When it comes, it will probably go down just like this.

A virus mutates and makes the leap from animal to human in the crowded, under-monitored Chinese food chain. Humans catch it in Hong Kong and fly home — through Paris, Chicago or Frankfort. They catch trains and buses, eat in airport restaurants. They cough and hack, then they sicken, convulse and die in every corner of the Earth.

Steven Soderbergh’s “Contagion” is a frosty, clinical breakdown of the mathematics of a pandemic, the masses who suffer, the people who battle to contain it and the societal consequences.  It’s a skilled technical exercise in montage — many scenes are quick-edit montages, set to vaguely creepy music, following this sick character (many of them nameless) or that one, zooming in on the door handle they grab, the peanut bowl they sneeze into, the hand they shake just after a wheeze.

But as slick and polished as this “real” version of “28 Days Later” is, it’s an utterly heartless affair. From that first victim — a Minneapolis wife and mother played by Gwyneth Paltrow — onward, Soderbergh struggles with the whole empathy thing. She had an assignation on a layover in Chicago. Thus, we feel a little less when she dies, graphically, on film. The titters in the audience at her autopsy weren’t just from the mysterious Paltrow-haters cult.

“Oh my God,” her pathologist mutters, on cutting open her head.

“Should I call someone?” his assistant asks.

“Call EVERYone,” he growls.

We feel a little more when we see her very young son die. But Matt Damon, the husband and stepfather who loses both of them the same day, isn’t given a moment to grieve. Soderbergh is too anxious to rush us into the Centers for Disease Control, where Laurence Fishburne, Kate Winslet and Jennifer Ehle are in a race against time to stem this viral tide, or at the World Health Organization in Geneva, where Marion Cotillard is dispatched to Hong Kong and Macau to find where this started.

Bryan Cranston and Enrico Colantoni are Homeland Security people who treat this as a possible terrorist plot. Jude Law is the wild-eyed blogger-journalist who pushes viral videos about the virus, sees conspiracies under every rock, who shrieks out warnings and prophecies online, some of them false.

Too many characters, too little time to care that Sanaa Lathan is getting married or that scientist Elliott Gould is breaking government protocols in a rush to isolate the virus. It’s only when the luminous Ehle, forever Elizabeth Bennett to Colin Firth’s Mr. Darcy in the TV “Pride & Prejudice,” takes center stage that “Contagion” crawls out of the petri dish and into something less clinical.

As the settings change — “Minneapolis, population 3.3 million,” to “Tokyo, population 36.6 million” — we sort-of follow the contagion’s spread and what follows. Hospitals are overrun, riots in pharmacies, a kidnapping in China, members of Congress and the CDC protecting themselves and their families first, garbage piling up, health care workers dying or going on strike to save their lives. We see small-minded budget hawks of state government gripe about the cost of setting up triage centers in armories and school gyms, and government turf wars that threaten to slow the hunt for the cause and the cure.

Through it all, Soderbergh is the dispassionate distant observer, looking through his camera as if peeking into a microscope. There is little urgency to this spiraling disaster. Soderbergh has made a lot of noise this past year about quitting directing and taking up a less collaborative, more solitary pursuit — painting. This is an anti-social painter’s movie. Millions are dying, but he doesn’t care that much. So why should we?

MPAA Rating: PG-13 for disturbing content and some language.

Cast: Gwyneth Paltrow, Kate Winslet, Matt Damon, Laurence Fishburne, Marion Cotillard, Jennifer Ehle, Elliott Gould

Credits: Directed by Steven Soderbergh, written by Scott Z. Burns. A Warner Brothers release. Running time: 1:45