Effect of anti-inflammatory processes on the development of inflammation in a reaction-diffusion model

Inflammation is considered as a fundamental defense mechanism of our organism, responding to various damages engendered to living tissue. This work presents a generic inflammation model based on reaction-diffusion equations that describe the concentrations of uninflamed cells, inflamed cells, pro-inflammatory mediators of inflammation (classically activated macrophages and pro-inflammatory cytokines) and anti-inflammatory mediators of inflammation (alternatively activated macrophages and anti-inflammatory cytokines). The mathematical analysis of the system shows several regimes of inflammation propagation. We also focus on the impact of the anti-inflammatory mechanism and we examine the wave speed of inflammation progression by analytical and numerical methods. Finally, we perform numerical simulations and suggest biological interpretations of the results.