Controls
Vaccinated beforehand?
Readings
- Day now
- 52days
- Antibody now
- 296units
- Response lag
- 2.0days
- Infection to protection
- 2.5days
- Peak level
- 307units
- Time to peak
- 6.0days
- Vaccinated ÷ unvaccinated peak
- 5.1times
- Status
- Protected
How to use this simulation
- The left panel shows the blood. Red spiky balls are antigens (the germ). Blue Y shapes are antibodies. Below them are B cells, a plasma cell that makes antibodies, and a row of memory cells.
- The right panel is the graph of antibody level against days. The amber line is a person who was never vaccinated and the blue line is a person who was vaccinated on day 0. The playhead sweeps along the days, and the blood scene follows it.
- Press play and watch the infection day. For the unvaccinated person, the antibody level stays at zero for several days, then rises. For the vaccinated person, it rises almost at once and reaches a much higher peak.
- Use the buttons to switch between vaccinated and unvaccinated. The readings below show the lag, the time until the protective level and the peak for the chosen person.
- Drag the infection-day slider to see how antibody left over from the vaccine fades with time. Drag the memory-boost slider to make memory stronger or weaker, and the protective-level slider to move the green line.
- Press reset to return to the defaults, then check your numbers against the solved problems below.
The germ that was beaten before it started
Two children are exposed to the same germ in the same week. The first was vaccinated last year. The second never was. The first barely feels ill, because her blood already carries antibodies, and within a day or two of the germ arriving, she is making far more. The second child has to start from nothing. He has no antibody ready, and it takes his body days to find the right B cells and build a force. During that wait, the germ multiplies freely, and he gets sick.
The two children have the same immune system. The difference is memory. A vaccine gives the body a safe, harmless preview of the germ. The body answers it, and keeps a record of how.
This page lets you run that story as a graph. You can see the delay, the size of the response, and how both depend on whether the body has met the antigen before.
Two lines of defence
The body has a fast, general defence and a slow, specific one. Both run at once during an infection.
| Innate (non-specific) | Adaptive (specific) | |
|---|---|---|
| Speed | Minutes to hours | Days the first time |
| Target | Any germ, using the same tools | One particular antigen |
| Examples | Skin, mucus, stomach acid, phagocytes, fever | B cells and antibodies, T cells |
| Memory | None | Yes: memory cells |
| Improves with repeat exposure | No | Yes: a faster, bigger second response |
Words you need first
Immunology has a short vocabulary. Learn these before reading the graph.
| Term | What it means |
|---|---|
| Antigen | Any molecule the immune system recognises as foreign, such as a protein on a germ’s surface. |
| Antibody | A Y-shaped protein made by plasma cells that binds to one specific antigen. |
| B cell | A white blood cell that carries a receptor for one antigen and can turn into antibody-making cells. |
| Plasma cell | An activated B cell that makes and releases large amounts of antibody. |
| Memory cell | A long-lived cell kept after an infection or vaccine, ready to respond faster next time. |
| T cell | A white blood cell that helps B cells (helper T) or kills infected cells (killer T). |
| Primary response | The slow, small response on the first meeting with an antigen. |
| Secondary response | The fast, large response on a later meeting with the same antigen. |
| Vaccine | A harmless form of a germ, or part of it, that trains the immune system without causing the disease. |
| Lag phase | The wait between meeting the antigen and the first rise in antibody. |
| Booster | A repeat dose that calls up memory cells and lifts the antibody level again. |
The primary response: starting from nothing
When an antigen arrives for the first time, very few B cells fit it. Each B cell carries a receptor for one antigen shape, and only a handful of cells in the whole body match. Those cells must be found, helped by T cells, and told to multiply. Then they must grow into plasma cells and start making antibody. All of that takes time.
In the model, the first meeting has a lag of 5 days with no antibody at all. The level then rises over 8 days to a peak of 60 units on day 13, and falls with a half-life of 12 days. The model uses arbitrary units, so the shape matters more than the number.
The long wait is the danger window. In real infections, the germ multiplies during the lag, and symptoms often appear before the antibody level is high enough to stop it.
lag → rise → peak → decaythe four stages of a response
level after the peak = peak × (½)^(days since peak ÷ half-life)exponential decay
The secondary response: memory at work
After the first infection or vaccine, some B cells do not become plasma cells. They become memory cells and stay for a long time. When the same antigen returns, there is already a large army of the right cells, so they multiply and make antibody at once.
In the model, the second response has three changes. The lag shrinks from 5 to 2 days. The rise takes 4 days instead of 8. The peak is 5 times higher, 300 units, and the half-life doubles to 24 days. The three changes stack: earlier, taller and longer.
The memory-boost slider controls just the height of the peak. In real life, how much stronger the second response is depends on the antigen, the vaccine and the person, so the number is a teaching choice, not a fact about any vaccine.
| Feature | Primary response | Secondary response |
|---|---|---|
| Lag before antibody rises | 5 days | 2 days |
| Time to rise to the peak | 8 days | 4 days |
| Peak level | 60 units | 300 units |
| Half-life after the peak | 12 days | 24 days |
| Cells responding | Few; must multiply first | Many memory cells ready |
Why memory makes it faster
The reason is a rule called clonal selection. An antigen does not make B cells fit it. It finds the few that already fit and tells them to multiply. All the copies, called a clone, carry the same receptor.
Some of the clone become short-lived plasma cells, which make the antibody and then die. Others become long-lived memory cells. Memory cells wait in the lymph nodes and spleen. If the same antigen comes back, those cells start from a bigger group, so each step comes sooner.
This is also why immunity is specific. Memory for one antigen does nothing for a different one. A new germ with a different surface starts a fresh primary response.
Reading the graph
Look at the antibody graph and ask these questions of it.
- Where is the infection? The dotted vertical line. For the vaccinated person there is a second dotted line at day 0, the vaccine.
- Why does the blue line rise twice? The first bump is the primary response to the vaccine. The second, much taller, is the secondary response to the real infection.
- Why is the blue line not zero when the infection arrives? The vaccine’s antibody is fading but not gone. At the default infection day it has dropped to 9.4 units, below the green protective level of 20.
- What does the green line mean? It stands for the level of antibody needed to stop the germ. Above it the person is protected in the model; below it the germ has room to multiply.
- Which curve is higher and sooner? The vaccinated one, on both counts. That is the whole point of vaccination.
Vaccines and boosters
A vaccine contains something the immune system can recognise, but that cannot cause the full disease. It might be a weakened germ, a killed germ, a harmless piece of the germ’s surface or a set of instructions for making such a piece. Whatever the type, the body treats it as an antigen and starts a primary response.
The antibody from a single dose fades. That is why some vaccines need a booster. A booster is a second meeting. It calls up the memory cells, produces a taller peak and builds a bigger and longer-lived memory.
Notice the cost-benefit: the first dose is slow and small, but it is the one that creates the memory. After that, the body is ready.
What the sliders change
Each slider moves one part of the picture. They do different jobs.
| Control | What it changes | What it leaves alone |
|---|---|---|
| Vaccinated or not | Whether the infection finds memory cells waiting | The primary response to the vaccine itself |
| Day of infection | How much vaccine antibody has faded by then, and where the real response sits on the axis | The shape of each response |
| Memory boost | The height of the secondary peak | The lags and the half-lives |
| Protective level | The height of the green line and so the time to protection | The curves themselves |
What the model leaves out
This is a teaching model. Real immunity is richer, and you should not use these numbers for any real decision.
- There are several classes of antibody, and the early class differs from the later one. The model merges them into one level.
- T cells, which are vital to a full response, are not drawn on the graph.
- Real lag times, peaks and half-lives depend on the germ, the vaccine, the dose and the person. These are invented round values.
- The model does not simulate the germ’s growth, only a simple clearing rule in the picture on the left.
- Some germs change their surface, so memory for an old version may not fit a new one. The model assumes the same antigen both times.
Try it in the simulation
Spend ten minutes on these experiments. Each is a question an examiner could ask.
- Choose unvaccinated and watch the infection day. How long does the level stay at zero? Compare with the lag reading.
- Switch to vaccinated. What is different about the lag, the peak and the time to the protective level?
- Drag the infection day to its minimum. Is the vaccinated person protected the moment the infection arrives? Why?
- Drag it to its maximum. What has happened to the vaccine antibody by then, and does memory still help?
- Set the memory boost to its smallest and then its largest value. Which readings change and which do not?
- Raise the protective level to its maximum. How does that change the time to protection for each person?
- Switch off the comparison line to study one person at a time.
Solved problems
Each solution states the rule first, then substitutes the numbers. Every figure is computed by the same code that drives the simulation.
Problem 1: the timeline of a primary response
Lag 5 days, then a rise of 8 days: the peak comes on day 13 after the antigen, at 60 units. After that the level halves every 12 days.
Problem 2: how long does the vaccine alone protect?
Protection ends when the level falls below 20 units. From the peak of 60: days after the peak = half-life × log₂(peak ÷ level) = 12 × log₂(60 ÷ 20) = 19.0 days. That is day 32.0, counting from the vaccine.
Problem 3: antibody left from the vaccine on day 45
The vaccine’s peak was on day 13. By day 45, 45 − 13 days have passed, so the level is 60 × (½)^((45 − 13) ÷ 12) = 9.4 units, below the protective level of 20.
Problem 4: the unvaccinated person
A first meeting on day 45: no antibody for 5 days, then a smooth rise. The model reaches 20 units 8.1 days after infection. Seven days after infection the level is still 9.4 units, below the protective level. The peak is 60 units, 13.0 days after infection.
Problem 5: the vaccinated person
The second meeting has a lag of 2 days and a rise of 4. It sits on top of the 9.4 units of old antibody, so the protective level of 20 is reached 2.5 days after infection, which is 5.6 days sooner than the unvaccinated person. Seven days after infection the level is 297.8 units. The peak is 306.7 units, 6.0 days after infection: the new peak of 300 plus a little leftover antibody.
Problem 6: the peak ratio
Peak vaccinated ÷ peak unvaccinated = 306.7 ÷ 60 = 5.1. That matches the memory boost of 5, with a small extra from the leftover antibody.
Problem 7: a bigger boost (10 times)
The secondary peak becomes 600 units and the vaccinated peak 606.7, a ratio of 10.1. The protective level is now reached 2.4 days after infection. The boost barely changes the time to protection because the level crosses 20 on the steep early part of the rise, before the peak matters. A taller peak lasts longer; it does not arrive sooner.
Problem 8: infection early (day 15) or late (day 60)
On day 15 the vaccine antibody is still 53.5 units, already above 20, so the person is protected at once (time to protection 0.0 days). On day 60 only 4.0 units remain, so the secondary response must do the work, and protection comes 2.6 days after infection. Memory covers the gap when antibody has faded.
Common mistakes
These are the slips that cost marks every year.
- Saying vaccines contain antibodies. Most contain an antigen. The body makes the antibodies.
- Mixing up memory cells and antibodies. Antibodies fade; memory cells persist.
- Writing that the secondary response is only larger. It is also faster, and it lasts longer.
- Thinking one vaccine protects against every germ. Immunity is specific to the antigen.
- Confusing the lag phase with the time to the protective level. One is when antibody starts to rise, the other is when it is enough.
- Saying the immune system “learns” in the first minutes. The first response takes days.
- Forgetting that the protective level is a line on the graph, not a property of the antibody itself.
Where you see it in real life
Childhood vaccination schedules are built on this graph. A first dose creates memory. Later doses, called boosters, are timed to lift the level again before it fades too far.
Blood tests that count antibodies against a germ are read as a snapshot of this curve. A high level soon after exposure suggests a recent response. A low but steady level suggests old memory.
Some infections give lifelong protection after one illness, because memory lasts. Others, where the germ keeps changing its surface, can infect the same person again, because the old memory does not fit the new antigen.
Antivenom and some emergency treatments give ready-made antibodies from outside. That gives protection at once, but only for a short time, because the body has made no memory of its own.
Exam corner
Typical questions, and what a full-mark answer contains.
| Question | Key points |
|---|---|
| Distinguish primary and secondary immune responses | Primary: slow, small, short-lived. Secondary: fast, large, long-lasting, because of memory cells. |
| What are memory cells? | Long-lived B and T cells kept after the first exposure, that respond quickly to the same antigen. |
| How does a vaccine work? | It exposes the body to a harmless antigen, causing a primary response and memory cells. |
| Why is a booster given? | To trigger a secondary response and raise the antibody level and memory. |
| Define an antigen and an antibody | Antigen: a foreign molecule. Antibody: a Y-shaped protein that binds one specific antigen. |
| What is clonal selection? | An antigen picks the B cell that fits it, which multiplies into plasma and memory cells. |
Revision summary
A first meeting with an antigen gives a primary response: a lag (5 days in the model), a slow rise to a modest peak (60 units) and a decay with a half-life of 12 days. A later meeting gives a secondary response, driven by memory cells: a shorter lag (2 days), a faster rise, a higher peak (300 units) and a longer half-life (24 days). A vaccine causes the first meeting safely. At the default setting, the vaccinated person reaches the protective level 2.5 days after infection and the unvaccinated person 8.1, and the vaccinated peak is 5.1 times higher. Antibodies fade; memory cells last.
Frequently asked questions
What is the difference between the primary and secondary immune response?
The primary response is the slow, small response on the first meeting with an antigen. The secondary response is faster, larger and longer-lasting on a later meeting with the same antigen, because memory cells are ready.
How do vaccines create immunity?
A vaccine gives the body a harmless form of an antigen. The immune system makes a primary response and keeps memory cells, so a real infection later triggers a quick secondary response.
What are memory cells?
Memory cells are long-lived B and T cells kept after an infection or vaccine. They recognise the same antigen and respond to it much faster than naive cells.
Why does the antibody level fall after the peak?
Antibody molecules break down over time and plasma cells die once the antigen is cleared, so the level decays. In the model it halves every fixed number of days.
Why are booster doses needed?
A booster is a second meeting with the antigen. It triggers a secondary response, raising the antibody level again and strengthening memory.
What is an antigen, and what is an antibody?
An antigen is a foreign molecule the immune system recognises, such as a protein on a germ. An antibody is a Y-shaped protein made by plasma cells that binds to one specific antigen.
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