Composable probabilistic models can lower barriers to rigorous infectious disease modelling
And a change of mind about the backend
14 August 2026
Talk plan
- What modelling evidence has to be, and why we rarely manage all of it
- Chaining models loses information, joint models cannot be taken apart
- Parts validated on their own, then fitted together
- One replication, a common
EpiNow2configuration in three hours - Why the backend is the part I am least sure about
- Whether JAX is the way forward, and whether Julia is the place
samabbott.co.uk/JuliaCon2026/composable
JuliaCon 2026, Muschel — N3, Friday 14 August 2026, 16:45.
The gap: timely, rigorous, and collaborative evidence
- Chris Whitty, then Chief Scientific Adviser and later Chief Medical Officer for England, set out what modelling evidence has to be to inform policy effectively
- It has to be timely, rigorous, and collaborative
- Most of what we build manages two of the three
Whitty (2015), doi:10.1186/s12916-015-0544-8
The gap: COVID-19 showed what is possible
- COVID-19 models integrated cases, prevalence, severity, and hospital occupancy for policy
- Fitting all the data and processes together provided evidence that supported policy decisions
- They required expertise across multiple domains and long development timelines
Birrell et al. (2025), doi:10.1093/jrsssa/qnaf030
The gap: flexibility for new contexts
- In 2022 mpox spread internationally through sexual contact networks, and the response needed modelling quickly
- The COVID-19 models were not adapted to it. New single-source models were built instead
- A different contact structure and different behaviour needed explicit representation
Endo et al. (2022), doi:10.1126/science.add4507
The gap: integrating diverse data
- Cross-sectional viral loads carry information about epidemic dynamics
- They are not in most policy models, even where they are already collected
- Adding a data source to an existing model means rebuilding it
Hay et al. (2021), doi:10.1126/science.abh0635
The gap: multi-model efforts
- Multi-model efforts combine forecasts from several teams, and can improve predictive accuracy
- The teams rarely collaborate on model components
- Common components would let a difference in results be attributed to an assumption rather than an implementation
The US COVID-19 Forecast Hub dataset. Cramer et al. (2022), doi:10.1038/s41597-022-01517-w
Analysing data and processes separately
- The ONS COVID-19 Infection Survey tested over four million swabs from more than 150,000 households at a cost above £500 million
- Modellers outside saw the published prevalence, not the swabs
- Prevalence fed incidence, incidence fed \(R_t\), and those fed variant transmissibility and severity
- Uncertainty was approximated at each step and assumptions were inherited unchecked
Prevalence (A), incidence (B), antibody prevalence (C) and \(R_t\) (D) fitted together as one model instead. Abbott and Funk (2022), doi:10.1101/2022.03.29.22273101. Survey figures from the paper’s introduction
Analysing all data and processes together
- Lison et al. found biases at each step of a chain, in date imputation and in the nowcasting count model
- Those biases carried into \(R_t\). Fitting the steps together avoided them
- Joint models are difficult to develop within policy timelines, and need expertise across several domains
Lison et al. (2024), doi:10.1371/journal.pcbi.1012021
The \(R_t\) estimation ecosystem
- At least seven packages estimate \(R_t\) by renewal in Stan. Only two of them share any component, and I wrote both
- The wastewater \(R_t\) tools make different choices about how much of the sampling to represent, and share nothing
- Shared parts do exist.
primarycensoredis one, and uptake outside my own packages is thin - The unit of reuse is the whole model, not the epidemiology underneath
The two sharing a component are EpiNow2 and epinowcast, both vendoring primarycensored.stan · epiforecasts.io/EpiNow2
Design considerations
- Uncertainty and inference. Joint and staged inference that avoids the cascading biases, and automatic differentiation for fitting
- Model structure. Components separated by process type, and models nested inside models
- Workflow. One specification that is useful for simulation and for inference
Warning
These were developed by the authors and have not yet received broader community input.
Table 1 of the paper pairs each requirement with the problem that motivates it, under six themes. Three of the twelve are on the left. All twelve are at epiaware.org/approaches
The proof of concept is ComposableTuringIDModels.jl
- A thin language for epidemiology over Turing.jl, which does the fitting
- Three component families. Infection processes, latent processes, and observation models
- Components carry their own priors, so domain expertise travels with the component
- Model definitions do not know about the data, so one definition simulates and fits
Registered in General at v0.1.1, so ] add ComposableTuringIDModels works · github.com/EpiAware/ComposableTuringIDModels.jl · Abbott et al., Composable probabilistic models can lower barriers to rigorous infectious disease modelling, in CDC clearance
Four illustrative applications, not implementations. The incubation period model appears in all four and the latent infection model in three
What composition looks like
using ComposableTuringIDModels, Distributions, Turing, Accessors
ar2 = AR(;
damp = [truncated(Normal(0.2, 0.2), 0, 1),
truncated(Normal(0.1, 0.05), 0, 1)],
ϵ_t = HierarchicalNormal(std = HalfNormal(0.1)))
ma1 = MA(;
θ = [truncated(Normal(0.0, 0.2), -1, 1)],
ϵ_t = HierarchicalNormal(std = HalfNormal(0.1)))
arma21 = @set ar2.ϵ_t = ma1
arima211 = DiffLatentModel(arma21, Normal(0, 0.2); d = 1)
mdl = IDModel(
DirectInfections(; Z = arima211, initialisation = Normal()),
PoissonError())
chain = sample(as_turing_model(mdl, cases, n), NUTS(), 1_000)@set is Accessors.jl, not ours, and works because the components are plain immutable structs · Keywords track main. The paper’s artefact pins an earlier release, where these were damp_priors, θ_priors and std_prior
Note
AR was never told that MA exists.
Real-time nowcasting, one EpiNow2 configuration
- Reuses the ARIMA(2,1,1) and the negative binomial from the worked example
broadcast_weeklywraps the ARIMA for piecewise constant weekly \(R_t\), andascertainment_dayofweekadds day-of-week reporting- Two
LatentDelaywrappers add the incubation period and the reporting delay - A to D validate each part on its own. E and F are the joint fit, recovering cases through the delays and \(R_t\) with them
Important
No component was edited. The replication took three hours.
Figures 2 and 4 of the paper. Replicating a common configuration of EpiNow2, real-time estimation accounting for reporting delays, right truncation and day-of-week effects. Abbott et al. (2020), doi:10.12688/wellcomeopenres.16006.2. Daily COVID-19 cases from Italy, February to June 2020, shipped with EpiNow2. One configuration replicated, not a benchmark against the package
Thank you
Important
Tell me what you would build this on, if not a probabilistic programming language.
- Counter-examples. Where is practice already timely, rigorous, and collaborative? I would like to be shown the problem is smaller than I think
- Other ways to compose. Category theory, symbolic approaches, or something I have not thought of
- Build it in Julia. The infectious disease ecosystem here is small. If you are about to write a tool, come and find me first
- The prompts that wrote these decks
samabbott.co.uk/JuliaCon2026/composable
The prototype is ComposableTuringIDModels.jl, github.com/EpiAware/ComposableTuringIDModels.jl
Sam Abbott, LSHTM · epiaware.org · github.com/seabbs
Reusing that AR(2) for South Korea
- The first replication takes the AR(2) from the worked example, a renewal process with a discretised serial interval, and a negative binomial observation model
- A to C are prior predictive checks on each part, D compares the continuous serial interval with its discretised form
- E and F recover the paper’s finding. \(R_t\) in South Korea peaked near 10 and dropped below 1 in early March 2020
Replicating Mishra et al. (2020). Figure from the paper
Swap the infection process, keep the rest
- The third replication drops the renewal process and uses an SIR model built with
ODEProcessover the SciML solvers instead - Everything downstream is unchanged. A Poisson observation model, and a second version wrapping it in
Ascertainmentdriven by an AR(1) - C shows both landing on the same posterior \(R_0\). E and F show the deterministic fit is the worse calibrated of the two
Important
The infection process changed and nothing downstream had to.
Replicating Chatzilena et al. (2019), doi:10.1016/j.epidem.2019.100367. An influenza outbreak in an English boarding school, 1978. Figure 5 of the paper. The paper’s text reads \(R_0 \approx 2\) off this panel. Panel C looks closer to 4 to me, and I have not resolved which is right
Composable probabilistic models
What is composable modelling?
Components can be reused across contexts and combined in different configurations whilst maintaining statistical rigour.
- Chaining models keeps you flexible and loses information. Uncertainty is approximated at each hand-off and assumptions are inherited unchecked
- Joint models avoid that and produce something nobody can take apart. England’s COVID-19 models were not adapted to mpox in 2022
- Composable components are validated on their own, then fitted together, and carry their own priors, so domain expertise travels with the component
Whitty (2015), doi:10.1186/s12916-015-0544-8 · Birrell et al. (2025), doi:10.1093/jrsssa/qnaf030 · Endo et al. (2022), doi:10.1126/science.add4507 · Lison et al. (2024), doi:10.1371/journal.pcbi.1012021
Four illustrative applications, not implementations. The incubation period model appears in all four, the latent infection model in three, and the band beneath is what those shared components are themselves made of. Figure 1 of the paper, which is in CDC clearance. The design considerations behind it are at epiaware.org/approaches
One EpiNow2 configuration, rebuilt out of parts
- An ARIMA(2,1,1) latent process and a negative binomial observation model, both lifted unchanged from other applications
broadcast_weeklyfor weekly \(R_t\), day-of-week ascertainment around the observation model, and twoLatentDelaywrappers for the incubation period and the reporting delay- A to D validate each part on its own. E and F are the joint fit, recovering cases through the delays and \(R_t\) with them
Important
Nothing here required editing a component that already existed. The replication took three hours.
One of three replications in the paper, alongside a renewal model of South Korea and an ODE model of influenza. Replicating EpiNow2 (Abbott et al., 2020). Figures from the paper, which is in CDC clearance. The prototype is ComposableTuringIDModels.jl