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Fig. 1 | BMC Medicine

Fig. 1

From: Fast and accurate dynamic estimation of field effectiveness of meningococcal vaccines

Fig. 1

Schematic representation of the Monte Carlo maximum likelihood method to infer vaccine effectiveness. a An age-structured stochastic compartmental model reproduces the transmission and vaccination dynamics of Neisseria meningitidis. The population is stratified by age a, infection status (susceptible S or asymptomatic carrier C), and vaccination status (V), where the additional I indicates that the vaccination induced full immunity to the invasive disease. All compartments are subject to demographic transitions: birth, ageing, and death (not shown). At each time step, susceptibles are infected with probability λ a and recovery from carriage to susceptible status happens with probability ρ. The force of infection λ a is reduced by 1−VEind for those susceptibles who are successfully immunized (SVI). Individuals are vaccinated with probability γ a . A fraction VEdir of them becomes fully immune to the invasive disease, while the remaining fraction is vaccinated but not immune. For a fraction ω a of the immunes, the acquired immunity wanes after a time period τimm. The outcome of the transmission model is the number of infections by age group in non-vaccinated and vaccinated compartments during an epidemiological year: J a and JV a . We use these numbers in the observational disease model (b). Given the probability of developing the invasive disease for a single age group θ a , calibrated using data before vaccination, and given the number of cases observed in reality, we compute the likelihood function of VEind and VEdir (c). The likelihood maximum will correspond to the best estimates of the two vaccine’s effectiveness. The two-dimensional likelihood is sliced in correspondence of its maximum to calculate confidence intervals around the best estimates

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