Fig. 2. Statistical model of influenza B infections by birth year.

Extending the model developed by Gostic et al.¹⁰, for each influenza B season we predicted the fraction of cases observed in each cohort based on cohort-specific infection histories and on additional factors. The probabilities of the different infection histories in Table 1 are derived in the “Methods” using a discrete-time probabilistic model of infection. As an example, the diagram shows how the probability that a person is first infected with B/Yamagata depends on the frequency of B/Yamagata in the years after birth. Given a person’s first influenza B infection occurs in a particular year, we assumed that the probability this infection was caused by a particular lineage is equal to the frequency of the lineage in that year. We obtained the total probability of being first infected with a particular lineage by summing across all possible years when the first influenza B infection might have occurred. The susceptibility of each cohort is then calculated as a weighted sum of the susceptibilities associated with each infection history. In addition to infection history, other factors that affect the fraction of cases observed in a birth cohort include the cohort’s size relative to the total population and the effect of age itself (rather than year of birth) on infection risk and on the probability that an infection receives medical attention and becomes a case. We fitted the model by maximum likelihood assuming the distributions of cases by birth year in different seasons were independent multinomial draws.