In stage 4 of the epidemiologic transition, countries often face challenges related to an aging population and the associated health care needs. The two challenges from the options provided are:
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High elderly support ratios - As the population ages, there is an increased burden on the working-age population to support the elderly, both financially and in terms of health care needs.
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High cost of public assistance for health care - With advancements in health care and an aging population, the costs associated with providing health care can increase significantly.
So, the correct challenges are high elderly support ratios and high cost of public assistance for health care.