A New and Better Covenant

The covenant God made with the children of Israel in the Old Testament, isn't the covenant made with Abraham, although it is based on it.

It's the covenant made with Moses.

The problem was that the nation and people of Israel repeatedly disobeyed God, forgot His ways and broke their covenant with Him.

They always brought curses on themselves.
That's why God started speaking of a new covenant:
"Behold, the days are coming," says the Lord, "when I will make a new covenant with the house of Israel and with the house of Judah, not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt, My covenant which they broke, though I was a husband to them," says the Lord, "But this is the covenant that I will make with the house of Israel after those days, says the Lord: "I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people.
No more shall every man teach his neighbor, and every man his brother, saying, Know the Lord, for they all shall know Me, from the least of them to the greatest of them," says the Lord.
"For I will forgive their iniquity, and their sin I will remember no more." 
Jeremiah 31:31-34

This new covenant is fulfilled in the Lord Jesus Christ. First, He has redeemed us from the curse of the old Mosaic covenant, including all the sickness and disease brought on by that curse.

He did it by becoming a curse for us!

"Christ has redeemed us from the curse of the law, having become a curse for us [for it is written, 'Cursed is everyone who hangs on a tree'], that the blessing of Abraham might come upon the Gentiles in Christ Jesus."
Galatians 3:13,14

Not only did Jesus become a curse, so that the power of the curse over us might be broken; He also became sin so that the power of sin over us might be broken.

"For He [God] made Him [Jesus] who knew no sin to be sin for us, that we might become the righteousness of God in Him" 
2 Corinthians 5:21

Jesus established the new covenant based on the shedding of His blood at the Cross.
Read Mark 14:22-24

As great as the Old Testament covenant was and as wonderful as all its blessings were; Hebrews 8:6 says that the new covenant in Jesus' blood is even better.

When we receive the Lord Jesus Christ, we enter into the new covenant and a new righteousness.

The good news of the Gospel is that Jesus has already done it for us.

We receive His righteousness through faith in Him.

This new covenant in Jesus is just as much a healing covenant than the old one, because the Healer Himself is now in us by His Spirit.