The tragic deaths this week of the father and grandparents of Lee Teuk, leader of K-pop boy band Super Junior, are raising calls for South Korea's government to do more to lighten the burden for dementia patient's families.

The superstar's father and grandparents were found dead at their home in southern Seoul. According to media reports, police said a note at the scene suggests Mr. Lee's 59-year-old father, who for several years had been sole caregiver for his parents—both suffering from dementia—committed suicide after killing them. The case is still under investigation.

The financial, physical and psychological stress of dealing with dementia is hitting more and more people in South Korea, where looking after these patients is widely regarded as a "family matter."

Taking care of one's parents is a Confucian value many South Koreans still strongly adhere to. Seeking outside help is deemed undutiful—not that such help is easily available. As the number of senile-dementia patients in this rapidly aging country climbs, the social-welfare system lags far behind.

The number of dementia patients age 65 or over who visited a doctor for treatment in 2011 hit 288,987—more than three times the number five years earlier, which works out to an average annual growth rate of 24%. And the number of dementia sufferers not getting professional help is believed to be much higher.