Immunity and epidemiology: study guide

Key ideas

The immune system and public health share a toolkit: cells with defined jobs, and a handful of formulas for how far a disease spreads and how well a test or vaccine works.

• Macrophages engulf pathogens and present antigens, helper T cells coordinate the response, cytotoxic T cells kill infected cells, B cells become plasma cells that make antibodies, and memory cells give a faster second response.
• Herd immunity needs a fraction 1 − 1 ÷ R₀ of the population to be immune. A disease with R₀ = 4 needs 75 %.
• Vaccine efficacy = (attack rate in the unvaccinated − attack rate in the vaccinated) ÷ attack rate in the unvaccinated × 100.
• Sensitivity = TP ÷ (TP + FN) is how many sick people are detected. Specificity = TN ÷ (TN + FP) is how many healthy people are cleared. Positive predictive value = TP ÷ (TP + FP).

Key equations

• herd immunity threshold = 1 − 1 ÷ R₀
• VE = (ARU − ARV) ÷ ARU × 100
• sensitivity = TP ÷ (TP + FN)
• specificity = TN ÷ (TN + FP)
• PPV = TP ÷ (TP + FP)

Worked example

If 10 % of unvaccinated and 1 % of vaccinated people fall ill, the efficacy is (10 − 1) ÷ 10 = 90 %. A test gives 90 true positives, 10 false negatives, 180 true negatives and 20 false positives: sensitivity = 90 ÷ 100 = 90 %, specificity = 180 ÷ 200 = 90 % and PPV = 90 ÷ 110 = 82 %.

Common mistakes

• Confusing sensitivity (detecting the sick) with specificity (clearing the healthy).
• Using the vaccine attack rate alone as efficacy instead of comparing it with the unvaccinated.
• Believing that a high sensitivity guarantees a high PPV. PPV also depends on how common the disease is.

Practice

Test yourself with practice questions on this topic: Immunity and epidemiology