Arbovirus Modeling and Uncertainty Quantification Toolbox

ARBO: Arbovirus Modeling and Uncertainty Quantification Toolbox is a comprehensive Matlab/C++ package designed for the simulation and analysis of arbovirus nonlinear dynamics. Developed with an educational approach, ARBO is intuitive and user-friendly, making it accessible for researchers and students alike.

Table of Contents

• Overview
• Features
• Usage
• Documentation
• Reproducibility
• Authors
• Citing ARBO
• License
• Institutional support
• Funding

Overview

ARBO was developed to simulate the nonlinear dynamics of an epidemic model to describe the Zika Virus outbreak in Brazil. It includes modules for solving initial value problems, calibration problems, model enrichment, and uncertainty quantification.

This code was developed to simulate the nonlinear dynamics of a epidemic model to describe Zika Virus outbreak in Brazil. It also solves an inverse problem to calibrate the underlying dynamic model parameters using real data as reference. These results are reported in the following paper:

• E. Dantas, M. Tosin, A. Cunha Jr, Calibration of a SEIR–SEI epidemic model to describe the Zika virus outbreak in Brazil, Applied Mathematics and Computation, vol. 338, pp. 249-259, 2018 DOI

A third module includes a model enrichment approach, that uses discrepancy operator calibrated with data to compensate epidemic uncertainties in the epidemic model structure. The framework and some results are reported in:

• R. E. Morrison, A. Cunha Jr, Embedded model discrepancy: A case study of Zika modeling, Chaos, v. 30, pp. 051103, 2020 DOI

The code also includes an uncertainty quantification module, that uses a probabilistic model to deal with the model parameters uncertainties. This framework and some results of the stochastic simulations are reported in:

• E. Dantas, M. Tosin, A. Cunha Jr, An uncertainty quantification framework for a Zika virus epidemic model, Journal of Computational Interdisciplinary Sciences, v. 10, pp. 91-96, 2019 DOI

Features

• Data Sets: Preprocessed data for simulations
• Initial Value Problem: Solves forward problems using ODE solvers
• Model Calibration: Calibrates model parameters using real data
• Model Enrichment: Enhances models with discrepancy operators
• Uncertainty Quantification: Propagates uncertainties via Monte Carlo method

Usage

To get started with ARBO, follow these steps:

1. Clone the repository:

   git clone https://github.com/americocunhajr/ARBO.git

2. Navigate to the code directory:

   cd ARBO/ARBO-1.0

The Matlab main routines and functions of the code are described below:

• main_SEIR_SEI_IVP_XX.m - Defines parameters and IC for the forward problem; solves the IVP with ode45; plots the time series
• rhs_SEIR_SEI.m - System of diferential equations for the IVP
• main_SEIR_SEI_TRR_XX.m - Sets up scenarios for the inverse problem and options for the TRR solver; plots time series
• ObjFun_SEIR_SEI.m - Sets up the objective function used in the main file for the inverse problem
• main_SEIR_SEI_MC_XX.m - Compute the propagation of uncertainties via Monte Carlo method

A description C++ program can be seen inside model_enrichment directory, where you can find a README file with instructions.

Documentation

The routines in ARBO are well-commented to explain their functionality. Each routine includes a description of its purpose, as well as inputs and outputs.

Reproducibility

Simulations done with ARBO are fully reproducible, as can be seen on this CodeOcean capsule

Authors

• Michel Tosin
• Eber Dantas
• Americo Cunha
• Rebecca E. Morrison

Citing ARBO

If you use ARBO in your research, please cite the following publications:

• M. Tosin, E. Dantas, A. Cunha Jr, R. E. Morrison, ARBO: Arbovirus modeling and uncertainty quantification toolbox, Software Impacts, vol. 12, pp. 100252, 2022 https://doi.org/10.1016/j.simpa.2022.100252
• E. Dantas, M. Tosin, A. Cunha Jr, Calibration of a SEIR–SEI epidemic model to describe the Zika virus outbreak in Brazil, Applied Mathematics and Computation, vol. 338, pp. 249-259, 2018 https://doi.org/10.1016/j.amc.2018.06.024
• E. Dantas, M. Tosin, A. Cunha Jr, An uncertainty quantification framework for a Zika virus epidemic model, Journal of Computational Interdisciplinary Sciences, v. 10, pp. 91-96, 2019 http://dx.doi.org/10.6062/jcis.2019.10.02.0163
• R. E. Morrison, A. Cunha Jr, Embedded model discrepancy: A case study of Zika modeling, Chaos, v. 30, pp. 051103, 2020 https://doi.org/10.1063/5.0005204

@article{Tosin2022ARBO,
   author  = {M. Tosin and E. Dantas and A. {Cunha~Jr} and R. E. Morrison},
   title   = "{ARBO: Arbovirus modeling and uncertainty quantification toolbox}",
   journal = {Software Impacts},
   year    = {2022},
   volume  = {12},
   pages   = {100252},
   doi     = {10.1016/j.simpa.2022.100252},
}

@article{Dantas2018p249,
   author  = {E. Dantas and M. Tosin and A. {Cunha~Jr}},
   title   = {Calibration of a {SEIR–SEI} epidemic model to describe the {Z}ika virus outbreak in {B}razil},
   journal = {Applied Mathematics and Computation},
   year    = {2018},
   volume  = {338},
   pages   = {249-259},
   doi     = {10.1016/j.amc.2018.06.024},
}

@article{Dantas2019p91,
   author  = {E. Dantas and M. Tosin and A. {Cunha~Jr}},
   title   = {An uncertainty quantification framework for a {Z}ika virus epidemic model},
   journal = {Journal of Computational Interdisciplinary Sciences},
   year    = {2019},
   volume  = {10},
   pages   = {91-96},
   doi     = {10.6062/jcis.2019.10.02.0163},
}

@article{Morrison2020p051103,
   author  = {R. E. Morrison and A. {Cunha~Jr}},
   title   = {Embedded model discrepancy: {A} case study of {Z}ika modeling},
   journal = {Chaos},
   year    = {2020},
   volume  = {30},
   pages   = {051103},
   doi     = {10.1063/5.0005204},
}

License

ARBO is released under the MIT license. See the LICENSE file for details. All new contributions must be made under the MIT license.

Institutional support

   

Funding