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  1. The basic reproduction number R_0 for an infection age and vaccination age structured epidemic model is investigated. The connection of R_0 to the infection age transmission rate and the vaccination age immunization rate is analyzed. The model emphasizes the importance of pre-symptomatic infectiousness and vaccination efficacy. The model is applied to the COVID–19 epidemic in New York State. 
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    Free, publicly-accessible full text available April 1, 2026