Stability Analysis of a Mathematical Model of Hepatitis B Virus with Unbounded Memory Control on the Immune System in the Neighborhood of the Equilibrium Free Point

Abstract

In the current paper, I research the influence of IL-2 therapy and I introduce the regulation by distributed feedback control with unbounded memory. The results of the stability analysis are presented. The proposed methodology in the article uses the properties of Cauchy matrix C(t,s), especially symmetry property, in order to study the behavior (stability) of the corresponding system of integro-differential equations.

Factorization of abstract operators into two second degree operators and its applications to integro-differential equations

“…Integro-differential equations (IDEs) are used to model many problems in science, engineering, economics, medicine, control theory, micro-inhomogeneous media and viscoelasticity [1][2][3][4][5][6][7][8][9]. Very important tools in solving of Boundary Value Problems (BVPs) with IDEs are the Parametrization Method [10] and the Factorization (Decomposition) method, but the applicability of the last method is confined to certain kinds of integro-differential operators, corresponding to BVPs and cannot be universal for all problems.…”

Stabilization of n-Order Function Differential Equations by Parametric Distributed Control Function with Palindromic Parameters Set

“…Distributed feedback control stabilization of mathematical models, is also significant in medicine (see, for example, [12][13][14][15], where the mathematical model of testosterone regulation and model of the hepatitis B virus were researched).…”

A Procedure for Factoring and Solving Nonlocal Boundary Value Problems for a Type of Linear Integro-Differential Equations

“…Integro-differential equations arise in many areas in sciences and engineering. For example, Fredholm and Volterra integro-differential equations are used in [1][2][3] for modeling neural networks; Fredholm integro-differential equations are utilized in [4,5] to model the response of plates and shells in the theory of elasticity; Volterra integro-differential equations are employed in [6][7][8] to simulate thermal problems in the glass-forming process, drug concentrations in pharmacokinetics, and Hepatitis B Virus infection in medicine, respectively.…”