Cell Population Dynamics in Continuous Time Domain¶

Description¶

This project explores the mathematical modeling of cell population dynamics using the McKendrick–Von Foerster equation. The focus is on understanding the time-independent case where cell division and death rates depend on the cell's age.

Learning Outcomes¶

• Understand the McKendrick–Von Foerster equation for population dynamics.
• Apply separation of variables to solve partial differential equations.
• Derive and interpret the Euler-Lotka equation for population growth rates.

Requirements¶

Academic¶

• Basic knowledge of differential equations and mathematical modeling.
• Familiarity with population dynamics concepts.

System¶

• Python 3.11 or newer
• MkDocs for documentation generation
• Miniconda (recommended for managing dependencies)

Getting Started¶

1. Clone the repository and navigate to the project directory.
2. Set up a virtual environment and install the required dependencies:

   conda create --name cell-population-dynamics python=3.11
   conda activate cell-population-dynamics
   pip install -r requirements.txt
   

Project Structure¶

.
├── docs
├── notebooks
├── src
│   ├── __init__.py
|   ├── cells_manager.py   # Cell population manager
|   ├── plots.py           # Plotting functions
|   ├── run.py             # Main script to run the simulation
|   ├── simulation.py      # Core simulation logic
│   └── utils.py           # Utility functions
├── mkdocs.yml
├── requirements.txt
└── README.md

MkDocs Documentation¶

To generate local documentation, run the following command:

mkdocs serve

License¶

This project is licensed under the BSD-3-Clause license