The effect of migration on the transmission of HIV/AIDS using a
fractional model: local and global dynamics and numerical simulations.
Abstract
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/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 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 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.