It was to he, a normal family visit. Ahmed Sheikh Hassan, studying at a religious school in Somalia, returned around Christmas last year to the rocky desert northeast of here where his family herded sheep, camels and goats.

While there, Hassan broke out in the telltale rash that means smallpox - once a worldwide scourge but now isolated to that tiny corner of the earth where Somalia, Ethiopa and Kenya meet.

When Hassan departed Ledhi, has family's settlement of 10 crude huts, he left behind four more cases of smallpox, his sister Jaira Sheikh Hassan, 23, and three of her young daughters.

These are the last known cases of smallpox to occur anywhere. Since Feb. 5 when the rash showed up on four-month old Fatima Adan, no cases of smallpox have been reported anywhere in the world despite a close watch being kept in Asia and Africa by the World Health Organization (WHO). She may go down in history as the last known victim of the disease.

The last known case in Pakistan was reported in October 1974; India followed by May 1975, and Bangladesh's last case was reported five months later.

This was trumpeted as the possible end of smallpox. But on Sept. 23, two new cases showed up in Mogadishu, the capital of Somalia. These victims had come from Ethiopian villages more than 200 miles away. That was the beginning of an outbreak in Somalia that eventually spread to Kenya.

Not it has been a month and a half since a new case of smallpox has been discovered. Despite intensive efforts by WHO and health workers from Somalia and Kenya, however, Hassan - the man who infected three other members of his family - has not been located.

Health authorities do not know where Hassan got the disease nor whether he passed it on to anyone else beside his sister and three nieces.

They know that Hassan traveled in late December from Mogadishu to Blahao, a Somalia border town next to the Mandera district of Kenya. First he visited a brother in the Kenyan hamlet of Kalalio before going to Ledhi where his mother, sister and other family member lived. It was there he broke out with the smallpox rash. He could spread the disease for the next four weeks.

By the time health workers in the area arrived in Ledhi, Hassan had left. Moreover, the 11 members of his family had moved across the border to Kato in Ethiopia seeking better forage and water for the flocks. They, too, were possible smallpox spreaders.

Health workers finally isolated the family in two huts on the Ethiopian side of the desert, supplying them and their animals with food and water and hiring a guard to make sure no one approached them. They are still under observation.

Meanwhile, the hunt continued at watering points and isolated villages in the vast desert both for new cases of smallpox and for Hassan, the brother who started the chain.

Nonetheless, there have been no new cases of smallpox reported in Somalia since Jan. 17 and no cases reported in Ethiopia since last August.

WHO experts studying this last outpost of smallpox are cautiously optimistic that the incurable disease, which as recently as 1967 killed at least a million people in Third World nations, will now be eliminated.

If so, it will be the first disease in the history of the world to be totally eradicated by man.

There have been many false cries of success in the past two years as WHO's 10-year campaign to eradicate smallpox, begun in 1967, drew to a close. Now, WHO experts hope to do the job by the fall of 1977 - one year later than they originally planned.

Last September, before the outbreak in Hassan's family the world had gone seven weeks without a reported case of smallpox.

Normally an area is considered free of smallpox if six weeks passes without a report of a new infection and if the area is thoroughly searched for new cases.

Because of the size of the Ogoden, the roughness of the terrain and the nomadic nature of the population, WHO authorities have decided it will take as long as six months to make sure there have been no unreported cases of smallpox.

In a cooperative effort by authorities of the three countries, health experts and local residents are conducted room-by-room and hut-by-hut searches of the entire region using helicopters to spot new settlements and migratory patterns.

"It's difficult to trace the chain of transmission," said Dr. Isao Arita who heads WHO's smallpox eradication unit. "One day people are here and the next day they are already 50 miles away. They have their own regular paths but for us its a very irregular movement."

When the WHO campaign to wipe out smallpox began in 1967, the disease was considered to be an ever-present illness in 33 nations around the globe. There were between 10 million and 15 million cases that year, WHO authorities estimated, and more than 1 million people died from it.

The disease is still incurable and all doctors can do is keep the patient comfortable and treat the symptoms. The more virulent Asian smallpox kills 20 to 40 per cent of its victims. The milder form found in Africa has a 1 per cent death rate.It leaves all its victims with the characteristic pitted scars of the disease.

While there is no way to treat or cure smallpox there is a sure method of prevention: vaccination with small amounts of cowpox, discovered by Edward Jenner in 1796. WHO experts refined Jenner's techniques to make it possible for trained health workers to give millions of vaccinations without a doctor in underdeveloped nations of the world.

The WHO program has cost about $300 million since it began in 1967. But the cost of vaccinations and Quartantine activities around the world cost $1 billion a year.

Smallpox predates written history. The mummified remains of Pharaoh Ramses V, who dies in 1160 B.C., shows the pitted remains of smallpox. The Spanish conquistadors brought it to the new world in the 15th Century and George Washington carried scars from his bout with the disease.

The reason it is possible to eradicate smallpox is that unlike other diseases it exists in humans alone. There are no animals that harbor the smallpox virus and can spread it.