The law of the red heifer for purification in its entirety is a prophetic picture of Messiah:
… a red heifer, faultless, with no blemish, and upon which never came a yoke. Num 19:2
Messiah is faultless and without blemish (1 Pet 1:18-19).
And the priest shall take cedar wood, and hyssop, and scarlet, and cast it into the midst of the burning of the heifer. Num 19:6
Wood, hyssop, and scarlet together is a sign of Messiah in Torah:
Then Moses called for all the elders of Israel and said to them, “Pick out and take lambs for yourselves according to your families, and kill the Passover lamb. And you shall take a bunch of hyssop, dip it in the blood [scarlet] that is in the basin, and strike the lintel and the two doorposts [wood] with the blood that is in the basin. And none of you shall go out of the door of his house until morning. For the Lord will pass through to strike the Egyptians; and when He sees the blood on the lintel and on the two doorposts, the Lord will pass over the door and not allow the destroyer to come into your houses to strike you.” Exo 12:21-23
As for the living bird, he shall take it, the cedar wood and the scarlet and the hyssop, and dip them and the living bird in the blood of the bird that was killed over the running water. And he shall sprinkle it seven times on him who is to be cleansed from the leprosy, and shall pronounce him clean, and shall let the living bird loose in the open field. Num 14:6-7
In each of these three instances, in Exo 12, in Num 14, and in Num 19, Israel was being delivered from death. (There are only three places in Torah that I could find, where the wood, scarlet, and hyssop appear together. Three, by the way, is also a sign of Messiah in Torah.) The ashes of the red heifer were kept to purify someone who had touched death (Num 19:11-18). The blood of the Passover lamb does not allow the angel of death to enter. Messiah is our Passover lamb, our sin sacrifice offered on the wood of the cross. His blood, which ran scarlet, imparts resurrection life (as the living bird was set free), cleansing us from a walking death (as leprosy was a fatal disease)!
Hyssop appears in a few more places in Scripture connected with purification:
Purge me with hyssop, and I shall be clean; wash me, and I shall be whiter than snow. Psa 51:7
For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and goats, with water, scarlet wool, and hyssop, and sprinkled both the book itself and all the people, saying, “This is the blood of the covenant which God has commanded you.” Then likewise he sprinkled with blood both the tabernacle and all the vessels of the ministry. And according to the law almost all things are purified with blood, and without shedding of blood there is no remission. Heb 9:19-22
And the ashes of the red heifer was for purification from sin; Messiah being the perfect purification from sin.
… the ashes of the heifer … shall be kept for the congregation of the children of Israel for a water of sprinkling; it is a purification from sin. Num 19:9
For if the blood of bulls and goats and the ashes of a heifer, sprinkling the unclean, sanctifies for the purifying of the flesh, how much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, cleanse your conscience from dead works to serve the living God? Heb 9:13-14