Three simple approaches to forecast the COVID-19 epidemic in Jordan were previously proposed by Hussein, et al.: a short-term forecast (STF) based on a linear forecast model with a learning database on the reported cases in the previous 5–40 days, a long-term forecast (LTF) based on a mathematical formula that describes the COVID-19 pandemic situation, and a hybrid forecast (HF), which merges the STF and the LTF models. With the emergence of the OMICRON variant, the LTF failed to forecast the pandemic due to vital reasons related to the infection rate and the speed of the OMICRON variant, which is faster than the previous variants. However, the STF remained suitable for the sudden changes in epi curves because these simple models learn for the previous data of reported cases. In this study, we revisited these models by introducing a simple modification for the LTF and the HF model in order to better forecast the COVID-19 pandemic by considering the OMICRON variant. As another approach, we also tested a time-delay neural network (TDNN) to model the dataset. Interestingly, the new modification was to reuse the same function previously used in the LTF model after changing some parameters related to shift and time-lag. Surprisingly, the mathematical function type was still valid, suggesting this is the best one to be used for such pandemic situations of the same virus family. The TDNN was data-driven, and it was robust and successful in capturing the sudden change in +qPCR cases before and after of emergence of the OMICRON variant.