SEIR Epidemic Model
Susceptible-Exposed-Infectious-Recovered ODE dynamics
S
E
I
R
R₀ (basic reproduction):
2.5
σ (1/incubation days):
0.20
γ (1/infectious days):
0.10
μ (birth/death rate):
0.002
Run / Reset
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.