Epidemic Control — Optimal Vaccination Strategy

SEIR dynamics, herd immunity threshold, targeted vs random vaccination

SEIR Dynamics

Phase portrait & R₀ threshold

Final size vs vaccine coverage

Optimal timing of intervention

Network heterogeneity effect

Basic reproduction R₀ 2.50 Latent period 1/σ (days) 5.0 Infectious period 1/γ (days) 7.0 Vaccine coverage v (%) 0 Vaccine efficacy ε (%) 90

R₀ = — | Herd immunity threshold: —% | Effective R: —
Final epidemic size: —% | Peak prevalence: —% | Days to peak: —