TY  - EJOU
AU  - Ali, Muhammad Tariq 
AU  - Baleanu, Dumitru 
AU  - Rafiq, Muhammad 
AU  - Awrejcewicz, Jan 
AU  - Ahmed, Nauman 
AU  - Raza, Ali 
AU  - Iqbal, Muhammad Sajid 
AU  - Ahmad, Muhammad Ozair 

TI  - Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics
T2  - Intelligent Automation \& Soft Computing

PY  - 2023
VL  - 36
IS  - 2
SN  - 2326-005X

AB  - 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.
KW  - SIR model; existence analysis; numerical methods; stability analysis

DO  - 10.32604/iasc.2023.033157