The code in this repository accompanies the medRXiv preprint A beta-Poisson model for infectious disease transmission by Joe Hilton and Ian Hall which introduces a beta-Poisson mixture model for secondary case count data in the early stages of an infectious disease outbreak. The preprint is available here: https://www.medrxiv.org/content/10.1101/2023.03.24.23287701v1
The secondary case datasets used in our study are stored in datasets.py.
The functions used in our study are stored in functions.py. These include functions for:
- calculating the log likelihood of parameters given data for each of the candidate models from our study (Poisson, geometric, negative binomial, zero-inflated Poisson (ZIP), and beta-Poisson);
- calculating maximum likelihood estimates for the parameters of the negative binomial, ZIP, and beta-Poisson distributions;
- calculating the probability mass function of the ZIP and beta-Poisson models;
- calculating the probability generating function of each of the candidate models;
- calculating the extinction probability of a branching process with offspring distribution given by each of the candidate models;
- creating a dictionary object given some data, which stores the parameter MLE's for each candidate model;
- creating a dictionary object which stores the MLE's of the variance of each candidate model given some data;
- creating a dictionary object which stores the MLE's of the superspreading proportion of each candidate model given some data;
- creating a dictionary object which stores the MLE's of the proportion of zeros in each candidate model given some data;
- creating a dictionary object which stores the log likelihoods and AIC's of each candidate model with maximum likelihood parameters given some data;
- calculates confidence intervals for a statistic from a set of bootstrap samples.
The script parallel_confidence_intervals.py calculates MLEs and confidence intervals of model parameters and statistics for each candidate model for a dataset chosen by the user from those stored in datasets.py, with the number of bootstraps used in the confidence interval calculation also chosen by the user. The script sensitivity_analyses.py performs a sensitivity analysis for a dataset chosen by the user, with log likelihoods given the dataset calculated over a range of beta-Poisson model parameters. The script plot_outputs.py generates the plots presented in our manuscript from the outputs of parallel_confidence_intervals.py, while plot_llh_curves.py generates the plot presented in our appendix from the outputs of sensititivity_analysis.py.
The outputs generated for the study itself and used in our plots are provided in the reference-outputs folder. Running the scripts will not overwrite this folder.