SIR Epidemic Model — Verification & Validation

A Python-based SIR (Susceptible-Infected-Recovered) epidemic model simulator with formal property verification, exhaustive parameter tuning, and predictive validation against real-world Influenza data.

Course: Introduction to Computational Modelling
Institution: University of the Punjab, College of Information Technology
Instructor: Dr. Syed Waqar ul Qounain Jaffry

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Overview

This program simulates the spread of infectious disease using the classic SIR compartmental model, solved numerically via the Euler method. It was applied to real Influenza spread data from the USA and Netherlands during 2009–2011 to demonstrate model verification, validation, and prediction.

What It Does

Feature	Description
Trace Generation	Simulate SIR dynamics with any custom parameters (N, I₀, R₀, β, γ)
Property Verification	Check 3 formal mathematical properties across 10,201 parameter combinations
Parameter Tuning	Exhaustive grid search over β and γ to find the best fit to training data
Model Prediction	Apply tuned parameters to unseen test data and report testing error
Import / Export	Export simulation traces to CSV; import empirical I(t) data from CSV

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Mathematical Model

The SIR model divides a population of size N into three compartments:

dS/dt = -β * I * S / N
dI/dt =  β * I * S / N  -  γ * I
dR/dt =  γ * I

Symbol	Meaning
S	Susceptible population
I	Infected population
R	Recovered population
β	Transmission rate (infection spread speed)
γ	Recovery rate (how fast people recover)
Δt	Euler integration time step (0.1)

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Formal Properties Verified

Three logical properties are checked on every simulation trace:

#	Property	Mathematical Definition
P1	Conservation	S(t) + I(t) + R(t) = N for all t
P2	Non-negativity	S(t) ≥ 0, I(t) ≥ 0, R(t) ≥ 0 for all t
P3	Monotonicity	S(t+1) ≤ S(t) for all t

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Dataset

Real-world weekly Influenza case counts from the USA and Netherlands:

Dataset	Period	USA Population	NL Population	Weeks
Training	2009–2010	60,000	5,000	55
Testing	2010–2011	60,000	5,000	55

Parameter Search Space

Parameter	Range	Step Size
β (transmission)	[0.00, 1.00]	0.01
γ (recovery)	[0.00, 1.00]	0.01
Δt (time step)	0.1	—
Total combinations	10,201	—

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How to Run

Prerequisites

• Python 3.6 or higher (no external libraries needed)

Execution

python sir_model.py

Menu Options

  1. Generate SIR Trace
  2. Check Formal Properties
  3. Parameter Tuning (Exhaustive Search)
  4. Model Prediction (Test Phase)
  5. Export / Import
  6. Exit

Recommended Workflow

1. Run Option 2 to verify formal properties
2. Run Option 3 to find the best parameters via exhaustive search
3. Run Option 4 to test the tuned model against 2010–2011 data

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Sample Results

Best Parameters Found (Training Data 2009–2010)

Country	β	γ	Training MSE
USA	0.76	0.54	722,367.13
Netherlands	1.00	0.74	11,616.37

Prediction Results (Test Data 2010–2011)

Country	Testing MSE
USA	1,968,936.01
Netherlands	3,166.06

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Generated Reports

Running the program automatically creates these report files:

File	Contents
Properties_Report.txt	Formal property verification results
Tuning_Report.txt	Top 1% parameter settings with training errors
Prediction_Report.txt	Testing errors for the best-tuned model

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Project Structure

├── sir_model.py           # Main program (single file, menu-driven)
├── Properties_Report.txt  # Auto-generated after Option 2
├── Tuning_Report.txt      # Auto-generated after Option 3
├── Prediction_Report.txt  # Auto-generated after Option 4
└── README.md              # This file

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Technologies

• Language: Python 3
• Libraries: csv, sys (standard library only — zero dependencies)
• Numerical Method: Euler forward integration

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License

This project is for educational purposes as part of CS-501 coursework.