The first time I studied Leviticus carefully (about 13-14 years ago), one of the things that stood out to me was the fact that ritual uncleanness transfers very easily, but cleanness does not. If someone is unclean for whatever reason, touching someone or something clean renders the clean person or thing unclean. It doesn't go the other way. Going from unclean to clean requires certain ritual ceremonies, and it often takes time, sometimes even a week or more. Going from clean to unclean simply requires exposure.
That's one of the reasons that it's particularly impressive that in the gospels Jesus touches people who have skin diseases or unhealthy menstrual conditions when he heals them, since those conditions were ritually unclean under the Torah ritual system. And it's clear that this wasn't out of some notion that the Torah ritual system was an ancient superstition that should be discarded. He insists in his teaching about Torah that it is the word of God and will be eternally true. But he also insists that it is eternally true not because it perpetually applies but because he fulfills it himself.
So what's going on when he heals people whose conditions would normally require a week or more of cleansing ceremonies? Sometimes he does tell them to go to the priests in the temple and do the ceremonies the Torah prescribes. Other passages don't mention him saying that. But certainly what's odd about it is that he touches them himself, when there are plenty of cases where he heals people without touching them. Are we to assume that he takes on the uncleanness himself voluntarily and then has to go through the rituals to be cleansed himself? The first would be a nice symbol of how he elsewhere describes what he would do at the cross, but I don't think that's the right way to think about these cases, because he's even telling them in some cases that he has simply made them clean (e.g. Matthew 8:3, although there he does say to make the sacrifices with the priest, but he says it's to be done for proof, not for actually making the guy clean).
I've long thought of this as just an exception. Normally cleanness doesn't spread to the unclean, but these passages are presenting Jesus as demonstrating something about himself as different. He can make unclean clean instantly, and that shows that he's superior to the Torah ritual system, which only looked forward to him.
But that turns out to be wrong, on closer inspection. For one thing, it can't be mere superiority. The Bible is clear across the entire canon that God can't entangle himself with sin or sinful beings, and that's why sacrifices are needed to begin with to deal with that sin. Isaiah 59:2 describes sin as separation from God. Jesus couldn't, merely by being God, do something that the scriptures clearly present God as not being able to do without sacrifice. So it has to be tied to sacrifices in some way, and it would be nice if we could find something explicit in the ritual ceremonies that looks more like what Jesus was doing in these passages.
It turns out that these cases in the gospels are not unprecedented. There is at least one mention in Leviticus of a case where holiness spreads to something common (although it isn't described as cleanness spreading to something unclean). That's in the description of the sin offering in Leviticus 6:27, where anyone who touches the flesh of the animal offered as a sin offering is made holy. I know of no other place where something is made holy merely by touching something in the entire Hebrew Bible, although maybe there are others that I just never connected with this issue.
What's going on in the gospel passages, then, given that there is a precedent for holiness spreading from a sin offering to something else? Perhaps the implication is that Jesus could reverse the normal flow of the symbolic status of ritual uncleanness to the clean because, as a future sin offering, he is in fact able to touch something and make it holy, whereas being divine without being the sin offering wouldn't do that. That seems to make these things fit together a lot better than the way I had been thinking about it.