Abstract:
Atherosclerosis is a chronic in
ammatory cardiovascular disease in which arteries
harden through the build-up of plaques. This work is devoted to the mathematical
modeling and analysis of the in
ammatory process of atherosclerosis. We propose
a mathematical model formed by three coupled partial di erential equations of
reaction-di usion type. We take into account three key-role players: the immune
cells (M), the in
ammatory cytokines (A) and the oxidized LDL (L).
8>>>>>>>>>><
>>>>>>>>>>:
@M
@t
= d1
@2M
@x2 + L +
1A
1 + A= 1
+ ML
ML 1M
@A
@t
= d2
@2A
@x2 +
2A
1 + A= 2
M 2A
@L
@t
= d3
@2L
@x2 +
M
1 +M= 3
3L
A stability analysis of the kinetic system is performed followed by a detailed
discussion about the biological interpretation. Several cases may occur ; every
case corresponds to a biological situation. Then a holistic conclusion is established.
We investigate as well the existence of solutions of traveling waves type
along with numerical simulations that show the wave propagation in the di erent
cases. These results con rm and generalize previous results published in [1, 2].
