3
Explain
SEIR and More Complex Models
Learning Objectives
- Explain why an Exposed (E) compartment is needed for many diseases
- Write the SEIR differential equations
- Define latent period and incubation period
- Compare SIR and SEIR dynamics
- Identify when more complex models are needed
The SEIR Model
Many diseases have a latent period where individuals are infected but not yet infectious:
S
Susceptible
E
Exposed
I
Infectious
R
Recovered
SEIR Equations
dS/dt = -beta * S * I / N
dE/dt = beta * S * I / N - sigma * E
dI/dt = sigma * E - gamma * I
dR/dt = gamma * I
Where sigma = 1/(latent period) is the rate at which exposed individuals become infectious.
Latent Periods for Common Diseases
| Disease | Latent Period | Infectious Period |
|---|---|---|
| Influenza | 1-2 days | 3-5 days |
| COVID-19 | 3-5 days | 5-10 days |
| Measles | 8-12 days | 4-8 days |
| Tuberculosis | Weeks to years | Variable |
Activity: Compare SIR and SEIR
Extend your SIR spreadsheet model to include the E compartment:
- Use N = 1000, I(0) = 1, E(0) = 0, beta = 0.5, gamma = 0.1, sigma = 0.2
- Compare the timing and height of the epidemic peak
- How does the latent period affect the speed of the outbreak?
- What happens if sigma is very large (short latent period)?
Key Takeaway
The SEIR model adds biological realism by accounting for the latent period between infection and infectiousness. This delay affects the dynamics of outbreaks and is important for accurate prediction. The choice of model depends on the disease characteristics and the questions being asked.