This is an international, multicenter, open-label, long-term safety study of ZX008 in pediatric and young adult subjects with Dravet syndrome who have successfully completed 14 weeks of treatment in one of the core studies (ZX008-1501 and ZX008-1502) and are candidates for continuous treatment for an extended period of time. Subjects will be permitted to participate in the present study after they complete the final evaluation at Day 113 in one of the core studies. This trial will consist of a 12-month Open-Label Extension (OLE) Treatment Period and a 2-week Post-Dosing Period. Thus, subjects who complete this trial will have been treated with ZX0008 for a minimum of up to 1 year (including their participation in both the core study and this study).