Bayesian Data-driven epidemiological modeling

See the paper:

Bayesian epidemiological modeling over high-resolution network data: opportunities for optimized control.

The release code version

About

This collection of computational scripts were used for the results in the paper: Bayesian data-driven epidemiological modeling.

The code is built for the purpose of i) to infer the parameters of the epidemiological model given network- (transport) and surveillance- data, and ii) to use the posterior for a Bayesian framework in a public health setting, exploring detection and mitigation strategies.

In the code structure, there is an R-package which acts as a wrapper for main simulator, SimInf. The package is written as a class (R6) which can be called from scripts and it connects the three main parts of the inference: a) the simulator, b) the summary statistics, and c) the Bayesian sampler (estimator).

A summary of the quantitative result

We are able to with the code and data in this repository to first approximate the posterior of the STEC endemic in the cattle population

If we visually define our problem, we have a (a) local $\text{SIS}_E$ spread of the infection withing herds. The herds are (b) connected via a a national transport network with other herds. In the timeframe of bacterial sampling, the herds are (c) sampled for the bacteria were 1 indicates that the herd was found infected while 0 is a negative result.

On the network, we have observational data, and using SLAM (an approximate Bayesian computation) approach to approximate the parameter posterior (green). We then later affirm the found posterior by re-iterating the same procedure with synthetic data generated from the parameter posterior mean (blue & orange)

To judge the posterior, we can run 250 sampled trajectories and compare the number of positive samples per quarter. Blue triangles are the observations, solid black line is the mean of the trajetories and the shaded grey area is the 95% CI.

Using this posterior we can simulate different scenarios, and easily carry a Bayesian credible interval with us. First we explore different detection procedures, were we try and find the best possible grouping when deciding on sentinel node groups. We plot the probability of detection mean and 95% CI for each node selection group against time.

Latter we study some intervention procedures, and see how the population prevalence decay with time. Here we also plot the mean and 95% CI for the different techniques considered.

Structure

The catalog structure follows,

• BPD
  • Scripts
    • DATA
    • INFERENCE
      • 1600system
      • realsystem
    • PREVDEC
  • README.md
  • SimInfInference
    • R
    • src
  • Figures

Scripts

All the scripts used for the computations, using the class from SimInfInference.

• DATA, The collection of data used in the paper.

• INFERENCE, Divided into three subfolders, the 1600 synthetic data (1600system) and the full dataset (realsystem).

• PREVDEC, The experiments that use the posterior generated from INFERENCE in the frame of public health.

SimInfInference Class inspired code structure presented as a

R-package. Acts as a wrapper around SimInf.

4 main compartments are used:

• Simulator: what simulator to use, we wrap around SimInf, but can be easily extended to other alternatives.
• SummaryStatistics: how to summarize the data.
• Proposal: how to propose new parameters.
• Estimator: what parameter estimator to use.

The code is written in two folders, R and src. Where R hold the R code and src the RCPP. RCPP was used for some task for easy speed-up.

Run the code (Replicate the result)

First make sure that all dependencies are installed by runnung 'make aldepend'. Then install the SimInfInference package by running make rcpp followed by make install

The inference for each dataset is perfomed by using the assigned script. If one wish to extract the multi-set matrix plots, or tables, one also need to save each file. The suggested location is /Scripts/DATA/posterior/. In said directory, the results presented in the paper is stored and available to explore.

To further replicate our results, we suggest using a computational cluster, and creating multiple (parallel) "Markov chains" and using these together for better performance.

References

• The Baysian inference methods

[1] Sisson SA, Fan Y, Beaumont M (2018) Handbook of Approximate Bayesian Computation. (Chapman and Hall/CRC).

[2] Wood SN (2010) Statistical inference for noisy nonlinear ecological dynamic systems. Nature 466(7310):1102–1104.

[3] Haario H, Saksman E, Tamminen J, , et al. (2001) An adaptive Metropolis algorithm. Bernoulli 7(2):223–242.

• The simulator, epidemiological models

[4] Widgren S, Bauer P, Eriksson R, Engblom S (2018) SimInf: An R package for data-driven stochastic disease spread simulations. Accepted for publication in J. Stat. Softw.

• The work is influenced and succeeds the series of previously published works

[5] Bauer P, Engblom S, Widgren S (2016) Fast event-based epidemiological simulations on national scales. Int. J. High Perf. Comput. Appl. 30(4):438–453.

[6] Widgren S, et al. (2016) Data-driven network modelling of disease transmission using com- plete population movement data: spread of VTEC O157 in Swedish cattle. Veterinary Res. 47(1):81.

[7] Widgren S, Engblom S, Emanuelson U, Lindberg A (2018) Spatio-temporal modelling of vero- toxigenic E. coli O157 in cattle in Sweden: Exploring options for control. Veterinary Res. 49(78).