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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.
  • S. L’KIMA,
  • Abdelouahed Allahamou,
  • E. AZROUL
S. L’KIMA
Universite Sidi Mohamed Ben Abdellah Faculte des Sciences Dhar El Mahraz-Fes

Corresponding Author:safae.lkima@usmba.ac.ma

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Abdelouahed Allahamou
Universite Mohammed V de Rabat
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E. AZROUL
Universite Sidi Mohamed Ben Abdellah Faculte des Sciences Dhar El Mahraz-Fes
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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.
25 Mar 2023Submitted to Mathematical Methods in the Applied Sciences
25 Mar 2023Submission Checks Completed
25 Mar 2023Assigned to Editor
31 Mar 2023Review(s) Completed, Editorial Evaluation Pending
03 Apr 2023Reviewer(s) Assigned
12 Aug 2023Editorial Decision: Revise Major
15 Oct 20231st Revision Received
17 Oct 2023Submission Checks Completed
17 Oct 2023Assigned to Editor
17 Oct 2023Review(s) Completed, Editorial Evaluation Pending
22 Oct 2023Reviewer(s) Assigned
15 Nov 2023Editorial Decision: Revise Major