MSED - Modelación de Socio-Economic Dynamics

A mathematical modeling project for analyzing population dynamics, health sector expenditure, and tourism economics in Chile and Mexico using differential equations and statistical regression.

Overview

MSED (Modelación de Socio-Economic Dynamics) provides a comprehensive framework for modeling and forecasting demographic and economic trends through:

• Population Modeling: Analysis of age-group dynamics (children 0-14, adults 15-64, elderly 65+)
• Health Sector Analysis: Healthcare expenditure trend modeling
• Tourism Economics: Analysis of tourism arrivals and revenue patterns
• Numerical Methods: Runge-Kutta 4th-order (RK4) methods for solving differential equations

Project Structure

MSED/
├── code/                      # Analysis notebooks and scripts
│   ├── poblaciones/          # Population dynamics (Chile & Mexico)
│   ├── sectores_economia/    # Economic sector modeling
│   └── sectores_salud/       # Health sector analysis
├── data/                      # Datasets
│   ├── raw/                  # Original data (Excel/CSV)
│   └── processed/            # Cleaned and processed data
├── documentation/             # Analysis documentation
│   └── Analisis_poblacional/ # LaTeX reports for Chile & Mexico
├── utils/                     # Reusable utilities
│   ├── RK.py                 # Runge-Kutta solver implementation
│   ├── modelacion.py         # Regression + ODE workflow
│   ├── tasas.py              # Exchange rate utilities
│   └── requirements.txt      # Python dependencies
└── archive/                   # Previous deliverables and scripts

Methodology

The project follows a structured workflow for socio-economic modeling:

1. Data Collection

• Gather historical data from census, government reports, and economic databases
• Store raw data in data/raw/ (population, health expenditure, tourism statistics)

2. Data Preprocessing

• Normalize European notation and handle missing values
• Clean and structure data for analysis
• Output processed datasets to data/processed/

3. Statistical Analysis

• Apply linear regression using statsmodels.OLS to fit trends
• Extract coefficients to build differential equations
• Validate statistical significance of models

4. Differential Equation Construction

• Convert regression models into systems of ordinary differential equations (ODEs)
• Define initial conditions based on historical data
• Specify time periods for prediction

5. Numerical Solution

• Implement Runge-Kutta 4th-order (RK4) method for ODE solving
• Generate predictions through specified time periods
• Compare model outputs with actual data

6. Visualization & Reporting

• Create graphs and visualizations using matplotlib
• Generate comprehensive reports using LaTeX
• Document findings in Jupyter notebooks

Technologies

Python Stack:

• pandas & numpy - Data processing and numerical operations
• statsmodels & scipy - Statistical modeling and optimization
• matplotlib - Visualization
• jupyter - Interactive notebooks for analysis

Documentation:

• LaTeX - Professional report generation
• Markdown - Notebook documentation

Installation

Prerequisites

• Python 3.7+
• pip package manager

Setup

1. Clone the repository:

git clone https://github.com/Lunaaaalj/MSED.git
cd MSED

2. Install dependencies:

pip install -r utils/requirements.txt

3. Launch Jupyter notebooks:

jupyter notebook

Usage

Population Analysis Example

Navigate to population analysis notebooks:

cd code/poblaciones
jupyter notebook

Open the desired notebook (e.g., Chile or Mexico analysis) to:

• Load historical population data
• Run regression analysis on age groups
• Solve population dynamics ODEs using RK4
• Generate forecasts and visualizations

Health Sector Analysis

Analyze healthcare expenditure trends:

cd code/sectores_salud
jupyter notebook

Tourism Economics

Study tourism patterns:

cd code/sectores_economia
jupyter notebook

Key Features

Runge-Kutta 4th Order Solver

The utils/RK.py module provides a custom RK4 implementation for solving systems of ODEs:

from utils.RK import runge_kutta_4
# Solve ODE system with initial conditions and time steps

Modeling Pipeline

The utils/modelacion.py module integrates regression and ODE solving:

from utils.modelacion import modelo_poblacion
# Run complete regression → ODE → prediction pipeline

Data Sources

The project analyzes data from:

• Population: Census data and demographic projections (2005-2019+)
• Health: Government expenditure on healthcare systems
• Tourism: Arrival statistics and revenue data with currency conversion
• Infrastructure: Supporting economic metrics

Documentation

Detailed analysis reports are available in documentation/:

• Analisis_poblacional/chile/modelacion_chile.pdf - Chile population model
• Analisis_poblacional/mexico/modelacion_mexico.pdf - Mexico population model

Each notebook contains inline documentation with:

• Markdown explanations of methodology
• Code comments for key operations
• Visualization interpretations

Contributing

This is an academic research project. For questions or collaborations, please open an issue.

License

Please refer to the repository license file for usage terms.

Acknowledgments

This project applies mathematical modeling techniques to real-world socio-economic data for Chile and Mexico, providing insights into demographic shifts, healthcare trends, and tourism economics.