A Local Analysis of a Mathematical Pattern for Interactions between the Human Immune System and a Pathogenic Agent

Abstract

In the present study, we introduce a four-dimensional deterministic mathematical pattern in order to study the interactions between the human immune system and a virus. The model is based on a system with four first-order ordinary differential equations, and the main aim of the paper is to perform a mathematical analysis of the local behavior of the associated dynamical system using the tools of the qualitative theory of dynamical systems. Moreover, two types of patterns with controls were introduced; consequently, some very interesting theoretical conclusions with medical relevance were obtained.

Keywords

• local stability
• dynamical systems
• mathematical model for immune system–virus interaction
• prey–predator model
• system of ordinary differential equations