Can we eradicate jealousy?
No. We cannot.
But we can make him our friend, and thereby get to know him well. And in coming to know and understand him well, we will likely find that his fear is insubstantial and unreal -- an illusion, a hoax, a fraud, an imposter.
When we go on the offensive, on the attack, against our feeling-thoughts, we alienate some part of us that wants to be understood, and, perhaps, tranformed. Or healed, even. So make friends with your jealousy. Take him out for lunch or tea.
Sit quietly and listen to him, and gently speak with him. Often. Ask him what he is afraid of, and why. Get to know him very well and shower him with love and affection--, and he may change his mind about you and your life.