Coronary heart disease (CHD) is caused by various reasons. One of the main causes of coronary heart disease is cholesterol. Cholesterol comes from two sources, namely, that which is produced by the liver and through the food consumed. This article discusses the mathematical model of coronary heart disease which refers to the SEI (Susceptible-exposed-infected) model, with modifications in the form of the addition of the recovered (R) variable and parameters in the form of a healthy lifestyle and surgery. Hereinafter this model is called the SEIR (Susceptible-Exposed-Infected-Recovered) model. This study aims to determine the problem of coronary heart disease in cholesterol sufferers and to analyze the effect of operating parameters and a healthy lifestyle on the patient's healing (R) is higher than the opportunity value of the other groups. And the opportunity value of an infected individual is much lower than that of other groups. This shows that the chances of recovery for people with coronary heart disease with a high operating route.

An Octa-Chain graph (OCm) is a graph formed by modifying the cycle graph C8 by adding an edge connecting the midpoints in C8. The minimum number of colors used to color the vertices in a graph so that every two vertices have a rainbow path is called the rainbow vertex-connected number denoted by rvc (G). While the minimum number of colors used to color the vertices in a graph so that every two vertices are always connected by a rainbow path is called a strong rainbow vertex connected number and is denoted by srvc (G). This study aims to determine the rainbow vertex-connected number (rvc) and the strong rainbow-vertex-connected number (srvc) in the Octa-Chain graph (OCm). The results obtained from this research are the rainbow vertex-connected number rvc (OCm)=2m and the strong rainbow-vertex-connected number srvc (OCm)=2m.