Dynamical mechanisms of inflammatory spatial distribution and its association with recurrence in Crohn's disease

Crohn's disease (CD) is a recurrent chronic autoimmune disease, which is an inflammatory disease of the intestine with epithelial granulomas. The number of patients has been increasing significantly, and its pathogenesis and treatments are arousing hot discussions in the academic community. Taking into account the spatial heterogeneity of lesion distribution and the periodic recurrence, this paper uses a partial functional differential system with the free diffusion of bacteria and immunocytes and immune response latency to model the process of CD, based on the Lauffenburger-Kennedy bacterial infection model. In order to describe the spatial distribution and recurrence, we analyze the stability of the inflammation equilibrium state, and deduce the diffusion-driven Turing bifurcations and delay-driven Hopf bifurcations, drive the critical conditions for occurrence. Furthermore, through the analysis of Turing-Hopf bifurcations, the coupling effect of two factors is explored to obtain spatiotemporal patterns that better reflect clinical manifestations of CD. In addition, both theoretical and numerical results reveal that the motility is a necessary factor in the production of intestinal epithelial granulomas, while the immune response latency is an important factor in the recurrence. A small effective diffusion rate and a large time delay would lead to two spatially non-homogeneous steady states and a stable periodic solution, ultimately giving rise to a pair of stable spatially non-homogeneous periodic solutions through Turing-Hopf bifurcations. Our conclusions may provide some insights into the control mechanisms for Crohn's disease.