Teacher sheet · Ages 15–16 · about 45–50 minutes
Vaccination, immune memory and herd immunity
Lesson page: echoesof.science/school/vaccines/ages-15-16/ · Pupil worksheet: echoesof.science/school/vaccines/ages-15-16/print/
Learning aims
- Distinguish active and passive immunity and describe the main vaccine types.
- Explain primary and secondary responses, memory cells and boosters.
- Calculate herd immunity thresholds from R₀ and test them with a stochastic model.
- Evaluate the assumptions of a model.
Lesson plan
| Time | Activity |
|---|---|
| 5 min | Starter: why was smallpox the first human disease to be eradicated? |
| 10 min | Read the text; antibody-time graph sketch. |
| 25 min | Random-number transmission model, class data pooling. |
| 5 min | Threshold calculations. |
| 5 min | Quiz or sorting game. |
Materials for the experiment
- Two ten-sided dice (or a random number table, or a spreadsheet with =RANDBETWEEN(0,99))
- Calculator
- Results table and graph paper
Safety: No hazards: this is a paper or spreadsheet model. Treat the topic sensitively: do not ask pupils about their own or their family's vaccination status.
Common misconceptions
| Pupils may think… | Actually… |
|---|---|
| Herd immunity means 100% of people must be vaccinated. | The threshold is about 1 − 1/R₀, which is below 100% and depends on how infectious the disease is. |
| Vaccinated people can never be infected. | No vaccine is 100% effective; vaccinated people are far less likely to become seriously ill. |
| Passive immunity lasts as long as active immunity. | Passive immunity is immediate but fades within weeks or months. |
Worksheet answers
- Primary: a lag of days to weeks, then a modest peak and fall. Secondary: a short lag and a much higher (tens to hundreds of times), longer-lasting peak.
- R₀ = 2: 50%; R₀ = 6: about 83%; R₀ = 15: about 93%. The more infectious the disease, the higher the coverage needed.
- Example: at 0% and 50% coverage cases grow rapidly (R = 4 and 2); at 75% (R = 1) results vary widely; at 90% (R = 0.4) chains die out quickly, matching the predicted threshold of 75%.
- Vaccines are not 100% effective; people do not mix randomly (families, schools, clusters with low coverage); R₀ estimates vary; immunity can fade over time.
Quiz answers
- Why does vaccination give active rather than passive immunity? The body makes its own antibodies and memory cells. Active immunity develops more slowly but lasts longer.[1]
- A toxoid vaccine contains… a toxin treated so it is harmless. Toxoids are bacterial toxins made non-toxic.[1]
- Compared with the primary response, the secondary response… is faster and produces far more antibody. Memory cells give tens to hundreds-fold more antibody.[5]
- What is the herd immunity threshold for a disease with R₀ = 5? 80%. 1 − 1/5 = 0.8.[8]
- Why are boosters given for some vaccines? They mimic repeat exposure and strengthen memory. Boosters mimic repeated exposures.[5]
- Why do some people rely on herd immunity? They cannot be vaccinated, for example very young babies. High coverage indirectly protects people who cannot have a vaccine.[7]
Going further
Change the model so that the vaccine protects only 9 out of 10 vaccinated contacts. Does the coverage needed to stop outbreaks go up or down? Compare with the 95% vaccination target for measles.
Sources used in this lesson
- [1] Explaining How Vaccines Work (Centers for Disease Control and Prevention (USA)): reliability High
- [2] How do vaccines work? (World Health Organization): reliability High
- [3] Why vaccination is important and the safest way to protect yourself (NHS (UK National Health Service)): reliability High
- [4] Concepts of Biology, 17.3 Adaptive Immunity (OpenStax, Rice University): reliability High
- [5] Biology, 42.2 Adaptive Immune Response (OpenStax, Rice University): reliability High
- [6] History of smallpox vaccination (World Health Organization): reliability High
- [7] What is herd immunity? (The Royal Society (UK)): reliability High
- [8] How Herd Immunity Works (History of Vaccines, The College of Physicians of Philadelphia): reliability Medium-high
Full list with links and a note on each source's reliability: echoesof.science/school/vaccines/sources/
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