Formula Reference

Agent (Chapter 1)

  • Infectivity = infected / susceptible × 100
  • Pathogenicity = clinical cases / exposed × 100
  • Virulence (case fatality) = deaths / cases × 100

Frequency (Chapter 4)

  • Prevalence = existing cases / population
  • Cumulative incidence (risk) = new cases / population at risk at start
  • Incidence rate = new cases / animal-time at risk
  • Prevalence ≈ incidence rate × average duration
  • True prevalence = (apparent + Sp − 1) / (Se + Sp − 1) (Rogan–Gladen)

Association (Chapter 5)

  • Relative risk RR = risk_exposed / risk_unexposed
  • Odds ratio OR = (a·d) / (b·c)
  • Attributable risk (exposed) ARe = risk_exposed − risk_unexposed
  • Attributable fraction (exposed) AFe = (RR − 1) / RR
  • Population attributable fraction PAF = (risk_total − risk_unexposed) / risk_total

Diagnostic tests (Chapter 6)

  • Sensitivity = TP / (TP + FN); Specificity = TN / (TN + FP)
  • PPV = TP / (TP + FP); NPV = TN / (TN + FN) (depend on prevalence)
  • LR+ = Se / (1 − Sp); LR− = (1 − Se) / Sp
  • Youden’s index = Se + Sp − 1

Sampling (Chapter 8)

  • Estimate a proportion: n = Z² · p(1 − p) / d²
  • Finite-population correction: n_adj = n / (1 + n/N)

Interventions (Chapter 10)

  • Vaccine effectiveness VE = 1 − RR
  • Herd-immunity threshold HIT = 1 − 1/R₀
  • Critical vaccination coverage Vc = HIT / VE

Surveillance (Chapter 12)

  • System sensitivity CSe = 1 − ∏(1 − Seᵢ)
  • Probability of freedom (one round): posterior = prior / [prior + (1 − prior)(1 − CSe)]

Evidence synthesis (Chapter 15)

  • Random-effects weight wᵢ = 1 / (vᵢ + τ²)
  • Heterogeneity I² = (Q − df) / Q × 100

Genetics (Chapter 16)

  • Heritability (half-sib) h² = 4 · σ²_sire / σ²_total
  • Genetic gain ΔG = i · accuracy · σ_a (breeder’s equation)