SEIR Epidemic Model

Susceptible-Exposed-Infectious-Recovered ODE dynamics

S
E
I
R
SEIR equations:
dS/dt = μ(1−S) − βSI
dE/dt = βSI − (σ+μ)E
dI/dt = σE − (γ+μ)I
dR/dt = γI − μR

β = R₀·(γ+μ)

Endemic equilibrium exists when R₀ > 1 + μ/σ. With μ>0 disease can persist; with μ=0 it always dies out.

Phase portrait below shows I vs S trajectory.