Approximation treatment for Linear Fuzzy HIV Infection Model by Variational Iteration Method

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.

Some properties of integration of real-valued function over a fuzzy interval

“…Lastly, the extension principle is shown to be very useful for defining settheoretic operations for higher fuzzy sets, then before building the properties of integration of a crisp real-valued function over a fuzzy interval we need some definitions related to our properties. To characterize the mathematical model of fuzzy HIV dynamics, the authors presented the approximate technique known as VIM in Saleh et al (2021). In the linear fuzzy HIV infection model, VIM is reformulated and studied in terms of the fuzzy domain.…”