🦠 SIR Model Simulation in MATLAB

This project explores epidemiological modeling using discrete-time SIR models in MATLAB. It simulates how diseases spread through populations under varying assumptions, including total population changes and loss of immunity.

🔬 What’s Inside

• Part 1 – Basic SIR Model
  Models the spread of a disease in a closed population using constant parameters.

• Part 2 – Variable Population SIR Model
  Includes births, deaths, and infection-related mortality in the total population over time.

• Part 3 – Immunity Loss SIR Model
  Adds the possibility of losing immunity, where recovered individuals may return to the susceptible group.

📈 Features

• Discrete updates using custom functions (no built-in solvers)
• Multi-part plotting with plot() and linspace()
• Variable control of transmission (α), recovery (β), death (γ), birth/death (μ), and immunity loss (ω)
• Visualizations:
  • Time evolution of susceptible, infected, recovered, and total populations
  • Phase plot: Infected vs. Susceptible

🧪 Topics Covered

• SIR (Susceptible-Infected-Recovered) modeling
• Epidemiology & population dynamics
• Discrete equation modeling
• Immunity waning models
• Parameter sensitivity

🚀 How to Run

1. Open MATLAB
2. Make sure Project5.m is in your working directory
3. Run it by typing:

Project5