Herd immunity math
Tue, Oct 13, 2026 · Week 8 · Genetics of Disease (Medical Interventions)
Today's goal: Calculate a herd immunity threshold from a reproduction number and explain who it protects.
This is a model of the work you should turn in today. Use it to check your own: match the structure and the level of detail, do not copy it. Your data and wording should be your own.
Herd immunity threshold work (sample)
Formula: HIT = 1 minus (1 divided by R-zero)
Disease A, measles, R-zero of 12
HIT = 1 minus (1 divided by 12) = 1 minus 0.083 = 0.917
So about 92 percent of the community has to be immune.
Disease B, seasonal influenza, R-zero of 1.3
HIT = 1 minus (1 divided by 1.3) = 1 minus 0.77 = 0.23
So about 23 percent has to be immune.
Why a higher R-zero needs a higher rate: one infectious person with measles infects about 12 others in a fully susceptible group, so nearly every route out of that person has to be blocked before the chain dies out. A disease whose average case infects only slightly more than one other person needs far fewer of those routes blocked, which is why the same 60 percent coverage can be comfortable for one disease and dangerous for another.
One group this protects who cannot be vaccinated: infants who are too young for the first MMR dose. They cannot be vaccinated yet, so the only thing between them and measles is that the people around them are immune. People receiving chemotherapy are in the same position, because their immune systems cannot mount a response to a live vaccine.
The ceiling on this calculation: the formula assumes a vaccine that works every time and a community that mixes at random. Neither is true for influenza, where the vaccine is partly effective and changes year to year, so 23 percent is the floor this model gives and not a public health target anyone would set.
What surprised me: 92 percent leaves very little room. A school at 85 percent coverage sounds high and is still under the measles threshold.
This model shows the level of evidence and organization needed to complete: Completes the herd immunity task: two threshold calculations with the formula and the work shown, one sentence on why a higher R-zero demands higher coverage, and one group that depends on herd immunity.
- Name the prompt or task.
- Answer it directly with the key evidence.
- Check that the response matches the requested format.
Keep the structure. Replace the question, facts, measurements, and evidence. Then recheck units, vocabulary, and whether the conclusion goes beyond the evidence.
Also due today: Submit both calculations and your explanation on Schoology before you leave.
Turn in: Herd immunity threshold calculations
Go to Schoology to turn this in.
Submit one PDF. Put your first and last name in the document header. Name the file: FirstName LastName - Assignment Title - YYYY-MM-DD.pdf.
Open Schoology PDF upload helpIf you cannot get in, see Mr. Mendoza. Do not skip the work.
Claim ceiling: Today's evidence supports a classroom claim about herd immunity math. It cannot prove causation, diagnose a real patient, or justify action outside this room.
One exam-style question that uses exactly what you practiced today. Try it before you reveal the answer, then read why each choice is right or wrong.
Tap an answer to see the full explanation. Nothing is recorded or graded.
It builds this reusable test skill: Computing a herd immunity threshold from R-zero and reading what it says about a community.
- Name the concept or data pattern being tested.
- Cross out choices that violate that rule or the evidence.
- Justify the best remaining choice before checking the answer.