanu, M. Rafiq, J. Awrejcewicz, N. Ahmed et al., "Numerical analysis for the effect of irresponsible immigrants on hiv/aids dynamics," Intelligent Automation & Soft Computing, vol. 36, no.2, pp. 1479–1496, 2023.

cc 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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