This paper presents the findings on modeling the demand for shared e-scooter services (SES); specifically, spatio-temporal variation of SES demand. A zero-inflated negative binomial (ZINB) model is developed using the count data of trip origins at the dissemination area level from Kelowna, Canada. The motivation for adopting the ZINB model is the presence of excess zeros in the count data. ZINB has two components: the zero-inflated component accounts for excess zeros, and the count component accounts for the over-dispersion characteristics of data resulting from excess zeros. In addition to the ZINB, several other count models including hurdle models are estimated. The goodness-of-fit measures suggest that the ZINB model outperforms other methods. The model results confirm the effects of temporal, weather, transportation infrastructure, land use, and neighborhood characteristics. For example, the count model results reveal that SES demand is more likely to be higher during summer, mid-day on weekends, afternoons of weekdays, and days without rainfall. Furthermore, higher e-scooter index, higher density of cycle tracks, heterogeneous land use, urban centers, lower elevation, and neighborhoods with higher density of hotels and younger population might induce higher demand. The zero component results of the model are consistent with the findings revealed by the count component. The model is validated using a hold-out sample, and the validation results confirm that the prediction performance of the model is reasonably satisfactory. The findings of this study provide important insights into when and where the demand is higher, which will assist in effective policy-making supporting e-scooter use.