### Journals Information

Mathematics and Statistics Vol. 9(3), pp. 342 - 349
DOI: 10.13189/ms.2021.090316
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## Approximation treatment for Linear Fuzzy HIV Infection Model by Variational Iteration Method

Hafed H Saleh 1, Azmi A. 1, Ali. F. Jameel 2,*
1 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
2 School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah, Malaysia

ABSTRACT

There has recently been considerable focus on finding reliable and more effective approximate methods for solving biological mathematical models in the form of differential equations. One of the well-known approximate or semi-analytical methods for solving linear, nonlinear differential well as partial differential equations within various fields of mathematics is the Variational Iteration Method (VIM). This paper looks at the use of fuzzy differential equations in human immunodeficiency virus (HIV) infection modeling. The main advantage of the method lies in its flexibility and ability to solve nonlinear equations easily. VIM is introduced to provide approximate solutions for linear ordinary differential equation system including the fuzzy HIV infection model. The model explains the amount of undefined immune cells, and the immune system viral load intensity intrinsic that will trigger fuzziness in patients infected by HIV. CD4+T-cells and cytototoxic T-lymphocytes (CTLs) are known for the immune cells concerned. The dynamics of the immune cell level and viral burden are analyzed and compared across three classes of patients with low, moderate and high immune systems. A modification and formulation of the VIM in the fuzzy domain based on the use of the properties of fuzzy set theory are presented. A model was established in this regard, accompanied by plots that demonstrate the reliability and simplicity of the methods. The numerical results of the model indicate that this approach is effective and easily used in fuzzy domain.

KEYWORDS
Fuzzy Set Theory, Fuzzy Differential Equations, Fuzzy HIV Infection Model, Analytical Solution, Variational Iteration Method (VIM)

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Hafed H Saleh , Azmi A. , Ali. F. Jameel , "Approximation treatment for Linear Fuzzy HIV Infection Model by Variational Iteration Method," Mathematics and Statistics, Vol. 9, No. 3, pp. 342 - 349, 2021. DOI: 10.13189/ms.2021.090316.

(b). APA Format:
Hafed H Saleh , Azmi A. , Ali. F. Jameel (2021). Approximation treatment for Linear Fuzzy HIV Infection Model by Variational Iteration Method. Mathematics and Statistics, 9(3), 342 - 349. DOI: 10.13189/ms.2021.090316.