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.