Analysis of the impact of time delay incorporation in mathematical models of cellular population dynamics

Abstract

In this work, we investigate the effects of introducing a time delay in a mathematical model of cellular population dynamics with relevance in the development of chronic autoimmune diseases. Then, we determine the equilibrium states of the delayed system and investigate their asymptotic stability. We construct a Lyapunov function and use LaSalle's invariance principle to study the global stability of a biologically meaningful disease-free equilibrium. Some numerical simulations are performed, in which we can observe the long-time behavior of the solution and its approach to a stable equilibrium state. The simulations also show how the delay affects the behavior of the solution and its asymptotic trend.