Kleenex often hears stories about people sharing the brand's tissues in opportune moments of kindness. Brand Manager Jon Kruesi has heard them himself, one from a friend who recounted how she was sniffling as she waited for a train at the end of a lousy day, only to have her spirits lifted by a stranger offering a Kleenex.

Now, the Kimberly-Clark Corp. brand is turning those stories into the centerpiece of its crucial cold-season marketing campaign breaking Wednesday. The #KleenexCare effort aims to get people talking about simple acts of kindness (preferably involving sharing tissues) through a digital, social-media, public-relations and TV campaign.

Of course, one way people can show kindness is not to spread germs around, so Kleenex will promote its Anti-Viral tissues as part of the effort. But Mr. Kruesi also said people often offer Kleenex to others at emotional moments, such as weddings.

A TV ad from JWT, New York, breaking Nov. 3, shows a younger man sharing a Kleenex pack that has one tissue left with an older woman when she sneezes. Then, when he sneezes, she tears the tissue in half and shares it with him. A voiceover urges people to share their Kleenex tissues with people in need – and share their stories at the campaign website KleenexCare.com.

JWT's WPP siblings VML and Geometry Global are handling digital and shopper marketing respectively, while Omnicom's Ketchum handles PR.

The effort comes amid some early indicators, captured via the Achoo.com Cold and Flu Predictor operated by Kleenex, that this cold and flu season will be tougher than last year's mild one, Mr. Kruesi said. Kimberly-Clark's market share is also improving, up 0.2 points to 46.8% of the $1.6 billion U.S. retail facial-tissue market, according to Nielsen data from Deutsche Bank, after falling about a point for the full 52-weeks amid some new competition from Georgia-Pacific Corp.'s Angel Soft.