🏥 SEIR Epidemic Model — Exposed & Intervention Dynamics

Extend the classic SIR model with an Exposed compartment (SEIR) to model incubation periods and pre-symptomatic spread. Compare intervention strategies — lockdowns, mask mandates, and vaccine rollout — to see how they flatten the curve and reduce total cases.

R₀: 2.5

Incubation 1/σ: 5 days

Infectious 1/γ: 7 days

Vax rate: 0%/day

Peak I: —%

Attack rate: —%

Days to peak: —

Herd imm. p_c: —%

R_eff: —

Physics / Epidemiology

SEIR model: dS/dt = −β·S·I/N; dE/dt = β·S·I/N − σ·E; dI/dt = σ·E − γ·I; dR/dt = γ·I. The incubation period 1/σ captures the time between exposure and becoming infectious. R₀ = β/γ. Interventions reduce β: lockdown ×0.4, masks ×0.7. Herd immunity threshold: p_c = 1 − 1/R₀. The SEIR model better captures diseases like COVID-19 (σ = 1/5 days) where infected people are contagious before showing symptoms.