It's entirely human to struggle with letting go of the past, but when this behaviour begins to infect society as a whole, it can create a mob mentality that's difficult to break.

Now mathematicians from Dartmouth college have shown how this powerful social phenomenon, known as 'hysteresis', can explain the dynamics of the anti-vaccination movement.

"Given all the benefits of vaccination, it's been a struggle to understand why vaccination rates can remain stubbornly low," says lead author Feng Fu, a mathematical biologist at Dartmouth.

"History matters, and we now know that hysteresis is part of the answer."

Hysteresis, which roughly translates to "remaining" in Greek, is essentially what happens when the past comes back to haunt the present.

The term was first applied in 1881 to describe the physics of magnetism, but since then this puzzling phenomenon has been applied to several other fields, including economics, marketing and human behaviour.

In physics, when a magnetic field is increased and then turned off, it is impossible for a magnet's flux to return to its exact original state, and this is exactly what is meant by the term hysteresis.

It's the same thing that occurs when unemployment rates remain high, even in the face of a recovering economy.

And now, strangely enough, mathematicians think it can also help explain social resistance to vaccinations.

Here's the thing: even though there is overwhelming evidence that vaccines are both safe and effective, in recent years vaccination rates have begun to plateau and the anti-vax movement has continued to grow.

It seems that no matter how many pro-vaccine campaigns are started, the world just cannot meet appropriate levels of herd immunity (the percentage of a population that needs to be vaccinated to develop sufficient disease resistance), and this puts all of society at risk.

The new research suggests that at least part of this resistance may be due to a lingering sense of unease, brought about by negative past events like the MMR- autism debacle.

It's memories like these, no matter how scientifically inaccurate, that create a negative history, trapping society in a hysteresis loop and stiffening public resolve against vaccines.

The root of the problem essentially stems from the nature of vaccines themselves. Since vaccines can sometimes produce unwanted side effects and can never confer full disease protection, the authors think it is especially easy for society to grow skeptical of their necessity.

"Once people question the safety or effectiveness of a vaccine, it can be very difficult to get them to move beyond those negative associations," explains Fu.

In other words, when society gets stuck in one of these loops, it can create a sort of friction, slowing the recovery of vaccination rates and leaving us all vulnerable to disease outbreaks.

The authors point out, for instance, that in England and Wales it took fifteen years to build vaccination rates from 30 percent to 91 percent - a feat that should have taken just a year under ideal circumstances.

What's more, in countries such as France, measles has been making a comeback, despite the availability of an effective vaccine.

"Vaccination levels in a population can drop quickly, but, because of hysteresis, the recovery in that same population can take many years," explains co-author Xingru Chen, a mathematician at Dartmouth.

The study represents the very first time that hysteresis has been found useful to analyse a public health issue, and the authors hope that if we can find a way around this roadblock, it could pull us out of our current vaccination rut.

"This study shows why it is so hard to reverse low or declining vaccine levels," says co-author Xingru Chen, a mathematician at Dartmouth.

"The sheer force of factual, logical arguments around public health issues is just not enough to overcome hysteresis and human behaviour."

Instead, the mathematical models suggest that vaccines need to reach a certain level of efficacy before the public is fully willing to accept them.

As such, the mathematicians are urging officials to focus on developing more efficient vaccines, and then afterwards making the public as aware of this efficiency as possible.

"Aside from the public health prevention perspective, vaccination campaign should promote vaccination as an altruistic behaviour that is desired for societal benefit," Fu told Newsweek.

You're not getting that jab just for yourself or your own kid - you're helping others, too.

This study has been published in the Proceedings of the Royal Society B.