Table 1.

Epidemiological complexities that present challenges for inference and prospects for addressing them

Challenge	Experimental data needs	Serosurveillance data needs	Proposed model refinements
1) Disease‐associated mortality	Time between infection and death for individuals that do not survive; proportion that do not survive	Samples from dead animals (record estimated time of death; test sample for target pathogen)	Incorporate censoring in within‐host model, g (δ, θ). Use experimental infection data to predict: (1) time between infection and death, (2) time between infection and a particular antibody titre, in a censoring framework.
2) Assay detection and quantitation	A. Sensitivity (false negative) and specificity (false positive) rates B. Titre variation from assay error		A. Incorporate assay error through the threshold of detection parameter (y*). B. Incorporate antibody kinetics error (ε term in y = g (δ ϕ, θ)+ ε)
3) Biased sampling design		Covariate data including behaviour, social group, spatial location or date (depending on system knowledge)	Incorporate spatial/temporal autocorrelation or other covariate information into probability determining state classification (as susceptible or seropositive).
4) Endemic dynamics and/or high individual‐level variation	Measure effects of covariates on titre variation (e.g. age, sex, time of year, indicators of stress, pathological signs distinguishing route of exposure, other immune factors, co‐infections, reproductive status, etc. = COVARIATE DATA)	Relevant COVARIATE DATA, x A. Repeated sampling over time of randomly sampled individuals B. Repeated sampling over time of the same individuals (e.g. Borremans et al. 2016) (Note: B requires substantially more effort than A)	A. Use model Supporting Information 4 (systematic sampling model); adapt within‐host model, g (δ, θ, x), to include covariate data x such that some variation in kinetics is parsed out by the individual‐level covariate data. B. Incorporate individual‐level correlation, i.e. modify y 2j model to include a covariance matrix describing all times individual j was sampled, y 2j ~ N (g(δj, θ, x j), ∑j, where ∑ accounts for correlation among observations for individual j
5) Anamnestic response	Anamnestic responses for multiple time points and COVARIATE DATA concurrently	COVARIATE DATA distinguishing titres in primary infections from anamnestic responses (see main text)	Similar to (4A): include different within‐host functions, g (δ, θ, x), for different types of responses (primary infection vs. anamnestic response).
6) Multiple strains (cross‐immunity; co‐infection)	Antibody responses to multiple strains in primary and cross‐infections (e.g. primary A and B, B after A, A after B)	Strain‐specific serosurveillance data	Similar to (4A): different within‐host functions, g (δ, θ, x), for each strain and cross‐reaction.
7) Contact structure		Population‐level data describing host contact structure (e.g. average number of individuals making contact)	Modify contact structure function in FOI derivation (currently proportional: newly infected/susceptibles) to reflect the true relationship of the number of susceptibles contacting newly infected hosts.
8) Complex antibody response (i.e. chronic or acute disease; recurrent antibody production due to latent infections)	Long‐term antibody titres and covariate data quantifying pathological signs, immune factors, external stressors or pathogen loads that distinguish chronic from acute infections, or initial infection from later stages	COVARIATE DATA as determined in experimental infections	If different stages/types of antibody responses can be informed by covariate data, modify model as in 4A: g (δ, θ, x), to include covariate data x Incorporate appropriate antibody response function by modifying g in g (δ, θ, x)

Shading indicates effort: low (white), medium (light grey), high (dark grey). Data needs are in addition to current data needs (antibody kinetics in experimental studies and cross‐sectional serosurveillance data).

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