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The effect of migration on the transmission of HIV/AIDS using a fractional model: Local and global dynamics and numerical simulations.
- Source :
- Mathematical Methods in the Applied Sciences; 5/30/2024, Vol. 47 Issue 8, p6868-6891, 24p
- Publication Year :
- 2024
-
Abstract
- Human immunodeficiency virus (HIV) is a serious disease that threatens and affects capital stock, population composition, and economic growth. This research paper aims to study the mathematical modeling and disease dynamics of HIV/acquired immunodeficiency syndrome (AIDS) with memory effect. We propose two fractional models in the Caputo sense for HIV/AIDS with and without migration. First, we prove the existence and positivity of both models and calculate the basic reproduction number R0$$ {\mathcal{R}}_0 $$ using the next generation method. Then, we study the local and global stability of the obtained equilibria. In addition, numerical simulations are provided for different values of the fractional order ρ$$ \rho $$ using the Adams–Bashforth–Moulton fractional scheme, to verify the theoretical results. Moreover, a sensitivity analysis of the parameters for the model with migration is carried out. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 47
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 177083253
- Full Text :
- https://doi.org/10.1002/mma.9946