If a program was used it could have been relatively simple, such as total number of sick days or it could have been more advanced and looked for specific patterns such as one or two days per month which could suggest misuse but exclude a single block which would imply a genuine illness. Only the upper levels know the exact markers used and the importance given to them.
A company the size of Emirates would have contingency plans drawn up to cater for various scenarios such as natural disasters, civil unrest etc, but I doubt many operators were prepared for a downturn on this scale or a sudden reduction in crew numbers which might approach 20%.