By the rule of thumb of New York health officials there is one rat in New York for each human being.

"In a slum area there might be four or five rats per person. On Park Avenue there ar four of five people per rat. It evens out," says Randy Dupree, who does battle with rats from his post as executive director for environmental health.

The average New Yorker, however, rarely sees one. For those who do, it is an unsettling experience, triffering man's deeply held fear of the rodents that have become symbols of betrayal, uncleanliness and all that is loathsome.

The good news for people is that rats are, if anything, even more afraid of humans. Given a choice, the rats wouldn't be seen at all, even though they have adapted themselves with great skill to a life in a man-made cities among man's leavings.

A rat attack like the recent one here on a street in which a fellow pedestrian had to help beat the rats off the woman's legs is almost unheard of. It came, Dupree is almost sure, because the rats' environment had been disturbed and the woman chanced among them as they foraged for a new food supply.

Rats are formidable jumpers, climbers and swimmers. A rat can survive a four-story fall, tread water for 72 hours, swim underwater for more than three minutes, chew through plaster, cement and some types of brick and jump up to three feet.

They are also formidable breeders. A female starts breeding at three months and can have more than four litters in a year. There are about eight pups in a litter.

Although the reproductive rate is high, the mortality rate is also very high. Dr. Kyle Barbehenn of the Environmental Protection Agency says that in a laboratory rats begin dying when are about two years old and are all dead by three.

There is more good news for New York. Three years ago, Dupree and other health officials were talking ominously of "super rat." He doesn't leap any higher or burrow any deeper than his unsuper fellow rats, but super rat could eat poison and survive.

New York, like Washington and other cities, uses large amounts of anticoagulants in a federally funded drive to control rat populations.

The super rats developed an immunity to the anticoagulants and had to be attacked with zinc phosphide.

A series of battles with super rat apparently have produced a victory. Dupree says that the sampling of about 200 rats a month that were trapped live and sent to a laboratory for testing have not turned up any super rats for over a year.

There has been little study of rats in their urban environment because as rat expert John B. Calhoun of the National Institute of Mental Health pointed out in his book-length study of the Norway rat, trapping, marking and releasing rats in a city meets with interference, not to mention complaints, from the neighbors.

Some cities, like Washington, have done better than New York in controling rats.

Dr. Bailus Walker Jr., director of environmental health for the District of Columbia, said about 10 percent of Washington's city blocks have rat problems down from over 50 percent when federal funding of rat control begain in 1968. The Department of Health, Education and Welfare budgeted $422,0000 for Washington rat control this year.

The warriors in the battle against rats don't speak of total victory, however, for the tougher the rat, the better it survives in the cities. But the same might be said of people.

In 1976, two Brooklyn College of Pharmacy doctors exposed 25 rats to simulated New York subway conditions with tape recordings of subway noise and a mechanical shaker that jerked their cages from side to side 150 times a minute.

After 16 weeks, four of the rats were dead and autopsies found enlarged adrenal glands. The adrenal glands produce hormones in response to stress.