In this study, the mathematical stability of EEG signal models represented by integral equations during epileptic seizures is investigated. The stability of such models is analyzed by applying Lyapunov's stability theorem, showing that stability is powerfully dependent on parameters such as seizure duration, intensity, and neural connectivity. Some parameter regimes yield stable behaviour, while others give rise to instability, making EEG interpretation complicated during epileptic seizures. Integral equation-based models highlight advantages in capturing transient dynamics of epileptic activity.