How can one deal with a husband who persists in engaging in illicit relationships, coupled with the fear of contracting sexually transmitted diseases?

If a husband admits to committing immoral acts and abandoning prayer, he is a bad husband and must make sincere repentance. It is not permissible for him to abandon his wife without a legitimate reason, and if he is someone who abandons prayer, his sin is even greater. The wife should continue to advise him, and if he repents, then praise be to Allah. Otherwise, there is no good in her remaining with him. One should not despair of supplication, for it is one of the causes for the relief of distress, and it might be a trial to raise one's ranks and expiate sins.