Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point

• Main Authors: Irina Volinsky, Salvo Danilo Lombardo, Paz Cheredman
• Format: Article
• Language: English
• Published: MDPI AG 2021-01-01
• Series: Symmetry
• Subjects: functional differential equations; exponential stability; Cauchy matrix; integro-differential systems; hepatitis B; feedback control
• Online Access: https://www.mdpi.com/2073-8994/13/2/166

Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices <inline-formula><math display="inline"><semantics><mrow><mi>C</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, which allow us to construct and analyze the stability of corresponding integro-differential systems.