Fig. 1

Structure and fit of the model. a Compartmental diagram of the transmission model. Susceptible individuals S move, following exposure, to the symptomatic or asymptomatic compartment, i^τ = 0, a^τ = 0, representing the first day of infection. The model explicitly tracks the day of infection τ such that the daily transmissibility is based on the daily viral load [41, 42]. Upon recovery, individuals transition to an R compartment, at which point they are fully protected for the remainder of the season. We also incorporated five age groups into the model, namely, 0–4, 5–19, 20–49, 50–64, > 65 years, and two risk groups within each age group, namely, high-risk and low-risk. Age and risk stratifications are not displayed to increase clarity in the diagram (Additional file 1). b, d Time series of recorded weekly symptomatic influenza cases and model fit to California and Texas (the model fit to Connecticut and Virginia is provided in Additional file 1, Figure S2). c, e Data and model fit to the age distribution among influenza cases