Consider a graph, choose some "p: 0<p<1" (probability to infect the neighbor node). Choose some random number "K" of nodes which are "infected" initially. So we can generate epidemic model on a graph - each time tick - neighbors of already infected nodes become also "infected" with probability "p".

Now assume we have an option to "vaccinate" some number of nodes "V", that means they will never be infected. It is clear intuitively that it is more reasonable to "vacciante" those nodes with many neighbors, i.e. high degree nodes, however, graph theory suggests that there are several more sophisticated measures of "importance" of nodes - i.e. "centrality measures". Intuitively it corresponds to the situation that node may have many neigbours, but its neigbours have low number of neigbours, that means second step of epidemy will not be so harmful. That is why it is not obvious that direct choice of nodes with highest degrees is optimal.

**Question:** Is there any research on choosing relevant nodes for vaccination ? What are the outcomes ?
If yes, how less effective would be the naive strategy to vaccinate nodes with the highest degrees comparing to more advanced ones ?

PS

There can be several ways to measure "effectiveness" of vaccination , as well as epidemic model may contain more parameters like - how long is node "infected", as well as answer might depend on type of a random graph considered - any information is welcome. Well, keeping real world situation in mind would be also nice.