Analysis of a mathematical model for interactions between T cells and macrophages

TL;DR

This paper provides a mathematical analysis of a differential equation model for T cell and macrophage interactions, establishing conditions for stationary solutions and stability, and exploring the existence of periodic behaviors.

Contribution

It offers new theoretical insights into the stability and solution structure of a biological interaction model, including conditions for multiple stationary solutions.

Findings

Theorems on the number and stability of stationary solutions.

Conditions under which periodic solutions or heteroclinic cycles do not exist.

Evidence that a simpler model can describe the same phenomena.

Abstract

The aim of this paper is to carry out a mathematical analysis of a system of ordinary differential equations introduced by R. Lev Bar-Or to model the interactions between T cells and macrophages. Under certain restrictions on the parameters of the model, theorems are proved about the number of stationary solutions and their stability. In some cases the existence of periodic solutions or heteroclinic cycles is ruled out. Evidence is presented that the same biological phenomena could be equally well described by a simpler model.