The calm is what’s so startling in Contagion — the cool precision with which Steven Soderbergh depicts a deadly virus that spreads throughout the world, quickly claiming millions of victims.

There’s no great panic in his tone, no hysteria. Soderbergh has amassed a dazzling cast of Oscar winners but this is not like those 70s disaster movies that had melodrama to match their star power.

Characters become increasingly confused and frustrated, they struggle to survive and then die in a matter-of-fact way. Even the eventual instances of looting and rioting that crop up — as they are wont to do in these kinds of movies when societal rules have long since been abandoned — feel like blips of intensity, understandable reactions to an incomprehensible situation.

Working from a script by Scott Z Burns, who also wrote his 2009 comedy The Informant!, Soderbergh takes us from suburban living rooms to labs at the Centre for Disease Control (CDC) to remote Asian villages with equally clear-eyed realism. The attention to detail — and to the infinite ways germs can spread that we probably don’t want to think about — provide the sensation that this sort of outbreak really could happen right now.

Contagion begins with Gwyneth Paltrow’s character, Beth, coughing as she reaches into a bowl of peanuts at an airport bar on her way home to Minneapolis from a business trip in Hong Kong. This is Day 2, we are told, and she will end up being Patient Zero. With the help of a low-key, but propulsive, electronic score, Soderbergh steadily focuses on the hands as he jumps from Chicago to Tokyo to London in these early scenes, fluidly revealing how we pass our credit card to a waitress or grasp a bus railing or press an elevator button.

Kate Winslet’s character, the steely Dr Erin Mears, who thrusts herself into the vortex as the virus starts developing, offers a chilling statistic to some skeptical medical administrators: We touch our hands to our face 2,000 to 3,000 times … a day. I don’t even want to finish writing this review for fear of what’s lurking on my own laptop. But I must.

As Soderbergh did in the superior Traffic, he intertwines various storylines to give us a complete picture of the devastation. Matt Damon, as Paltrow’s stoic husband, Mitch, tries to stay strong and protect his teenage daughter as it becomes clear that they’re both immune. Jude Law, believably skeevy as an online journalist with questionable ethics, digs for the truth of the story — but government scientists are just as keen on stopping the spread of information as they are the disease itself.

Marion Cotillard gets a bit lost in the shuffle, as Dr Leonora Orantes of the World Health Organisation, who’s working backward to find the disease’s origin. She’s gone for large chunks of time and her plot line feels unfinished; it’s an example of how, given the enormity of the cast and the subject matter, not all of the characters are fleshed out as well as you’d like them to be.

But then excellent character actors show up and lend weight to some of the smallest parts: Hey, there’s John Hawkes as a janitor. There’s Bryan Cranston as Laurence Fishburne’s boss at the CDC. And you’d like to see more of them, too.

Despite all the big names crammed together, Jennifer Ehle might just steal this thing as Fishburne’s right-hand woman, Dr Ally Hextall, who’s racing to find a vaccine even as the number of dead skyrockets. Like the film itself, she’s got an irresistible cool about her. But she’s also so confident and radiates such no-nonsense intelligence, she commands the screen every time she shows up. (And how great is it that three of the top scientists here are strong, decisive women?)

Her performance represents one of many elements of Contagion that will make you stop and think. And then wash your hands.