Fig 1.
Conceptual overview of the analytical approach used in serosolver, as applied to influenza A/H3N2.
Top panel: antigenic map for influenza A/H3N2 using coordinates from [24], with different viruses coloured by year of isolation. Solid points show centroids across all strains isolated in a given calendar year, hollow points show individual strains. Dashed line shows an antigenic summary path, generated by fitting a smoothing spline through the observed isolates. Points further apart in space are less cross-reactive. Middle panel: conceptual illustration of the antibody kinetics model. An individual is infected with the orange virus, which results in boosting and waning of homologous antibody titres. In parallel, antibodies that cross react with viruses at different points in antigenic space also boost and wane (purple and blue viruses). The individual is later infected by the purple virus, which leads to further boosting and waning of antibodies. Bottom panel: HI titres measured from serum samples taken at different times capture different parts of the homologous and cross reactive antibody kinetics. Different sampling strategies will represent different subsets of these measurements e.g. a cross-sectional study might inform a single subplot, whereas a longitudinal study might inform just the orange bars from each of the three subplots. Clearly a sampling strategy with multiple serum samples and many viruses tested per sample will provide the most information.
Fig 2.
Inputs and outputs for the serosolver R package.
Users input the serological data to be fitted, an antigenic map if considering an antigenically variable pathogen, the infection history prior and any priors on the antibody kinetics parameters. These inputs feed into the process model that can either be used to simulate data by itself, or combined with observed data and MCMC to obtain three posterior outputs: individual-level infection histories, population probabilities of infection, and antibody kinetics parameters. Once these posteriors have been obtained, serosolver can run MCMC diagnostics and plot key immunological and epidemiological processes.
Fig 3.
Simulated vs. analytical infection history prior metrics (α = β = 1).
Bars show density histograms of infections from 10,000 simulated infection histories for 100 individuals across 42 infection periods. Red lines show known probability mass function. Plots A, D and G show the prior on the total number of infections per discrete time period j. Plots B, E and H show prior on the total number of lifetime infections per individual. Plots C, F and I show the prior on the cumulative number of infections across 42 time periods for one individual. Black line shows prior median, dark gray region shows 50% credible intervals and light gray region shows 95% credible intervals. Note that priors 1 and 2 are equivalent under these assumptions.
Table 1.
Comparison of run time and posterior sampling efficiency across a range of serosurvey designs.
Fig 4.
Influenza A/H1N1pdm09 infection dynamics in Hong Kong cohort.
A: Exposure rates in unvaccinated and vaccinated individuals. Shaded regions show 80% (dark) and 95% (light) credible intervals (CI). Solid lines shows posterior medians. X-axis gives midpoint for that quarter. B: Age-specific exposure rates in unvaccinated individuals. Solid lines show median estimates for each age group (pink: <19 (n = 30), green: 19-64 (n = 264), blue: >64 (n = 17)) with 80% (dark) and 95% (light) CI shaded. C: Model predicted titres and inferred infections compared to observed titres for 4 representative individuals with inferred infections. Purple diamonds show observed titres; black dashed lines indicate posterior median model predicted titres; green shading shows 95% CI on model predicted latent titres (dark) and assay observations (light); orange shading indicates posterior probability of infection. Grey region shows titres outside the limit of detection. X-axis gives midpoint for that quarter. D: Posterior densities of antibody kinetics parameters and total number of infections (∑Zi). Vertical lines represent 2.5th, 50th, and 97.5th percentiles.
Fig 5.
Simulation-recovery of parameter and infection estimates using simulated single strain longitudinal data in same format as the Hong Kong dataset.
A: Model estimated attack rates vs. ‘true’ attack rates. Solid line shows estimated attack rate with 80% (dark) and 95% (light) credible intervals (CI); green line and points shows true attack rates. B: ‘True’ process parameters used for simulation compared to estimated posterior densities. Green vertical lines indicate true parameter values; vertical lines represent 2.5th, 50th, and 97.5th percentiles. C: Model predicted titres and inferred infections compared to observed titres and known infections. Green diamonds indicate observed titres; black dashed lines indicate posterior median model predicted titres; blue shading shows 95% CI on model predicted latent titres (dark) and assay observations (light); vertical lines indicate the timings of true infections; orange shading indicates posterior probability of infection.
Fig 6.
Influenza A/H3N2 dynamics in southern China.
A: Inferred historical attack rates. Shaded regions show 80% and 95% credible intervals (CI), solid line and points shows posterior median estimate; B: Frequency of inferred antibody responses (sero-responses) by age group. Boxplots show distribution across individuals based on posterior median total number of infections per individual per 10 years alive. C: Model predicted titres and inferred infections compared to observed titres (black diamonds). Shaded regions show 95% CI on model predicted latent titres (dark) and assay observations (light).