IT is one of those happier equations, in which demand equals supply. There are 26 million Americans over the age of 65, and 8 million of them live alone. At the same time, 10 million dogs and cats are put into animal shelters each year, and 8.5 million are never adopted. This can add up to companionship for the elderly and a home for pets.
Mathematics, of course, cannot quantify how Shylo, a white Bishon Frise, saved the life of Inez Ekstron, or how Ms. Ekstron saved Shylo's. The two recuperated together, taking ``siestas'' each day and feeding the birds outside Ekstron's house in Minneapolis. Shylo is no longer a skinny, mat-haired puppy terrified of people. Ekstron is no longer lonely.
Ekstron's daughter thought she might have to quit her job to take care of her mother after her previous dog died a year ago. ``But since she got the dog, she's turned around 180 degrees,'' says Donna Loegering.
Across the country, animal shelters are playing the dating game. Last week their efforts to match dogs and cats in shelters with senior citizens got a big boost when Ralston Purina launched its $1 million ``Pets for People Program.'' During the next year, Purina will foot the bill to get some 10,000 cats and dogs out of animal shelters and into the homes of the elderly.
This kind of program, coupled with a slew of local ones that have sprung up in the last couple of years, comes not a month too soon, says Philip Arkow, who runs the Pikes Peak Humane Society, in Colorado Springs, Colo. In March, a law passed in 1983 will go into effect allowing senior citizens in subsidized housing to keep cats and dogs in their apartments. That will open up 900,000 units.
While not all of those residents will find themselves a four-legged live-in, ``easily thousands and thousands of people are waiting for animals in federally subsidized housing,'' he says.
Scientists long have believed that pets are good for elderly people. Beside giving them an outlet for affection and a reason to get up in the morning, pets act as a ``social lubricant,'' says Randall Lockwood, a scientist at the Humane Society of the United States in Washington, D.C. ``One thing we all have in common is we like animals,'' he says.
Pets go a long way toward solving one of the biggest problems for the elderly - withdrawal from others - because ``you cannot be a pet owner and be disengaged,'' Mr. Lockwood says. At a minimum, ``you have to go shopping and take him for walks.''
Until the last few years, however, scientists have been unable to prove that animals have a healthy physiological effect on people. But studies indicate that pets can help people recover quickly.
At the same time, the notion that animals might be dangerous to have around older people is evaporating. A survey of nursing homes in Minnesota showed that animals posed less risk to patients - in causing accidents, for example - than other activities did.
All this is good news for homeless cats and dogs, which are suddenly star attractions as visitors at institutions like nursing homes and hospitals. Pets are going places no one ever dreamed of - including, Mr. Arkow hopes, an AIDS hospital in Houston soon.
``The barriers have really come down,'' as institutions recognize that animal visits are no more dangerous to older people than other activities, says Paula Kielich, who runs Philadelphia-based Pals for Life.
Her cadre of 30 volunteers borrows pets from six nearby shelters and takes them to some 20 facilities on a regular basis, generally once a month. Whereas institutions used to blanch at the idea of dogs and cats running around, ``now we have more demand than we can meet,'' she says.
The advantage of using shelter animals - as does Pals for Life, the Pikes Peak Humane Society, and perhaps the largest service, the San Francisco Society for the Prevention of Cruelty to Animals, which visits 1,500 people a month - is that the pets often get adopted. In the last two years, more than 130 animals have been snapped up by families of the people they visit, or by staff members of the institution, Ms. Kielich says.
Other visitation programs, like the Baltimore-based Pets on Wheels, have volunteers bring their own pets. That gives continuity to the relationship - both the human-animal and the human-human relationship, says Elaine Farrant, who runs the program for the city. Volunteers visit the same people each week, ``and a lot of these people wouldn't get any other visitors if it weren't for Pets on Wheels,'' she says.
Placement programs, which find an animal a permanent home with an elderly person, have been slower to get off the ground. Part of the reason is cost; the average cat or small dog costs $175 to $225 a year to feed and care for. One new program in Long Island, called Pioneers for Animal Welfare Society (PAWS), is using a $25,000 government grant not only to place shelter animals, but to cover all their costs if necessary. That includes food, training, veterinary services, and water bowls.
Ralston Purina is going nationwide with a scaled-back version. It will pay for the adoption and fee, initial vet services (including neutering), and provide leash, water and food bowls, and an initial supply of food. The senior citizen, who must be at least 60 to qualify, covers the costs after that.
The program has been test-marketed in 16 cities, putting pets in nearly 4,000 homes, says executive director Kathryn Wright. She says that adoption of shelter animals has increased 11.2 percent in those cities, in part because elderly are taking the pets, but mainly because many families are taking a pet as well.
As of last Wednesday, Purina will be working with the 90 largest shelters in 70 cities to match animals with people, eventually using a computer base. Purina will soon have an 800 number for getting more information; until it does, a person can write Purina in St. Louis or get in touch with the local humane society.
Many organizations match pets with senior citizens or arrange for pets to visit on a regular basis. If your area is not listed, your local humane society may know of a similar program.
The Delta Society also keeps track of such programs. For information, write Linda Hines, PO Box 1080, Renton, WA 98057, or call (206) 226-7357. Pet visitation programs: Pets on Wheels Baltimore City Commission on Aging and Retirement Education (301) 396-1762 Humane Society of the Pikes Peak Region PO Box 187 Colorado Springs, CO 80901 (303) 473-1741 San Francisco SPCA (415) 554-3060 Pals for Life Philadelphia (215) 525-7120 Greater Cincinnati Council for Pets Helping People (513) 683-0957 Companion Animal Association of Arizona Phoenix, Ariz. (602) 258-3306 Pet placement: People and Animals Coming Together (serving central Pennsylvania) (814) 865-1717