MANILA—The Philippine death toll from Typhoon Rai has crossed the 400 mark, the disaster agency said on Friday, as officials in some hard-hit provinces appealed for more supplies of food, water, and shelter materials about two weeks after the storm struck. Rai was the 15th and deadliest typhoon to hit the Southeast Asian nation this year. Reported deaths had reached 405, mostly due to drowning, fallen trees, and landslides, Ricardo Jalad, chief of the national disaster agency, told a news conference. He said 82 were missing and 1,147 injured. More than 530,000 houses were damaged, a third of which were totally wrecked, while damage to infrastructure and agriculture was estimated at 23.4 billion pesos ($459 million), Jalad said. The typhoon affected nearly 4.5 million people, including about 500,000 sheltering in evacuation centers, government data showed. It made landfall as a category 5 typhoon on Dec. 16, and left a trail …