Advances in the estimation of the reproduction number from compartmental models using contemporary Monte Carlo methods
Andrade, Jair
Andrade, Jair
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Publication Date
2024-03-08
Type
Thesis
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Abstract
The reproduction number represents the average number of secondary cases generated by a primary case. If the population is completely susceptible, it is referred to as the basic reproduction number (<0) and theoretically determines whether the pathogen can invade the population. Moreover, its magnitude is proportional to the effort needed to control the disease. Conversely, if the infection is spreading, it is referred to as the effective reproduction number (<t). It serves as an indicator of how extrinsic and intrinsic factors have affected transmission at any given time. Both <0 and <t can be estimated from compartmental models fitted to time series data. However, these estimates are sensitive to both model assumptions and calibration methods. Here, we show that by adhering to a rigorous inference workflow and utilising state-of-the-art algorithms and visualisation tools, one can obtain robust estimates. Using Hamiltonian Monte Carlo in a Bayesian approach, we found a linear relationship between the mean generation time and <0. This discovery allowed us to formulate a parameterisation that produces accurate <0 estimates regardless of the distribution of the epidemiological delays. On the other hand, we demonstrated, through a complementary workflow that spanned three Data Generating Processes (semi-deterministic and deterministic) and both schools of thought for statistical inference, that incorporating mobility data into the workflow can reduce the uncertainty in <t estimates. Nevertheless, this incorporation requires caution, given that mobility data can only be a proxy measurement of the transmission rate. Our results emphasise the importance of envisioning model calibration as a learning process that confronts embedded assumptions. We anticipate these findings will serve as a reference point for modellers that fit SIR-like structures to time-series data. These guidelines include which information to prioritise, how to approach the inference procedure, and how to interpret calibration results.
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NUI Galway