In this paper, we have established a SECADI model on the basis of the traditional epidemic model and under the consideration of factors such as the spread of the disease, the quantity of the medicine in need, the medicine production speedetc. We have improved the crowd classification standard and the spread styledifferential equation model in classical SIR model. We distinguished the crowd into six categories, including the susceptible, the exposed, the curable, the advanced, the dead and the immune, and we established integrated transformation relationships between them after taking control measures through qualitative and quantitative method, and then derive the adequate epidemic differential equation model before taking controls. We applied the method of computer simulation to solve the model, worked out uncertain parameters with the method of parameter identification, and we verified the validity and accuracy of the SECADI model. Meanwhile, we calculated with the actual data of Ebola in the epidemic area in WesternAfrica, simulated the evolution of the epidemic, analyze and offered effective approaches to control the epidemic situation. We further discussed development directions of this model in the end.