PyRenew: A Package for Bayesian Renewal Modeling with JAX and NumPyro.

The PyRenew package is a flexible tool for simulation and statistical inference of epidemiological models, emphasizing hierarchical multi-signal renewal models. Built on top of the numpyro Python library, pyrenew provides core components for model building.

A renewal model estimates new infections from recent past infections using a generation interval (the time between successive infections in a transmission chain). From this, it infers $R_t$, the time-varying reproduction number, which indicates whether the number of infectious individuals is increasing or decreasing. The core renewal equation is:

$$I(t) = R_t \sum_{s} I(t-s) , w(s)$$

where $w(s)$ is the generation interval distribution: the probability that $s$ time units separate infection in an index case and a secondary case.

However inference is complicated by the fact that observational data require their own models (Bhatt et al., 2023, §2). The observation equation links infections to expected observations:

$$\mu(t) = \alpha \sum_{s} I(t-s) , \pi(s)$$

where $\alpha$ is the ascertainment rate and $\pi(s)$ is the delay distribution from infection to observation.

The Pyrenew package provides configurable classes which encapsulate these components and methods to orchestrate the configuration and composition of these processes resulting in programs which clearly express the model structure and choices, allowing for both ease of model specification and dissemination. The fundamental building blocks are the Model metaclass, from which we can draw samples, and the RandomVariable metaclass which has been abstracted to allow for sampling from distributions, computing a mechanistic equation, or simply returning a fixed value. The PyrenewBuilder class orchestrates the composition process.

PyRenew's strength lies in multi-signal integration for information pooling across diverse observed data streams such as hospital admissions, wastewater concentrations, and emergency department visits where each signal has distinct observation delays, noise characteristics, and spatial resolutions. For single-signal renewal models, we recommend the excellent R package EpiNow2.

Installation

Install via pip with

pip install git+https://github.com/CDCgov/PyRenew@main

Models Implemented With PyRenew

• CDCgov/pyrenew-covid-wastewater: Models and infrastructure for forecasting COVID-19 hospitalizations using wastewater data with PyRenew.
• CDCgov/pyrenew-flu-light: An instantiation in PyRenew of an influenza forecasting model used in the 2023-24 respiratory season.

Resources

• The PyRenew documentation suite provides API reference documentation and tutorials on implementing multisignal renewal models with PyRenew.
• The Model Equations Sheet describes the mathematics of the multisignal renewal processes and models PyRenew supports.
• Additional reading on renewal processes in epidemiology
  • Semi-mechanistic Bayesian modelling of COVID-19 with renewal processes
  • Unifying incidence and prevalence under a time-varying general branching process

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