SIHRS Epidemic Model Website

Overview

This website provides an interactive simulation of the SIHRS epidemic model with death and reinfection compartments. The model extends the classic SIR model by adding hospitalization and death, while allowing recovered individuals to become susceptible again.

Mathematical Model

The SIHRS model defines $s, i, h, r, d : (0, \infty) \to \mathbb{R}_{\geq 0}$, with $s + i + h + r + d = 1$, by:

\begin{align} \dot{s} &= -\beta p_{SI} ~s i + p_{RS} \Lambda r,
\dot{i} &= \beta p_{SI} ~s i - \gamma ~ (1-p_{II}) i,
\dot{h} &= p_{IH} \gamma i - \alpha ~(1-p_{HH}) h,
\dot{r} &= p_{IR} \gamma i + p_{HR}\alpha h-p_{RS} \Lambda r,
\dot{d} &= p_{ID} \gamma i + p_{HD}\alpha h, \end{align}

Parameters

Transition Rates:

• $\beta$: Infection rate
• $\gamma$: I transition rate
• $\alpha$: H transition rate
• $\Lambda$: R transition rate (reinfection rate)

Transition Probabilities:

• $p_{SI}$: S → I probability
• $p_{II}$: I → I probability (stay infected)
• $p_{IH}$: I → H probability
• $p_{IR}$: I → R probability
• $p_{ID}$: I → D probability
• $p_{HH}$: H → H probability (stay hospitalized)
• $p_{HR}$: H → R probability
• $p_{HD}$: H → D probability
• $p_{RR}$: R → R probability (stay recovered)
• $p_{RS}$: R → S probability (reinfection)

Constraints:

• $p_{II} + p_{IH} + p_{IR} + p_{ID} = 1$
• $p_{HH} + p_{HR} + p_{HD} = 1$
• $p_{RR} + p_{RS} = 1$

Features

1. Interactive Parameter Control

• Real-time adjustment of all model parameters
• Validation of probability constraints
• Visual feedback for parameter changes

2. Dual Simulation Modes

• Stochastic: Multiple runs using Gillespie algorithm
• Deterministic: ODE solution using Euler integration
• Side-by-side comparison

3. Advanced Visualization

• Multi-compartment plotting (S, I, H, R, D)
• Uncertainty envelopes for stochastic runs
• Interactive charts with zoom and pan

4. Threshold Analysis

• R₀ calculation and display
• σ, σ̃, σ̃̃ threshold parameters
• Real-time threshold updates

5. Statistics Dashboard

• Peak infected proportion
• Peak time
• Final death proportion
• Total reinfection count

6. Data Export

• Download simulation data as CSV
• Export charts as PNG
• Pattern analysis results

Key Differences from SIHR Model

Usage

1. Open the website: Navigate to index_sihrs.html
2. Adjust parameters: Use sliders or number inputs
3. Run simulation: Click “Run Simulation”
4. Analyze results: View charts and statistics
5. Export data: Use download buttons

Technical Implementation

• Frontend: HTML5, CSS3, JavaScript
• Charts: Chart.js with custom styling
• Simulation: Custom Gillespie algorithm implementation
• ODE Solver: Euler integration method
• Validation: Real-time parameter constraint checking

Default Parameters

Based on realistic COVID-19 modeling:

• $\beta = 0.160$ (infection rate)
• $\gamma = 0.126$ (I transition rate)
• $\alpha = 0.100$ (H transition rate)
• $\Lambda = 0.007$ (reinfection rate)
• $p_{IH} = 0.040$ (4% hospitalization rate)
• $p_{ID} = 0.001$ (0.1% death rate from infection)
• $p_{HD} = 0.002$ (0.2% death rate from hospitalization)
• $p_{RS} = 0.980$ (98% reinfection probability)

Files Structure

SIHR Stochastic vs ODE/
├── index_sihrs.html          # Main SIHRS website
├── src/
│   ├── js/
│   │   ├── models/
│   │   │   └── sihrs-model.js    # SIHRS model implementation
│   │   ├── components/
│   │   │   ├── ui-controls.js    # UI control functions
│   │   │   ├── pattern-analysis.js # Pattern analysis
│   │   │   └── download-utils.js # Data export utilities
│   │   └── main-sihrs.js         # Main application logic
│   └── css/
│       └── styles.css            # Styling (shared with SIHR)
└── README_SIHRS.md              # This file

Browser Compatibility

• Chrome 80+
• Firefox 75+
• Safari 13+
• Edge 80+

Requires JavaScript enabled and Chart.js CDN access.

License

This project is for educational and research purposes.