"Serious sickness" in Japanese can be translated as 重病 (じゅうびょう, juubyou).
Here's the breakdown with hiragana:
重病 (じゅうびょう, juubyou)
重 (じゅう, juu) - serious, heavy
病 (びょう, byou) - illness, sickness
So, 重病 (じゅうびょう, juubyou) specifically refers to a serious or severe illness.