Epidemic Model Simulator
Epidemic Model Simulator simulates the spread of an infectious disease using the SIR model. Enter parameters for the total population \( N \), initial infected \( I_0 \), infection rate \( \beta \), and recovery rate \( \gamma \). The model computes the number of Susceptible (\( S \)), Infected (\( I \)), and Recovered (\( R \)) individuals over time.
Methodology Used in Epidemic Model Simulator
The SIR model is a compartmental model used in epidemiology to describe the spread of infectious diseases. The population is divided into three compartments: Susceptible (\( S \)), Infected (\( I \)), and Recovered (\( R \)). The model uses differential equations to simulate the dynamics over time.
SIR Model Equations:
\[ \frac{dS}{dt} = -\beta \frac{S I}{N} \] \[ \frac{dI}{dt} = \beta \frac{S I}{N} – \gamma I \] \[ \frac{dR}{dt} = \gamma I \]Where:
- \( S \): Number of susceptible individuals
- \( I \): Number of infected individuals
- \( R \): Number of recovered individuals
- \( N \): Total population (\( S + I + R \))
- \( \beta \): Infection rate (probability of transmission per contact)
- \( \gamma \): Recovery rate (inverse of average infectious period)
Algorithm Steps:
1. Input parameters: \( N \), \( I_0 \), \( \beta \), \( \gamma \), and simulation days.
2. Initialize: \( S_0 = N – I_0 \), \( I_0 \), \( R_0 = 0 \).
3. Numerically solve the SIR equations using the Euler method with a time step of 1 day.
4. Display results in a chart showing \( S \), \( I \), and \( R \) over time.
5. Render equations and results with LaTeX formatting.