• Five of these six are EpiNow2 co-authors. Nikos Bosse wrote scoringutils, the forecast scoring package
• Sebastian Funk, Samuel Brand and Kath Sherratt are co-authors on the live DRC model. Katelyn Gostic is at CDC

• Adrian Lison and Adam Howes are second only to me on epinowcast and epidist. Kaitlyn Johnson built baselinenowcast
• primarycensored is joint work with Thomas Ward, UKHSA, and Christopher Overton

• The Office for National Statistics (ONS) COVID-19 Infection Survey. 4M+ swabs, 150K households, £500M+, April 2020 to March 2023
• External modellers accessed only summarised prevalence, not underlying observations
• Lison et al. found biases at each step. Joint modelling of all steps together avoided these cascading biases
• But models are difficult to develop within policy-relevant timelines

• 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

Components can be reused across contexts and combined in different configurations whilst maintaining statistical rigour.

Abbott et al., Composable probabilistic models can lower barriers to rigorous infectious disease modelling

• EpiAware. Loosely an extension of the epinowcast community, and in its initial stages
• Top row. EpiAware, and the composable paper. Samuel Brand, Damon Bayer and Joseph Lemaitre built CensoredDistributions.jl with me. Hong Ge leads Turing.jl
• Bottom row. JuliaBayes, formed April 2026, building the tools around Turing.jl. Chains, regression models, a Bayesian workflow package

• A library of parts over Turing.jl
• Three kinds of part. An infection model, an observation model, and prior models nested in the slots of both
• Parts carry their own priors
• A model definition does not know about the data. One definition simulates and fits
• Adding a new application means defining only the new parts

• Write the epidemiology as Distributions.jl distributions. The probabilistic programming language becomes optional
• A case’s event history is a tree. sequential chains delays, resolve picks an outcome with a probability, compete races two
• The whole tree is itself a distribution. It slots in wherever a delay is needed inside a larger model
• Parameter uncertainty is an ordinary leaf

• Reuses the autoregressive prior from the paper’s first case study, swapping the Poisson observation model for a negative binomial one
• broadcast_weekly wraps it to give piecewise constant weekly \(R_t\) values
• ascertainment_dayofweek adds day-of-week reporting effects
• Two LatentDelay wrappers compose the incubation and reporting delays by nesting structs

• Today the slot holds a Gaussian process, or an autoregressive (AR) process. It is free to move and one data stream constrains it
• A network in the same slot. This is what a universal differential equation does. It learns what the Gaussian process cannot say. Behaviour, season, policy
• A network on the observation side. Several data streams fitted from the same latent infections
• Most exciting where there are many hard to model data sets to fit jointly in an otherwise well understood system
• How does this work with Bayesian modelling? Priors over weights, identifiability against a slot that already flexes, and what the posterior then means
• No neural network code in any EpiAware package yet

• A physics-informed neural network (PINN) adds the residual of the differential equation to the data misfit in its loss, so the mechanism enters as a penalty rather than as structure
• Early in an outbreak we know almost nothing. Start with the network carrying most of the fit
• Then dial the mechanism up. Add equations as they become defensible, inside the same fit, rather than switching model
• Will it hold when the data are very sparse? That is the question for the first weeks, which is when we would want it
• Deterministic, so no uncertainty quantification by default

• A renewal process is an autoregressive transformation of \(R_t\) and past infections to today’s infections. It can be thought of as a neural network layer
• The layers compose. Inputs to \(R_t\), an \(R_t\) layer, delay and ascertainment layers, a likelihood on each stream. The same parts we already assemble by hand
• The network can stay small, because the epidemiology is in the layers rather than learned. That is what makes it plausible on the data an outbreak actually gives you
• Then build up. More streams and more structure by stacking, not by writing a new model
• Not seen this used in research yet. Proposed in Samuel Brand’s RenewalExamples repository

• Outbreak data change after the fact. On the DRC model the daily suspected stream stopped on 6 August. In May INSP, the DRC’s public health institute, reclassified suspected cases
• So pretrain on outbreaks as they were seen at the time, not on the final curves. CAPE pretrains on simulated epidemics, but on the curves
• We can simulate what it would need. Composable models generate early and mid-outbreak data, including complex surveillance streams, which could be the training set
• How do these methods hold up when the data change under them, in prospective settings?

• The workflow. Nine stages, from the research question to data integration, with feedback loops running back to earlier ones
• On BVDOutbreakSize agents wrote the code. The model structure and approach were specified by me at a high level. The judgements stayed with people
• Agents do best with something to check against. A simulation with known parameters, an analytic case, another group’s estimate
• 333 of 425 pull requests, the unit of change on GitHub, came from my bot account

• epidist. A meta-analysis model for published delay estimates, built from scratch in about a week. Onset to death for Bundibugyo virus disease, beside the study the estimates came from
• EpiDelays. A UHasselt package rewired onto the primarycensored likelihood in two days
• What kind of infectious disease modelling language works well for agents?

• Replication. The McCabe et al. Imperial report replicated in a few hours, the day after it appeared. Then a joint model across five situation report streams, the Uganda exports and a genomic bound
• Data. Agents read the French PDF situation reports, two blind reads each. Onsets are only a figure, so an agent-written digitiser, cross-checked by a second one in another language
• Checks on every rebuild. Predictive checks per stream, forecasts scored against later data, the replication. That much debugging would not have happened by hand
• Infrastructure and review were still needed to keep the agents in check
• Could agents build and check the simulators you learn against?

• Could a language model be the proposal step? Inside the inference algorithm rather than wrapped around it, proposing models rather than parameters
• Composability gives it a move set. If models are assembled from components, a proposal is a swap of one part, not a new program
• Open questions. How to enforce domain knowledge, and how to pick the evaluation target

• The time between two events in one case. Infection to symptom onset is the incubation period
• We want the whole distribution over days across a population, not a mean
• Nowcasts, forecasts and transmission models take one as an input and do not re-estimate it

• The primary event falls somewhere in a window \([0, w_P]\)
• Mix the delay over where in the window it sat, a convolution on the cumulative distribution function (CDF)
• The secondary event is recorded to the day as well
• The probability of a daily bin is a difference of the primary-censored CDF

\[ F_{\mathrm{PEC}}(t) = \int_{0}^{w_P} g(\tau)\, F(t - \tau)\, d\tau \]

\[ \Pr\!\big(T \in [n, n + w_S]\big) = F_{\mathrm{PEC}}(n + w_S) - F_{\mathrm{PEC}}(n) \]

• A pair enters the data only if the secondary event happened before the cutoff \(C\)
• Condition on being observed. Divide by the CDF at the horizon
• Move the cutoff and watch the mean of what you can see. Continuous LogNormal(1.6, 0.6) delays, every primary event at day zero

\[ L^{\mathrm{RT}} = \frac{F_{\mathrm{PEC}}(n + w_S) - F_{\mathrm{PEC}}(n)} {F_{\mathrm{PEC}}(C - P)} \]

• At a cutoff seven days after the primary events, and 5.3 days at fourteen

• primarycensored, R. d, p, q and r prefixes, as in base R
• epidist, R. The same likelihood through brms. Delays vary by district, by age and by wave
• CensoredDistributions.jl. Each adjustment is a wrapper on a Distributions.jl object. The stack is still a distribution, so Turing takes it as it is

• epiaware.org/approaches. The design considerations and the two approaches
• ComposableTuringIDModels.jl and ComposedDistributions.jl
• primarycensored, epidist and CensoredDistributions.jl
• BVDOutbreakSize. The live DRC outbreak model
• The prompts that wrote these decks