“…According to the model, the time that a person spends in is distributed according to the probability density function is Erlang distributed with shape parameter n V = 6 and rate parameter k V = 0.3 d -1) . As can be seen in Appendix Figure 8, the cumulative distribution function of this Erlang distribution reasonably captures the empirical cumulative distribution of waiting times observed in the longitudinal study of Korodi et al (4) . Thus, in the model, passage through V 1 , …, V 6 with rate constant k V = 0.3 d -1) accounts for the variable and significantly non-zero amount of time required for development of a protective antibody response after vaccination. The parameters f 0 > f 1 , f 1 > f 2 , and f 2 are fractions that characterize the average effectiveness of vaccines used in the US and that determine the sizes of (mutually exclusive) subpopulations of vaccinated persons having different susceptibilities to productive infection (i.e., an infection that can be transmitted to others): S V ,1 , S V ,2 , S V ,3 , and S V ,4 (Figure 1, Appendix Figure 1).…”