We simulated the transmission dynamics of rotavirus and predicted impact of vaccination using an age-structured compartmental model that we previously developed and fit to statewide data on rotavirus hospitalizations in New York (9). Briefly, the model assumes that individuals are born at a rate B(t) (equal to the annual mean crude birth rate in New York State) with maternal immunity (M) and are protected from infection for a period of 1/ωM and then become susceptible to first infection (S0). First infections (I1) occur at a rate λ, and individuals recover at a rate γ1 into a temporarily immune (R1) state. This immunity wanes at a rate ω1, and individuals become susceptible again (S1) but are reinfected at a reduced rate σ1λ. Second infections (I2) are assumed to have infectiousness reduced by a factor ρ2 and a faster recovery rate γ2. Individuals are again assumed to be temporarily immune (R2) following infection, then lose this immunity, and become partially susceptible (S2). Once in S2, individuals can be reinfected at a rate σ2λ, but subsequent infections (IA) are assumed to be subclinical and have reduced infectiousness (ρA). Recovery from subclinical infection is again assumed to occur at an increased rate γ2 and lead to temporary immunity (RA) that wanes at a rate ω2. We assumed that individuals with first rotavirus infection (I1) have a probability d1 of developing severe diarrhea, while those with second infection (I2) develop severe diarrhea with probability d2 < d1. The fixed and estimated parameter values (table S2), as well as the differential equations describing the model, are presented in the Supplementary Materials.

To model the impact of vaccination, we assumed that each dose of the vaccine was equivalent to one natural infection, thereby moving individuals from M or S0 to R1 (bypassing I1) following the first dose and from R1 or S1 to R2 (bypassing I2) following the second dose. Contrary to our 2009 analysis, we had data on both the proportion of infants receiving at least one dose of rotavirus vaccine as well as the proportion receiving a full course of vaccination. We assumed that 95% of individuals responded to vaccination (and thus received any benefit of the vaccine) following two or more doses, consistent with seroconversion data from vaccine trials in the United States and Finland (40), and assumed that the relative efficacy of an incomplete vaccine series (i.e., protection following receipt of the first dose) was 70 to 90% (fig. S1), consistent with our previous analysis (9). The long-term pattern of predicted seasonality and age-specific impact from the model were compared with the observed hospitalization and laboratory-based surveillance data for January 2008 to December 2016. We calibrated the model by determining the value of the relative efficacy conferred by one dose of the vaccine that minimized the sum of squared errors between the model-predicted number of cases and both the hospitalization and laboratory-reported postvaccination data (fig. S2).

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