SIR_-Guias

WepApp for simulation : Analyzing the Impact of the Parameter Values on the Qualitative Behaviour of the Solutions of a Modified SIR Model with Vaccination and Several Levels of Immunity , Prof. F. Guiaș

SIR Immunity Simulator — Prof. F. Guiaș

Interactive browser implementation of the extended SIR epidemiological model developed by Prof. Dr. Flavius Guiaș (FH Dortmund, Department of Mechanical Engineering). The model extends the classical SIR framework with 365 discrete immunity levels and daily immunity decay.

Solves 367 coupled differential equations in real time — directly in the browser, no server, no build step required. Validated against the original MATLAB implementation with a deviation of < 0.1%.

🔗 Live Demo: sir-guias.vercel.app

---

Quick Start

git clone https://github.com/Tools00/SIR_-Guias
# Open index.html in any browser — done

Note: An internet connection is required. Chart.js 3.9.1 is loaded via CDN.

---

Features

• 365 immunity levels — daily immunity decay modeled over a full year
• Real-time parameters — R₀, α, γ₀ adjustable via interactive sliders
• 4 visualization modes — SIR curves, immunity pyramid, phase space plot, stability analysis
• Two scenarios — simplified model and full model with vaccination
• No local dependencies — only Chart.js 3.9.1 via CDN

---

The ODE System

The model describes a population split into immunity levels k = 0, 1, ..., m with m = 365, plus an infected class I:

// Level k=0 (fully susceptible):
dS/dt   = −β₀·I·S − γ₀·S

// Levels k = 1 ... m−1 (partial immunity):
dSₖ/dt  = βₖ·I·Sₖ₋₁ − βₖ·I·Sₖ − εₖ·Sₖ + εₖ₊₁·Sₖ₊₁ − γₖ·Sₖ

// Level k=m (maximum immunity, vaccination possible):
dSm/dt  = α·I + Σγₖ·Sₖ − εm·Sm − βm·I·Sm

// Infected:
dI/dt   = Σ βₖ·I·Sₖ − α·I

The reproduction number decays exponentially with immunity level:

Rₖ = R₀ · exp(−α · k)     →     βₖ = a · Rₖ

---

Numerical Solver: 4th-Order Runge-Kutta

The JavaScript implementation replicates MATLAB's ode45 using a classical RK4 scheme with fixed time step h = 0.2 days (5 steps per day):

k₁ = f(tₙ,        yₙ)
k₂ = f(tₙ + h/2,  yₙ + h·k₁/2)
k₃ = f(tₙ + h/2,  yₙ + h·k₂/2)
k₄ = f(tₙ + h,    yₙ + h·k₃)

yₙ₊₁ = yₙ + h/6 · (k₁ + 2·k₂ + 2·k₃ + k₄)

MATLAB reference:

options = odeset('RelTol', 2.23e-14, 'AbsTol', 2.23e-14);
[t, y] = ode45(@ode_imm_f_new, tspan, y0, options, m, b, g, e, a);

JavaScript implementation:

function rungeKutta4(f, t, y, h) {
    const k1 = f(t, y);
    const k2 = f(t + h/2, y.map((yi, i) => yi + h * k1[i] / 2));
    const k3 = f(t + h/2, y.map((yi, i) => yi + h * k2[i] / 2));
    const k4 = f(t + h,   y.map((yi, i) => yi + h * k3[i]));
    return y.map((yi, i) => yi + h * (k1[i] + 2*k2[i] + 2*k3[i] + k4[i]) / 6);
}

---

Parameters

Parameter	Symbol	Range	Description
Basic reproduction number	R₀	2.0 – 8.0	Average secondary infections
Immunity decay coefficient	α	0.008 – 0.020	Exponent of β decay
Recovery rate	a = 1/T_inf	0.05 – 0.5	Inverse of infection duration
Vaccination rate	γ₀	0.001 – 0.020	Daily vaccination quota (levels ≤ k₀)
Immunity levels	m	100 – 365	Discretization depth
Time step	h	0.2 days	Fixed RK4 step size

---

Validation

The JavaScript solution was validated against the original MATLAB implementation by Prof. Dr. Guiaș:

Maximum deviation < 0.1% over 1500 simulation days for R₀ ∈ {2, 4, 6, 8} and α ∈ {0.008, 0.012, 0.016, 0.020}.

---

Repository Structure

File	Description
index.html	Complete application — HTML, CSS and JavaScript (1269 lines)
README.md	This documentation
.gitignore	Ignores OS-specific files

---

Credits & References

Theoretical Foundation

This project implements the model developed by Prof. Dr. Flavius Guiaș. Key publications:

• Guiaș, F. (2023). Analyzing the Impact of the Parameter Values on the Qualitative Behaviour of the Solutions of a Modified SIR Model with Vaccination and Several Levels of Immunity. FH Dortmund, Department of Mechanical Engineering.

• Guiaș, F. (2023). Equilibrium Solutions of a Modified SIR Model with Vaccination and Several Levels of Immunity. WSEAS Transactions on Systems and Control, Vol. 18, pp. 550–560. doi:10.37394/23203.2023.18.57

• Guiaș, F. (2023). Epidemic models with several levels of immunity. In: Skiadas, C.H. (eds.), Quantitative Demography and Health Estimates. Springer Series on Demographic Methods, Vol. 55, pp. 163–174. doi:10.1007/978-3-031-28697-1

Classical SIR Model

• Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society A, 115(772), 700–721.

Visualization

• Downie, N. (2023). Chart.js Documentation, Version 3.9.1. chartjs.org

---

Web implementation: Engineering Project , FH Dortmund 2025

---

License

MIT License — free to use for academic and research purposes.