As an insured person of the statutory health insurance funds, you are only partially insured on holiday. It is therefore worthwhile to take out travel health insurance / foreign health insurance for a longer stay abroad, such as a trip around the world. This protects you and your family from high costs in the event of illness abroad.
If, for example, you need to be repatriated from your destination country for medical reasons, you would have to bear the costs for this completely yourself, even if you have private health insurance. Even in cases where the treating doctor does not recognise the European Health Insurance Card and demands a private fee from you, your statutory health insurance at home will only reimburse you the respective contract rate of your travel country.
Further information: Advantages and benefits of the annual health insurance abroad and guide to Private travel health insurance