Home Health Aides demand their strike continue: Home care agencies scrambled to send nurses or other aides to care for the patients as the city's largest health care union, 1199/S.E.I.U., called a three-day strike. The union is seeking raises of 43 percent, hoping to increase the wages of 23,000 aides to $10 an hour from the current $7. Union leaders asserted that the strike was highly effective, saying that 12,000 home care aides - nearly all black and Hispanic women - demonstrated yesterday at a Midtown rally in which Senator Charles E. Schumer and Howard Dean, the former Vermont governor and Democratic presidential candidate, took part. But the home care agencies said the walkout did little damage, saying that more than half of the 23,000 workers crossed the picket line to care for patients. At the rally, Dennis Rivera, 1199's president, announced to huge applause that he had just reached a settlement with Partners in Care, which had agreed to pay its 4,000 aides $10 an hour. Mr. Rivera told the boisterous crowd that the union's leaders were recommending that the strike planned for today and tomorrow be canceled and that the union's leaders be given 30 days to negotiate with 10 other agencies. Mr. Rivera said the union could renew its strike against any agencies that did not reach a contract within 30 days. To Mr. Rivera's visible surprise, the workers - shouting an emphatic "No!" in a voice vote - rejected his recommendation. "This is democracy in action,'' Mr. Rivera said. At one point, mumbling to himself, he added, "I wasn't expecting this.''