SARS-CoV-2 vaccines are effective at limiting disease severity, but effectiveness is lower among patients with cancer or immunosuppression. Effectiveness wanes with time and varies by vaccine type. Moreover, previously prescribed vaccines were based on the ancestral SARS-CoV-2 spike-protein that emerging variants may evade. Here, we describe a mechanistic mathematical model for vaccination-induced immunity. We validate it with available clinical data and use it to simulate the effectiveness of vaccines against viral variants with lower antigenicity, increased virulence, or enhanced cell binding for various vaccine platforms. The analysis includes the omicron variant as well as hypothetical future variants with even greater immune evasion of vaccine-induced antibodies and addresses the potential benefits of the new bivalent vaccines. We further account for concurrent cancer or underlying immunosuppression. The model confirms enhanced immunogenicity following booster vaccination in immunosuppressed patients but predicts ongoing booster requirements for these individuals to maintain protection. We further studied the impact of variants on immunosuppressed individuals as a function of the interval between multiple booster doses. Our model suggests possible strategies for future vaccinations and suggests tailored strategies for high-risk groups.