The role of anti-cytokines in atherosclerosis is to reduce the 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 nature. 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 is discussed for 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 discussed. The analytical and numerical studies evidently indicate that inflammation behaves differently when a certain amount of anti-inflammatory cytokines will behave like pro-inflammatory cytokines. The numerical simulations are demonstrated for different impact of reduction rate of macrophages due to presence of anti-inflammatory cytokines, inhibition time, and the portion of anti-inflammatory cytokines behaving like pro-inflammatory cytokines through graphically.
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