Tumor-Immune Dynamics Model
01. Overview
An interactive web platform for exploring the Nonlinear Tumor-Immune Unstable Hybrid Dynamical Model (NTIUNHDM) — a mathematical framework investigating the complex interactions between tumor cells, immune response, and dietary factors through differential equations and numerical methods.
The Objective
To make complex cancer research mathematics accessible through interactive visualizations and real-time differential equation simulations.
The Outcome
A fully interactive research platform combining rigorous mathematical modeling with intuitive cell simulations, accessible to researchers, students, and the general public.
02. Stack Architecture
03. Key Features
Interactive real-time cell simulation (normal, tumor, and immune cells)
Differential equation explorer with adjustable parameters
Research results visualized through interactive charts
ODE solver comparison and error analysis
Dark/light mode toggle
Fully responsive design
04. Engineering Pipeline
Studied the NTIUNHDM paper and translated its equations into numerical solvers
Designed modular React components for each page section (equations, results, code)
Integrated Framer Motion for smooth page transitions and data-driven animations
Deployed to Vercel with continuous integration via GitHub
05. Challenges & Execution
The Constraint
Visualizing complex differential equation behavior in real time
The Execution
Built a custom Canvas-based animation engine for real-time cell interaction visualization.
The Constraint
Making advanced cancer research mathematics accessible to non-specialists
The Execution
Implemented MathJax for crisp inline equation rendering paired with plain-language explanations.
The Constraint
Accurately representing multi-variable cell population dynamics on a canvas
The Execution
Layered interactive parameter sliders so users can observe how changes affect tumor-immune equilibria.