### Journals Information

Mathematics and Statistics Vol. 12(3), pp. 219 - 228
DOI: 10.13189/ms.2024.120301
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## Computational Solution and Analysis of Fuzzy Nonlinear HIV Infection Model via New Multistage Fuzzy Variational Iteration Method

Hafed. H. Saleh 1, Amirah Azmi 1,*, Ali. F. Jameel 2,3
1 School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia
2 Faculty of Education and Arts, Sohar University, Oman
3 Institute of Strategic Industrial Decision Modelling (ISIDM), School of Quantitative Sciences (SQS), Universiti Utara Malaysia (UUM), Malaysia

ABSTRACT

In order to obtain sufficient solutions for fuzzy differential equations (FDEs), reliable and efficient approximation methods are necessary. Approximate numerical methods can not directly solve fuzzy HIV models. Meanwhile, the approximate analytical methods can potentially provide more straightforward solutions without the need for extensive numerical computations or linearization and discretization techniques, which may be challenging to apply to fuzzy models. One significant advantage of approximate analytical methods is their ability to provide insights into solution accuracy without requiring an exact solution for comparison, where an exact solution may not be readily available. In this work, the fuzzy nonlinear HIV infection model is analyzed and solved using the new fuzzy form of an approximate analytical method. Fuzzy set theory mixed with standard fuzzy variational iteration method (FVIM) properties is utilized to produce a new formulation denoted by the multistage fuzzy variational iteration method (MFVIM) to process and solve a fuzzy nonlinear HIV infection model. MFVIM offers an effective method for attaining convergence in the series solution presented as a polynomial function. This approach enables efficient solutions to diverse mathematical challenges. The solution methodology is reliant on fuzzy differential equations conversion into systems of ordinary differential equations, utilizing the parametric form regarding its r-level representations, and considering the approximate solution of the system in a sequence of intervals. Subsequently, the equivalent classical systems are resolved by applying FVIM algorithms in each subinterval. Also, the existence and unique solution analysis of the proposed problem have been described, along with a fuzzy optimal control analysis. A tabular and graphical representation of the MFVIM of the proposed models is presented and analyzed in comparison with the numerical method and FVIM. The new method produces better performance in terms of solutions than a numerical method with a simple implementation for solving fuzzy nonlinear HIV infection model associated with FIVPs. The ability to better comprehend the behavior of the system under investigation can enable researchers and scientists to work on models incorporating systems with long memories and ill-defined notions to make more effective design and decision-making.

KEYWORDS
Fuzzy Initial Value Problems, Fuzzy Nonlinear HIV Infection Model, Control Function, Fuzzy Variational Iteration Method, Multistage Fuzzy Variational Iteration Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Hafed. H. Saleh , Amirah Azmi , Ali. F. Jameel , "Computational Solution and Analysis of Fuzzy Nonlinear HIV Infection Model via New Multistage Fuzzy Variational Iteration Method," Mathematics and Statistics, Vol. 12, No. 3, pp. 219 - 228, 2024. DOI: 10.13189/ms.2024.120301.

(b). APA Format:
Hafed. H. Saleh , Amirah Azmi , Ali. F. Jameel (2024). Computational Solution and Analysis of Fuzzy Nonlinear HIV Infection Model via New Multistage Fuzzy Variational Iteration Method. Mathematics and Statistics, 12(3), 219 - 228. DOI: 10.13189/ms.2024.120301.