Atherosclerosis is a chronic inflammatory cardiovascular disease in which arteries harden through the build-up of plaques. This work is devoted to the mathematical modeling and analysis of the inflammatory process of atherosclerosis. We propose a mathematical model formed by three coupled partial differential equations of reaction-diffusion type. We take into account three key-role players: the inflammatory immune cells, the inflammatory cytokines and the oxidized low density lipoproteins. A stability analysis of the kinetic system is performed. It leads to the presence of three stable fixed points relevant to appropriate biological states of atherogenesis; no inflammation, stabilized inflammation (stable plaque) and advanced inflammation (vulnerable plaque). The cases that may occur are subject to the variation of the parameters values. A detailed discussion showing how the model fits the biological phenomena is then established. We investigate as well the existence of solutions of traveling waves type along with numerical simulations that show the wave propagation in different cases. This shows that the inflammatory process propagates inside the intima as a traveling wave. Then, we consider the effect of high density lipoprotein (HDL) on the atherosclerotic plaque formation. To do that, we elaborate a map that determines the level of risk of plaque formation with respect to the prevalence of HDL in the blood. These results confirm but also generalize previous results published in the literature. They also give a deeper understanding to the propagation of the inflammation inside the artery in terms of the interplay among the different main players in the whole process.

动脉粥样硬化是一种慢性炎症性心血管疾病，其中动脉通过斑块的积聚而变硬。这项工作致力于动脉粥样硬化炎症过程的数学建模和分析。我们提出了一个由三个反应扩散型耦合偏微分方程组成的数学模型。我们考虑了三个关键角色：炎性免疫细胞、炎性细胞因子和氧化的低密度脂蛋白。执行动力学系统的稳定性分析。它导致存在与动脉粥样硬化的适当生物学状态相关的三个稳定固定点；无炎症、稳定炎症（稳定斑块）和晚期炎症（易损斑块）。可能发生的情况受参数值变化的影响。然后建立显示模型如何拟合生物现象的详细讨论。我们还研究了行波类型解的存在以及显示不同情况下波传播的数值模拟。这表明炎症过程在内膜内作为行波传播。然后，我们考虑高密度脂蛋白 (HDL) 对动脉粥样硬化斑块形成的影响。为此，我们精心制作了一张图，根据血液中 HDL 的流行程度确定斑块形成的风险水平。这些结果证实但也概括了以前发表在文献中的结果。他们还从整个过程中不同主要参与者之间的相互作用方面更深入地了解动脉内炎症的传播。