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Vomiting and diarrhoea can affect the amount of medication absorbed from the gut into the blood stream. Mainly because nothing is staying in the gut long enough to be absorbed if you are unwell. This can cause a drop in blood levels of antiseizure medication, and consequently a higher risk of seizures. Illness and dehydration are also risk factors for seizures.
If vomiting happens within minutes of taking the medication, another dose can be taken. However, you will need to speak to your doctor about measures to take if vomiting and diarrhoea are persistent. Along with the approach your doctor suggests, it is also important to rest and try and keep your fluids up when sick.