The virus that causes COVID-19 changes over time, occasionally leading to Variants of Interest (VOIs) and Variants of Concern (VOCs) that can behave differently with respect to detection kits, treatments, or vaccines. For instance, two vaccination doses were 61% effective against the BA.1 predominant variant, but only 24% effective when BA.2 became predominant. While doses still confer protection against severe disease outcomes, the BA.5 variant demonstrates the possibility that individuals who have received a few doses built for previous variants can still be infected with newer variants. As previous vaccines become less effective, new ones will be released to target specific variants and the whole process of vaccinating the population will restart. While previous models have detailed logistical aspects and disease progression, there are three additional key elements to model COVID-19 vaccination coverage in the long term. First, the willingness of the population to participate in regular vaccination campaigns is essential for long-term effective COVID-19 vaccination coverage. Previous research has shown that several categories of variables drive vaccination status: sociodemographic, health-related, psychological, and information-related constructs. However, the inclusion of these categories in future models raises questions about the identification of specific factors (e.g., which sociodemographic aspects?) and their operationalization (e.g., how to initialize agents with a plausible combination of factors?). While previous models separately accounted for natural- and vaccine-induced immunity, the reality is that a significant fraction of individuals will be both vaccinated and infected over the coming years. Modeling the decay in immunity with respect to new VOCs will thus need to account for hybrid immunity. Finally, models rarely assume that individuals make mistakes, even though this over-reliance on perfectly rational individuals can miss essential dynamics. Using the U.S. as a guiding example, our scoping review summarizes these aspects (vaccinal choice, immunity, and errors) through ten recommendations to support the modeling community in developing long-term COVID-19 vaccination models.