Fig 1.
Schematic of influenza-like illness (ILI).
Individuals with influenza or other respiratory viruses likely seek treatment at different, unknown rates, and as such ILI counts include an uncertain mixture of diseases. Virological testing is uncommon outside high risk groups, but when performed it is possible to use the resulting confirmed influenza data to model the population level circulation of influenza, specifically. Red quantities are those with known/observed values. Note that some ILI samples sent for testing return with as positive to none of the tested diseases, suggesting that their ILI symptoms may have some other cause.
Fig 2.
Hierarchical observation process in the presence of confirmed influenza data and known denominators.
This structure allows us to directly model influenza without the other respiratory viruses that make up ILI. Red quantities are those with known/observed values, and blue quantities need to be estimated in a model.
Fig 3.
Individuals progress from a susceptible (S) class through exposed (E), infectious (I), and recovered (R). While infectious, individuals may choose to go to the doctor, at which case they move into an observed (O) class.
Table 1.
Marginal posterior parameter estimates—H1N1pdm09 seasons.
Fig 4.
(above) Bivariate posterior distribution of and initial susceptible proportion in 2011 for H1N1pdm09. Points indicate accepted ABC parameter sets. Contours indicate posterior credible intervals, such that each contour contains deciles of kernel-smoothed posterior probability density. (below) Marginal posterior kernel density estimate (blue) and prior distribution (red) for
(left), and initial susceptible proportion in 2011 (right) for H1N1pdm09. Note the difference between high-density regions in the bivariate plot vs the marginals.
Fig 5.
Marginal posterior kernel density estimate (blue) and prior distribution (red) for pobs, for H1N1pdm09.
Fig 6.
The relationship between and the population level attack rate of simulated realisations of the process, across 2011 and 2013 H1N1pdm09.
For each accepted particle, the process was simulated again, and the total number of infected individuals from these new realisations was recorded, and converted into an annual attack rate (by dividing by the total population, and by 2 as it is the average over two seasons). Point colour indicates the probability of an individual seeking treatment; larger attack rates correspond to smaller treatment probabilities given that they all fit the same data. The red line shows where the product of and the attack rate would be equal to one; this is the line around which the majority of posterior density for initial population susceptibility values was situated (i.e., the density in Fig 4). This can be interpreted as indicating that, for points under this line, not all susceptible individuals became infected during the season.
Table 2.
Marginal posterior parameter estimates—H3N2 seasons.
Table 3.
Relationship between fitted epidemic quantities and transformed model parameters.
Multiplying by 8 in these transformations is to account for using 8 timesteps per day.
Table 4.
Model transitions.
Table 5.
Single-timestep increments for each model compartment.