Regimes and Mechanisms of Inflammation Described by a Reaction–Diffusion System

ABSTRACT Inflammation is a biological response of the immune system to external stimuli such as injury or infection. It plays an important role in various diseases including atherosclerosis, cancer, and neurodegenerative diseases. This work presents a generic inflammation model based on reaction–diffusion equations that describes the concentrations of uninflamed cells, inflamed cells, classically activated macrophages, and pro‐inflammatory cytokines. The mathematical analysis of the model shows several regimes of inflammation progression, namely, the setup of a chronic inflammation, low‐grade inflammation, hyperinflammation, and a noninflammatory state. We also examine the existence of traveling wave solutions and focus on describing the wave speed of inflammation propagation by analytical and numerical methods. Finally, we present numerical simulation to show different regimes and mechanisms of inflammation propagation.