Local and systemic factors in the resolution of inflammation

Inflammation is a fundamental component of immune response, triggered by harmful stimuli to protect tissues, promote healing, and restore homeostasis. This process unfolds in distinct stages: initiation, amplification, and resolution. The transition from the amplification phase to resolution is crucial for restoring tissue homeostasis, and failure to achieve this transition can lead to chronic inflammation and the development of various diseases. Despite its importance, the biological mechanisms governing this transition remain insufficiently understood. In this work, we develop a mathematical model to explore the interplay between pro- and anti-inflammatory mediators in inflammation resolution. The model consists of a delayed integro-differential reaction-diffusion system that captures the spatial and temporal evolution of inflammation within tissue. Specifically, the model tracks the concentrations of uninflamed cells, inflamed cells, and pro-inflammatory mediators (classically activated macrophages and pro-inflammatory cytokines), as well as anti-inflammatory mediators (alternatively activated macrophages, tissue-resident macrophages (TRM), and anti-inflammatory cytokines). Mathematical analysis reveals several distinct states of inflammation propagation, highlighting conditions under which inflammation either resolves or transitions to chronic states. A particular focus is placed on the dynamic roles of both tissue-resident and circulating macrophages, demonstrating how these immune cells influence inflammation outcomes. Numerical simulations illustrate potential pathways toward inflammation resolution and offer biological interpretations that could inform therapeutic strategies targeting chronic inflammation.