Manuscript ID RSOS-251195

DOI:

Title: An integrated framework for modeling respiratory disease transmission and designing surveillance networks using a sentinel index.

Authors: Dérick G. F. Borges, Eluã R. Coutinho, Daniel C. P. Jorge, Marcos E. Barreto, Pablo I. P. Ramos, Manoel Barral-Netto, Alvaro L.G.A. Coutinho, Luiz Landau, Suani T. R. Pinho, and Roberto F. S. Andrade.

This repository contains code and data for evaluating the sentinel index in epidemiological surveillance described in the above article.

Repository Contents Codes implemented in Fortran

These algorithms are used to study the general network structure, leading to the construction of a dendrogram for community identification. Input data consists of a matrix containing the edge strengths of a weighted network, besides parameters indicating the number of nodes, threshold limits to project weighted network into a sequence of unweighted ones. Outputs of an algorithm will, in the sequence, be used as input to the forthcoming algorithm in the sequence. For the current case, the weights of the input network correspond to the number of persons moving from one to another IGR, extracted from the IBGE mobility data.

Fortran code

1. Convert weighted mobility network into unweighted counterpart: redecrit1mc13.for – This algorithm uses the dissimilarity concept to determine the best critical values of mobility weight to be used in the evaluation of Sentinel Index, both in the betweenness centrality analysis and in the meta-population SIR model.(Input data to start reproducibility of results is "ms_BA_rodo_34rgi_fs.dat")

2. Generates adjacency matrix for selected critical value of mobility weight: simi.f90 – This algorithm generates the adjacency matrix for the selected critical value of mobility weight selected by analyzing the results provided by redecrit1mc13.for .

3. Generates neighborhood matrix for selected critical value of mobility weight: madchar13.for – This algorithm uses the adjacency matrix for the selected critical value of mobility weight to generate the corresponding neighborhood matrix.

4. Determines community structure and build dendrogram using Newman-Girvan method: dendo2uQ.for – The Newman-Girvan algorithm is used to identify the community structure of the un-weighted network obtained at the selected critical value of mobility weight.

5. Computes betweenness centrality for the network: betweenness.f90 – This algorithm implements the Brandes algorithm to calculate the betweenness centrality of the nodes in the unweighted network. Betweenness centrality measures the importance of each node in terms of the shortest paths passing through it, providing insights into network connectivity and key nodes for information or disease spread.

Requirements To run the algorithms, make sure you have a Fortran compiler installed: Gfortran Intel Fortran Compiler

Codes implemented in Python

The Python codes developed aim to model the spread of respiratory infections between Immediate Geographic Regions (IGRs) and identify those with the greatest relevance for epidemiological surveillance. The first algorithm estimates the potential for transmission between IGRs based on a metapopulation model, using data on respiratory syndrome-related healthcare encounters and population mobility flows provided by IBGE. The second algorithm calculates the Sentinel Index based on the population of each IGR, the total number of infections exported, and the betweenness centrality of the nodes in the mobility network, allowing the identification of regions with the highest potential for early outbreak detection.

Python Codes

1. Meta-Population SIR Model (SIRmeta_RGI.ipynb) – This notebook implements an SIR model to study disease spread across different IGRs, considering urban mobility data and primary healthcare data.

2. Sentinel Surveillance Index (Sentinel_index.ipynb) – This notebook evaluates surveillance indices to identify critical regions for disease monitoring.

The first algorithm is used to evaluate the potential number of infection transmission between IRG’s based on the metapopulation model. Input data consists of two tables, one containing the numbers of URTI related PHC encounters in each IGR, and the other one containing the number of persons moving from one to another IGR, extracted from the IBGE mobility data.

The second algorithm evaluates the Sentinel Index. Input data consists of three lists, containing the IGR population, the total number of infections exported by each IGR, and the betweeness centrality score of the network nodes evaluated at the selected value of the weight threshold.

Requirements To run the notebooks, make sure you have installed: Python 3.8+ Jupyter Notebook Libraries: numpy, pandas, matplotlib, scipy, seaborn

Code authors Dérick G. F. Borges and Roberto F. S. Andrade

Email address [email protected] or [email protected]