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

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 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 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.