Forge Capsule

Epidemiology: SIR Models, Herd Immunity, and R0

SIR model: dS/dt=-βSI/N, dI/dt=βSI/N-γI, dR/dt=γI. R0=β/γ (basic reproduction number). Epidemic if R0>1. Herd immunity threshold: 1-1/R0. COVID-19 R0≈2.5-3 (original strain), Delta ≈5-6, Omicron ≈8-15. SEIR adds Exposed compartment. SIR assumptions: homogeneous mixing, constant population, no reinfection. Network epidemiology: heterogeneous contact networks, superspreaders. Rt: effective reproduction number (time-varying). Non-pharmaceutical interventions (NPIs): reduce β. Vaccine efficacy: prevents infection (VE_I) or severe disease (VE_D). Excess mortality: true cost of epidemic. Forge DeSci: epidemiology capsules with WHO provenance chains.