Interictal spikes (IISs) are spontaneous high amplitude, short time duration <400 ms events often observed in electroencephalographs (EEG) of epileptic patients. In vitro analysis of resected mesial temporal lobe tissue from patients with refractory temporal lobe epilepsy has revealed the presence of IIS in the CA1 subfield. In this paper, we develop a biophysically relevant network model of the CA1 subfield and investigate how changes in the network properties influence the susceptibility of CA1 to exhibit an IIS. We present a novel template based approach to identify conditions under which synchronization of paroxysmal depolarization shift (PDS) events evoked in CA1 pyramidal (Py) cells can trigger an IIS. The results from this analysis are used to identify the synaptic parameters of a minimal network model that is capable of generating PDS in response to afferent synaptic input. The minimal network model parameters are then incorporated into a detailed network model of the CA1 subfield in order to address the following questions: (1) How does the formation of an IIS in the CA1 depend on the degree of sprouting (recurrent connections) between the CA1 Py cells and the fraction of CA3 Shaffer collateral (SC) connections onto the CA1 Py cells? and (2) Is synchronous afferent input from the SC essential for the CA1 to exhibit IIS? Our results suggest that the CA1 subfield with low recurrent connectivity (absence of sprouting), mimicking the topology of a normal brain, has a very low probability of producing an IIS except when a large fraction of CA1 neurons (>80%) receives a barrage of quasi-synchronous afferent input (input occurring within a temporal window of ≤24 ms) via the SC. However, as we increase the recurrent connectivity of the CA1 (P sprout > 40); mimicking sprouting in a pathological CA1 network, the CA1 can exhibit IIS even in the absence of a barrage of quasi-synchronous afferents from the SC (input occurring within temporal window >80 ms) and a low fraction of CA1 Py cells (≈30%) receiving SC input. Furthermore, we find that in the presence of Poisson distributed random input via SC, the CA1 network is able to generate spontaneous periodic IISs (≈3 Hz) for high degrees of recurrent Py connectivity (P sprout > 70). We investigate the conditions necessary for this phenomenon and find that spontaneous IISs closely depend on the degree of the network's intrinsic excitability.