Ten years ago, individuals and government spent about $1.8 billion a year on nursing home care for the elderly and infirm.

Today the figure is nearly $11 billion - one dollar in every 11 spent on personal health care. The increased demand for nursing home care has given birth to a giant new industry and is growing at a rate that threatens to engulf the program that pays for most of it - Medicaid.

Secretary of Health, Education and Welfare Joseph A. Califano Jr., recently told Congress that the $15 billion - $16 billion a year spent for Medicaid by federal and state governments soon will go for long-term care, primarily nursing home care of the elderly. The cost of nursing home care for the elderly and certain other groups is already 38 percent of all Medicaid outlays.

Today, more than 1.1 million elderly persons - one out of every 20 aged 65 or older is in skilled or intermediate-car nursing facilities. Officials say the figure may jump to 2.5 million by 1985.

The huge boost in outlays for nursing homes has drawn some big companies into the business.

Where once the old and the sick cared for themselves as best they could, moved in with their children or were sent to old-age homes for custodial "warehousing," there are now giant chains of nursing homes all over the country. The biggest, ARA, the food service firm, had 120 facilities with 20,000 beds as of mid-1977, according to the House Committee on Aging.

Although there have been widely publicized instances of fraud or substandard care, the result often has been far better care for elderly persons with chronic and recuperative medical complaints such as arthritis, senility, diabetes, cancer, stroke and heart disease.

Young persons have been released from a sometimes crushing financial and physical burden or from caring for disabled parents. Nursing home costs per person generally range from $600 to $1,200 a month - an outlay few families can bear.

But the cost of the program has meant an immense and growing burden for the states and the federal government - one which can only get worse and reach crisis proportions as the percentage of elderly in the overall population increases over the next generation.

These figures, recently developed by the Congressional Budget Officer and HEW, outline the financial problem:

In 1976, 1.3 million persons were living in skilled or intermediate-care nursing homes - and 89 percent of them (1.1 million) were 65 or older.

The total national outlay for these skilled and intermediate-care nursing homes was $10.6 billion, paid by relatives and by state and federal governments. Four-fifths of the total was spent for the aged.

Of the $10.6 billion, $4.7 billion came out of the pockets of relatives, $3.4 billion from the U.S. government (almost all from Medicaid) and $2.4 billion from state and local governments also largely from the state and local share of Medicaid outlays). The federal and state governments were thus paying $5.9 billion combined - more than half the costs.

The $10.6 billion spent for these nursing homes primarily for the aged, was slightly higher than the total public and private outlays for all other forms of long-term institutional care of disabled persons (such as homes for the blind and deaf, homes for the mentally disturbed and retarded, psychiatric hospitals and the like).

As the population ages, the number of persons in nursing homes is expected to rise rapidly, with a prospective growth to 2.5 million by 1985 and a potential cost of $4.2 billion, of which more than half will have to come from the federal and state governments.

In the past few years, there has been considerable evidence that some nursing home operators have been ripping off the government.

Investigations by U.S. attorneys in New York and Chicago and by the Senate Committee on Aging revealed that some nursing home operators had bought themselves mink coats, hi-fi sets and paintings by Matisse and Renoir and charged them to Medicaid. There have been successful prosecutions. The inspector general of HEW (a new position) will be monitoring the programs for further abuses.

Potentially far more costly even than the cheating and fraud, however, is the growing number of elderly in need of nursing care, Califano is desperately looking around for ways to cut costs without reducing needed services.

At the House Budget Committee, he hinted at the direction his efforts may take when he said, "Presently the law is skewed toward instituational longterm care."

What he meant, officials explained, is that not everyone who goes into a nursing home needs the full range of services provided there. Some may need only one or two services - injections, changes of dressings on surgical wounds, physical therapy and the like.

Many people who need one or two of these services simply can't get them easily if they live at home - so they end up in a nursing home.

Both the federal Medicare and Medicaid programs and the states have been experimenting with such alternatives and one HEW study three years ago estimated that 14-25 percent of those in nursing homes could be cared for in other ways, according to the House Committee on Aging. Committee Chairman Claude Pepper (D-Fla.) is extremely enthusiastic about this concept.

One high HEW official said in an interview last week, "The secretary has gave it priority. He wants us to lay out options."

Under one proposal HEW is considering, the official said, a person discharged from a hospital after treatment would be examined by a team of specialists that would determine if nursing home care were needed or if another type of care would suffice. This would avoid the automatic transfer to nursing homes of those who could be cared for more cheaply and just as well in other ways.

A second option under consideration is establishing a network of special centers, funded on a prepayment basis, that could offer services ranging from home care to institutional care.

A third proposal is much greater emphasis on the use of nurses and other health workers who could visit a patient's home.