Dynamical Behaviour of Pro- and Anti-Inflammatory Cytokines during Pathogenesis of Atherosclerosis

The role of anti-cytokines in atherosclerosis is to reduce inflammation in the intima. In some situations, certain anti-inflammatory cytokines like TGF-beta and IL-6 have shown the characteristics like a pro-inflammatory cytokines, which are showing different natures. In this study, a dynamical atherosclerosis model is proposed in the form of reaction-diffusion equation with consideration of immune cells, pro-inflammatory cytokines, and anti-inflammatory cytokines. The existence and uniqueness of the solutions are discussed for the proposed reaction dynamical system. The three equilibrium points, non-inflammatory, chronic, and coexistence, and their local stability are also determined for the model. Bellman and Cooke’s theorem is applied to illustrate the global stability at the coexistence equilibrium point. The effects of pro- and anti-inflammatory cytokines have also been discussed. The analytical and numerical studies evidently indicate that inflammation behaves differently when a certain number of anti-inflammatory cytokines behave like pro-inflammatory cytokines. The numerical simulations are demonstrated for different impacts of the reduction rate of macrophages due to the presence of anti-inflammatory cytokines, inhibition time, and the portion of anti-inflammatory cytokines behaving like pro-inflammatory cytokines through graphically. The results of this study suggest that chronic inflammation of the disease is likely to persist when a high concentration of ox-LDL and moderate concentration of cytokines are present in the intima. Coexistence inflammation is characterized by a high concentration of ox-LDL, moderate concentration of pro-inflammatory and high concentration of anti-cytokines; whereas a non-inflammatory condition would persevere if a low concentration of ox-LDL has been present in the intima.