Journal
CHAOS SOLITONS & FRACTALS
Volume 131, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2019.109500
Keywords
HIV viral dynamic model; Homotopy analysis method (HAM); Stability analysis; Lyapunov function; Reproduction number R-0; Auxiliary parameter (h)over-bar
Categories
Funding
- National Natural Science Foundation of China [11971375, 11571272, 11201368 and11631012]
- National Science and Technology Major Project of China [2018ZX10721202]
- China Postdoctoral Science Foundation [2014M560755]
- Natural Science Foundation of Shaanxi Province [2019JM-273]
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Viruses have different mechanisms in causing a disease in an organism, which largely depend on the viral species. The recent advancement, through coupling data analysis and mathematical modeling, has allowed the identification and characterization of the nature of the virus. In the present paper, the homotopy analysis method is applied to provide an approximate solution of the basic HIV viral dynamic model describing the viral dynamics in a susceptible population. The proposed method allows for the solution of the governing system of differential equations to be calculated in the form of an infinite series with components which can be easily calculated. The homotopy analysis method utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. By using the homotopy series solutions, firstly, several beta-curves using an appropriate ratio are plotted to demonstrate the regions of convergence and the optimum value of (h) over bar, then the residual and absolute errors are obtained for different values of these regions. Secondly, the residual error functions are applied to show the accuracy of the applied homotopy analysis method. Also, the convergence theorem of homotopy analysis method for the HIV viral dynamic model is proved. Mathematica software is used for the calculations and numerical results. The results obtained show the effectiveness and strength of the homotopy analysis method. (C) 2019 Elsevier Ltd. All rights reserved.
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