It appears that there's an issue with the indentation of the differential equations within the SEIR function, which is causing the function to not execute properly. In Python, proper indentation is crucial, as it defines the scope of the function.

Here's the corrected code with proper indentation:

pythonCopy code
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint

# Parameter model
N = 1000  # Total population
beta = 0.2  # Transmission rate
sigma = 0.1  # Rate of exposed individuals becoming infectious
gamma = 0.05  # Recovery rate

# Initial conditions
S0 = 950  # Initial susceptible population
E0 = 50   # Initial exposed population
I0 = 0    # Initial infected population
R0 = 0    # Initial recovered population

# Simulation time
t = np.linspace(0, 100, 1000)

# Function for the SEIR differential equations
def SEIR(y, t, beta, sigma, gamma, N):
    S, E, I, R = y
    dSdt = -beta * S * I / N
    dEdt = beta * S * I / N - sigma * E
    dIdt = sigma * E - gamma * I
    dRdt = gamma * I
    return [dSdt, dEdt, dIdt, dRdt]

# Initial conditions array
y0 = [S0, E0, I0, R0]

# Solve the differential equations
sol = odeint(SEIR, y0, t, args=(beta, sigma, gamma, N))
S, E, I, R = sol.T

# Plot the results
plt.plot(t, S/N, label='Susceptible')
plt.plot(t, E/N, label='Exposed')
plt.plot(t, I/N, label='Infected')
plt.plot(t, R/N, label='Recovered')
plt.xlabel('Time')
plt.ylabel('Proportion')
plt.legend()
plt.show()

Explanation of Key Parts

• Model Parameters: beta, sigma, and gamma represent the transmission rate, the rate of moving from exposed to infectious, and the recovery rate, respectively.
• Initial Conditions: The SEIR model assumes that individuals transition between susceptible (S), exposed (E), infected (I), and recovered (R) compartments over time.
• ODE Function: The SEIR function models the rates of change for each compartment using the SEIR equations.
• Plotting Results: The plt.plot function visualizes the progression of the SEIR compartments over time.

Would you like further details on any part of the code or the model?

Related Questions

1. How can we modify this model to include vaccination?
2. What if we introduce a birth and death rate to the model? How would the equations change?
3. Can we extend this model to multiple interacting populations?
4. How does varying the beta parameter affect the curve shapes?
5. Can we visualize the model with different initial conditions?

Tip

Experiment with different values for beta, sigma, and gamma to see how they impact the spread and recovery in the SEIR model. This helps in understanding disease dynamics under varying conditions.