This repository contains code for the paper:
Jair Andrade and Jim Duggan. Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data.
The analysis in this study can be reproduced by executing the files:
- S1_Text.rmd
- S2_Text.rmd
- S3_Text.rmd
- S4_Text.rmd
- S5_Text.rmd
- S6_Text.rmd
- S7_Text.rmd
- S8_Text.rmd
The effective reproduction number
()
is a theoretical indicator of the course of an infectious disease that
allows policymakers to evaluate whether current or previous control
efforts have been successful or whether additional interventions are
necessary. This metric, however, cannot be directly observed and must be
inferred from available data. One approach to obtaining such estimates
is fitting compartmental models to incidence data. We can envision these
dynamic models as the ensemble of structures that describe the disease’s
natural history and individuals’ behavioural patterns. In the context of
the response to the COVID-19 pandemic, the assumption of a constant
transmission rate is rendered unrealistic, and it is critical to
identify a mathematical formulation that accounts for changes in contact
patterns. In this work, we leverage existing approaches to propose three
complementary formulations that yield similar estimates for
based on data from Ireland’s first COVID-19 wave. We describe these Data
Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and
DGP2) correspond to stochastic process models whose transmission rate is
modelled as Brownian motion processes (Geometric and
Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts
for incidence and transmission rates, where mobility data is assumed as
a proxy of the transmission rate. We perform inference on these
structures using Iterated Filtering and the Particle Filter. The final
DGP (DGP3) is built from a pool of deterministic models that describe
the transmission rate as information delays. We calibrate this pool of
models to incidence reports using Hamiltonian Monte Carlo. By following
this complementary approach, we assess the tradeoffs associated with
each formulation and reflect on the benefits/risks of incorporating
proxy data into the inference process. We anticipate this work will help
evaluate the implications of choosing a particular formulation for the
dynamics and observation of the time-varying transmission rate.