SIR + Contact Tracing

Contact tracing allows identifying and quarantining exposed contacts before they become infectious. Even partial tracing can dramatically reduce epidemic size. There exists a critical tracing coverage f_c below which epidemics still occur and above which they are rapidly contained.

Susceptible
Infected
Recovered
Quarantined

Epidemic Parameters

R₀2.5
R_eff (with tracing)—
Total infected—
Peak infected—
StatusRunning
Contact tracing logic:
When a node is detected infected (with delay d), a fraction f of its neighbors are traced and quarantined.

Critical fraction:
f_c ≈ 1 - 1/R₀
At f > f_c, each case generates <1 non-quarantined secondary case → extinction

With delay d: contacts made in the last d days are missed; effectiveness scales as ~(1-d/τ_infect)