We study a reaction–diffusion mathematical model for the evolution of atherosclerosis as an inflammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction–diffusion system and lead to the complete characterisation of the \(\omega \)-limit for every initial condition. Qualitative properties of the solution are rigorously proved, some of them hinted at by the numerical study.

Sudden water inrush has been a deadly killer in underground engineering for decades. Currently, especially in developing countries, frequent water inrush accidents still kill a large number of miners every year. In this study, an approach for predicting the probability of fault-induced water inrush in underground engineering using the adaptive neuro-fuzzy inference system (ANFIS) was developed. Six parameters related to the aquifer, the water-resisting properties of the aquifuge and the mining-induced stresses were extracted as the major parameters to construct the ANFIS model. The constructed ANFIS was trained with twenty reported real fault-induced water inrush cases, and another five new cases were used to test the prediction performance of the trained ANFIS. The final results showed that the prediction results of the five cases were completely consistent with the actual situations. This indicates that the ANFIS is highly accurate in the prediction of fault-induced water inrush and suggests that quantitative assessment of fault-induced water inrush using the ANFIS is possible.