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SEIR models start to fall apart when you think about the underlying causes of the data. You need models that can allow for all possible states, and assess which ones matter for shaping the pandemic’s trajectory over time.

These techniques have enjoyed enormous success ever since they moved out of physics. They’ve been running your iPhone and nuclear power stations for a long time. In my field, neurobiology, we call the approach dynamic causal modelling (DCM). We can’t see brain states directly, but we can infer them given brain imaging data

Epidemiologists currently tackle the inference problem by number-crunching on a huge scale, making use of high-performance computers. Imagine you want to simulate an outbreak in Scotland. Using conventional approaches, this would take you a day or longer with today’s computing resources. And that’s just to simulate one model or hypothesis – one set of parameters and one set of starting conditions.

Using DCM, you can do the same thing in a minute. That allows you to score different hypotheses quickly and easily, and so to home in sooner on the best one.

This is like dark matter in the universe: we can’t see it, but we know it must be there to account for what we can see. Knowing it exists is useful for our preparations for any second wave, because it suggests that targeted testing of those at high risk of exposure to Covid-19 might be a better approach than non-selective testing of the whole population.

Our response as individuals – and as a society – becomes part of the epidemiological process, part of one big self-organising, self-monitoring system. That means it is possible to predict not only numbers of cases and deaths in the future, but also societal and institutional responses – and to attach precise dates to those predictions.

How well have your predictions been borne out in this first wave of infections?For London, we predicted that hospital admissions would peak on 5 April, deaths would peak five days later, and critical care unit occupancy would not exceed capacity – meaning the Nightingale hospitals would not be required. We also predicted that improvements would be seen in the capital by 8 May that might allow social distancing measures to be relaxed – which they were in the prime minister’s announcement on 10 May. To date our predictions have been accurate to within a day or two, so there is a predictive validity to our models that the conventional ones lack.

What do your models say about the risk of a second wave?The models support the idea that what happens in the next few weeks is not going to have a great impact in terms of triggering a rebound – because the population is protected to some extent by immunity acquired during the first wave. The real worry is that a second wave could erupt some months down the line when that immunity wears off.

the important message is that we have a window of opportunity now, to get test-and-trace protocols in place ahead of that putative second wave. If these are implemented coherently, we could potentially defer that wave beyond a time horizon where treatments or a vaccine become available, in a way that we weren’t able to before the first one.

We’ve been comparing the UK and Germany to try to explain the comparatively low fatality rates in Germany. The answers are sometimes counterintuitive. For example, it looks as if the low German fatality rate is not due to their superior testing capacity, but rather to the fact that the average German is less likely to get infected and die than the average Brit. Why? There are various possible explanations, but one that looks increasingly likely is that Germany has more immunological “dark matter” – people who are impervious to infection, perhaps because they are geographically isolated or have some kind of natural resistance

Any other advantages?Yes. With conventional SEIR models, interventions and surveillance are something you add to the model – tweaks or perturbations – so that you can see their effect on morbidity and mortality. But with a generative model these things are built into the model itself, along with everything else that matters.

Are generative models the future of disease modelling?That’s a question for the epidemiologists – they’re the experts. But I would be very surprised if at least some part of the epidemiological community didn’t become more committed to this approach in future, given the impact that Feynman’s ideas have had in so many other disciplines.

Taking cues from Éric Rohmer’s summertime romantic comedy-dramas, Petzold fills much of the film with routine errands, trips to the beach, and aimless conversations over dinner—scenes of leisure and languor that appear plotless.

In Afire, Petzold revisits the question posed in Transit. Does the search for humanity in cataclysm—a pursuit that can take over one’s life—make us, conversely, less human?

With the events in the last act of Afire, Leon finally possesses “real experience” of the sort that can rescue him from his solipsistic writing. His writing and conduct outwardly improve at a rapid clip. The newly mature Leon is thoughtful and expansive, yet there is something garish about his transformation at the eleventh hour.

The characters of Afire confront a crisis that threatens to vacate all narratives of meaning, and Leon comes out the other end with a feeble text. It’s better than what came before, but can it begin to make sense of what has taken place? This time, the atrocity is not historical but natural, and Petzold is cynical about the redemptive potential of melodrama in an age in which disasters, if still largely caused by human decisions, unfold beyond the grasp of our control. If he wants Leon to scrutinize the stories he tells about himself, the ending of Afire suggests that there is a possibility he finds even more concerning: a future with no stories at all.

Beitman defines a coincidence as “two events coming together with apparently no causal explanation.” They can be life-changing, like his experience with his father, or comforting, such as when a loved one’s favorite song comes on the radio just when you are missing them most.

Although Beitman has long been fascinated by coincidences, it wasn’t until the end of his academic career that he was able to study them in earnest. (Before then, his research primarily focused on the relationship between chest pain and panic disorder.)

He started by developing the Weird Coincidence Survey in 2006 to assess what types of coincidences are most commonly observed, what personality types are most correlated with noticing them and how most people explain them. About 3,000 people have completed the survey so far.

he has drawn a few conclusions. The most commonly reported coincidences are associated withmass media: A person thinks of an idea and then hears or sees it on TV, the radio or the internet. Thinking of someone and then having that person call unexpectedly is next on the list, followed by being in the right place at the right time to advance one’s work, career or education.

People who describe themselves as spiritual or religious report noticing more meaningful coincidences than those who do not, and people are more likely to experience coincidences when they are in a heightened emotional state — perhaps under stress or grieving.

The most popular explanation among survey respondents for mysterious coincidences: God or fate. The second explanation: randomness. The third is that our minds are connected to one another. The fourth is that our minds are connected to the environment.

“Some say God, some say universe, some say random and I say ‘Yes,’ ” he said. “People want things to be black and white, yes or no, but I say there is mystery.”

He’s particularly interested in what he’s dubbed “simulpathity”: feeling a loved one’s pain at a distance, as he believes he did with his father. Science can’t currently explain how it might occur, but in his books he offers some nontraditional ideas, such as the existence of “the psychosphere,” a kind of mental atmosphere through which information and energy can travel between two people who are emotionally close though physically distant.

In his new book published in September, “Meaningful Coincidences: How and Why Synchronicity and Serendipity Happen,” he shares the story of a young man who intended to end his life by the shore of an isolated lake. While he sat crying in his car, another car pulled up and his brother got out. When the young man asked for an explanation, the brother said he didn’t know why he got in the car, where he was going, or what he would do when he got there. He just knew he needed to get in the car and drive.

David Hand, a British statistician and author of the 2014 book “The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day,” sits at the opposite end of the spectrum from Beitman. He says most coincidences are fairly easy to explain, and he specializes in demystifying even the strangest ones.

“When you look closely at a coincidence, you can often discover the chance of it happening is not as small as you think,” he said. “It’s perhaps not a 1-in-a-billion chance, but in fact a 1-in-a-hundred chance, and yeah, you would expect that would happen quite often.”

the law of truly large numbers. “You take something that has a very small chance of happening and you give it lots and lots and lots of opportunities to happen,” he said. “Then the overall probability becomes big.”

But just because Hand has a mathematical perspective doesn’t mean he finds coincidences boring. “It’s like looking at a rainbow,” he said. “Just because I understand the physics behind it doesn’t make it any the less wonderful.

Paying attention to coincidences, Osman and Johansen say, is an essential part of how humans make sense of the world. We rely constantly on our understanding of cause and effect to survive.

“Coincidences are often associated with something mystical or supernatural, but if you look under the hood, noticing coincidences is what humans do all the time,”

Zeltzer has spent 50 years studying the writings of Carl Jung, the 20th century Swiss psychologist who introduced the modern Western world to the idea of synchronicity. Jung defined synchronicity as “the coincidence in time of two or more causally unrelated events which have the same meaning.”

One of Jung’s most iconic synchronistic stories concerned a patient who he felt had become so stuck in her rationality that it interfered with her ability to understand her psychology and emotional life.

One day, the patient was recounting a dream in which she’d received a golden scarab. Just then, Jung heard a gentle tapping at the window. He opened the window and a scarab-like beetle flew into the room. Jung plucked the insect out of the air and presented it to his patient. “Here is your scarab,” he said.The experience proved therapeutic because it demonstrated to Jung’s patient that the world is not always rational, leading her to break her own identification with rationality and thus become more open to her emotional life, Zeltzer explained

Like Jung, Zeltzer believes meaningful coincidences can encourage people to acknowledge the irrational and mysterious. “We have a fantasy that there is always an answer, and that we should know everything,”

Honestly, I’m not sure what to believe, but I’m not sure it matters. Like Beitman, my attitude is “Yes.”

many experts are starting to see building resilience as an effective way to prevent youth anxiety and depression.

One solution, according to experts, is to encourage risk-taking and failure, with a few guardrail

For instance, it’s important that children have a loving and supportive foundation before they go out and take risks that build resilience

“Challenges” are challenging only if they are hard. Child psychologists often talk about the “zone of proximal development” — the area between what a child can do without any help and what a child can’t do, even with help

How do you find the bar? Dr. Ginsburg recommends asking your child: “What do you think you can handle? What do you think you can handle with me by your side?”

The best way to build resilience is doing something you are motivated to do, no matter your age

Experts say the more activities children have exposure to, the better.

Sometimes parents just have to lay down the law and force children to break out of their comfort zone

“If you don’t persevere through something that’s a little bit hard, sometimes you never get the benefits,”

don’t expect your kid to appreciate your efforts, Dr. Kecmanovic said: “They will scream ‘I hate you