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To stop the spread of an infectious disease like measles, you don’t have to vaccinate everyone. But you do have to vaccinate many.

Just how many? To let you discover for yourself, we simulated an outbreak of a hypothetical disease, about as contagious as the flu. (A lot less contagious than measles.)

We’d like you to contain it. But first, some basics:

In a world where no one has immunity, infectious diseases spread exponentially. That’s what happened early in the Covid pandemic.

But for most infectious diseases, many people will already have some level of immunity — whether through a previous infection or through vaccination — and this can slow the spread.

Now it’s your turn to try.

Level 1: Less Contagious

How low can you set the vaccination rate to contain the outbreak?

This simulation uses randomness, so the results will turn out somewhat differently every time you play it. But there are patterns that you can discover: When the vaccination level is below around 40 percent, outbreaks are very likely. Above that level, they’re quickly extinguished.

That sharp gradient from red to white shows us this “herd immunity” threshold, where vaccination can halt an outbreak and protect the unvaccinated. (Including those who can’t be vaccinated, such as infants and people with weakened immune systems.)

The difference is stark. A little below that threshold, outbreaks easily grow out of control. Above it, they are quickly squelched. This is why it’s so important to keep vaccination levels above the herd immunity threshold.

Next, let’s see what happens with a disease that’s more contagious.

Level 2: More Contagious

How low can you set the vaccination rate to contain the outbreak?

Because this disease is more contagious, it can more easily slip through the gaps of unvaccinated people.

That’s why the vaccination level needed for herd immunity rose from around 40 percent to around 60 percent in this example: It takes greater levels of vaccination to contain a more contagious infectious disease.

So far, all our simulations have assumed that vaccination is evenly distributed. In reality, that isn’t the case.

Our final simulation tries to capture two neighboring communities. Think of them like two school districts in the same county. In one district, 75 percent of students are vaccinated. In the other, just 50 percent are.

That means the average vaccination rate for the county overall is 63 percent — right around the herd immunity threshold for our simulated disease. But see what happens.

Unvaccinated pockets

For the most part, the 75 percent district is protected, while the 50 percent district is overrun, even though they sit right next to each other. Herd immunity operates at a local level, and the average vaccination rate for a broad region can mask smaller communities at risk.

On a few tries, you might have gotten lucky and seen the outbreak fizzle out. This, too, mimics reality. But luck is not an effective public health strategy.

The simulated world you saw above mirrors a real-world problem: There are increasingly many parts of the U.S. where skepticism of vaccines has gained momentum and childhood vaccination rates have fallen.

And measles is far more contagious than the disease we simulated — because of space constraints, we could not even simulate it in this form. It’s so contagious that a vaccination rate of 50 percent or even 75 percent won’t contain an outbreak.

How contagious is measles?

Epidemiologists estimate the contagiousness of an infectious disease with a “basic reproductive number,” or R₀ — how many people a sick person infects, in a community with no protection.

A disease can grow out of control if an infected person infects more than one other person, on average. A person with the flu can infect one to two others — an R₀ between 1 and 2.

But a person with measles can infect 10 times as many:

For measles, a 1982 study put its R₀ between 12 and 18. A more recent review of studies found a very wide spread, with a median of around 15 in the Americas.

That means measles is one of the most contagious diseases known. And there’s a direct relationship between contagiousness and the level of protection needed for herd immunity.

Reaching herd immunity means each infected person can infect only one other person or fewer, on average. That means, at the high end of the measles range, you’d need to prevent 17 of 18 infections, or over 94 percent. That’s why health officials set a goal of vaccinating 95 percent of people against measles.

(The measles vaccine, unlike vaccines for some other infectious diseases, is very effective and its protection lasts decades; measles also is extremely unlikely to develop mutations that allow it to evade the vaccine.)

The average vaccination rate for kindergartners in the U.S. has fallen below that threshold since the pandemic. Most kindergarteners now live in states where the vaccination rates are below herd immunity.

Many kindergartners live in counties and go to schools where the rates have fallen even further, below 80 percent or even below half — making it possible for measles to spread like wildfire.