COVID-19 Disease Spread Simulation

A Python implementation of mathematical models to simulate COVID-19 epidemic dynamics and analyze intervention strategies.

Overview

This project uses non-linear modeling approaches to understand disease progression and evaluate the effectiveness of different public health interventions. The simulation helps analyze how lockdowns and vaccination campaigns impact epidemic spread patterns.

Mathematical Models

SIR Model

The primary model divides the population into three compartments:

• S: Susceptible individuals who can be infected
• I: Infected individuals who can transmit the disease
• R: Recovered/Removed individuals (immune or deceased)

Differential Equations:

dS/dt = -β(SI/N)
dI/dt = β(SI/N) - γI
dR/dt = γI

Key Parameters:

• β: Transmission rate (higher values = faster spread)
• γ: Recovery rate (1/γ = average infectious period)
• R₀: Basic reproduction number (β/γ)
• N: Total population size

Logistic Growth Model

Initial approach for understanding epidemic progression:

dN/dt = rN(1 - N/K)

Where N is infected population, r is growth rate, and K is carrying capacity.

Intervention Strategies

Lockdown Interventions

• Mechanism: Reduces transmission rate (β)
• Variables: Different reduction percentages and implementation timings
• Analysis: Effectiveness vs. timing (days 100-1000)

Vaccination Interventions

• Mechanism: Increases recovery rate (γ)
• Variables: Different vaccination speeds and campaign start times
• Focus: Long-term population immunity effects

Key Features

• Simulate epidemic progression over time
• Compare different intervention strategies
• Analyze timing effects (early vs. delayed interventions)
• Generate epidemic curves and visualizations
• Test various parameter combinations

Results Summary

Lockdown Findings:

• More effective lockdowns (higher β reduction) → lower peak infections
• Earlier implementation → significantly better outcomes
• Temporary effects requiring sustained measures

Vaccination Findings:

• Higher vaccination rates → faster epidemic resolution
• Early campaigns → more effective long-term control
• More durable protection compared to lockdowns

Key Insight: Combined approaches provide the most robust epidemic control.

Usage

The code includes simulation scripts for:

1. Basic SIR model runs
2. Intervention scenario comparisons
3. Parameter sensitivity analysis
4. Visualization of results

Run the main simulation files to generate epidemic curves and analyze different intervention scenarios.

Model Assumptions

• Homogeneous population mixing
• Fixed infection and recovery rates
• No reinfections (permanent immunity)
• No demographic changes during simulation period

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Course Project: Introduction to Modelling and Simulation
Team: Ama Annor, Austine Iheji, Edward Mensah, Eric Hantungimana, Susanna Agyapong
April 2025