Focal seizures begin in the epileptogenic zone (EZ), a theoretical concept that evades practical identification and definition. Recently researchers have considered the more experimentally tractable “core” to elucidate the origins and behaviors of focal seizures. This millimeter-scale core is recruited by a wavefront of hyper-excitatory activity, in which inhibitory neurons fail to fire despite supra-threshold excitation. Herein we argue that the same failure of inhibition (FoI) as in the focal core may be critical to a theoretical understanding of the EZ. In contrast, most models of neural population activity have assumed that with increasing pre-synaptic input, population activity only increases. Two population models have recently made the critical step to account for FoI, with substantial success in modeling data from focal seizures. We provide a first-principles derivation from a single neuron model to a novel population model analogous to prior models. We show that our model fits as well or better than prior ad hoc FoI models on synthetic neural input-response data. We motivate the tristability of our model: having states of rest, functional activity, and pathological seizure. By analysing the transitions between these states, we can characterize seizure susceptibility and rescuability relative to functional excitability and stability. Thus, by relating a drug’s mechanism of action to our model parameters , our model can predict not only its nuanced effect on focal seizure, but also its effect on functional activity. The balance of these two effects is a key consideration in the clinical feasibility of an anti-epileptic drug.