Stochastic SIRD Epidemic Simulation (CTMC)

Authors: MiguelGG14, andri-10, Abubakar17

This project implements and analyses a stochastic SIRD epidemic model using a Continuous-Time Markov Chain (CTMC) and Gillespie’s algorithm.
It was completed as part of the ISC2 – Introduction to Stochastic Modelling course at Université de Technologie de Compiègne.

The repository contains:

• notebook.ipynb – full implementation of simulations, analytics, and plots
• Task.md – list of all project questions and objectives
• README.md – overview and usage instructions

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Project Overview

The epidemic model includes four compartments:

• S – Susceptible
• I – Infectious
• R – Recovered
• D – Dead

Transitions between states follow a CTMC with rates:

• Infection: ( \beta \frac{SI}{N} )
• Recovery: ( \gamma I )
• Death: ( \nu I )

The simulation is performed using Gillespie’s algorithm, generating full stochastic trajectories until extinction of infection.

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Main Results (see notebook)

✔ 100 stochastic epidemic trajectories
✔ Mean and variance of extinction time
✔ Distribution of infections at half extinction time
✔ Final epidemic size (mean + variance)
✔ Plot of S, I, R, D for multiple trajectories
✔ Estimation of the basic reproduction number ( R_0 ) from early exponential growth
✔ SEIRD extension including a latent (exposed) compartment

(All results are reproducible directly from the notebook.)

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How to Run

1. Open the notebook:

Simulation_SIR(D).ipynb

2. Run all cells to reproduce:

• Simulations
• Plots
• Analytics
• ( R_0 ) estimation

Python libraries required:

• numpty
• pandas
• matplotlib