Volume 5, Issue 3 (March 2018), Pages: 39-45
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Original Research Paper
Title: Dynamical behavior of HIV immunology model with non-integer time fractional derivatives
Author(s): Farah Ashraf 1, *, Aqeel Ahmad 1, Muhammad Umer Saleem 2, Muhammad Farman 1, M. O. Ahmad 1
Affiliation(s):
1Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
2Department of Mathematics, University of Education Lahore, Lahore, Pakistan
https://doi.org/10.21833/ijaas.2018.03.006
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Abstract:
This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. Human immunodeficiency virus infection destroys the body immune system, increases the risk of certain pathologies, damages body organs such as the brain, kidney and heart or cause the death. Unfortunately, this infection disease currently has no cure to control the diseases. We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. The Caputo fractional derivative operator of order α∈(0,1] is employed to obtain the system of fractional differential equations. The basic reproductive number is derived for a general viral production rate which determines the local stability of the infection free equilibrium. The solution of the time fractional model has been procured by employing Laplace Adomian decomposition method (LADM) and the accuracy of the scheme is presented by convergence analysis Moreover, numerical simulation are performed to study the dynamical behavior of solution of the models. Simulations of different epidemiological classes at the effect of the fractional parameters α revealed that most undergoing treatment join the recovered class. The results show the both viral production rate and death rate of infected cells play an important role the disease in the society.
© 2018 The Authors. Published by IASE.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: HIV, Caputo fractional derivative, Convergence analysis, Epidemiological model
Article History: Received 12 October 2017, Received in revised form 2 January 2018, Accepted 5 January 2018
Digital Object Identifier:
https://doi.org/10.21833/ijaas.2018.03.006
Citation:
Ashraf F, Ahmad A, Saleem MU et al. (2018). Dynamical behavior of HIV immunology model with non-integer time fractional derivatives. International Journal of Advanced and Applied Sciences, 5(3): 39-45
Permanent Link:
http://www.science-gate.com/IJAAS/2018/V5I3/Ashraf.html
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