If the sentence ends with "outbreak," then what you have written is correct : "have now been infected in the outbreak." However, if another clause is added after "outbreak," then it is possible to put "now" at the beginning of the second phrase. Note that "now" would then modify the second phrase. For example, "Fifteen elderly people have been infected in the outbreak now that they are all eating together at the same time in the dining hall of the nursing home." Another example: "All the children have now finished lunch." "All the children have finished lunch, now that the lunch period has been extended. In these examples, the second clause explains the first. "Now that" is an expression that means, "since" or "due to the fact that."

"Have now been X" means up to and including this point in time, but "have been now X" is not a natural word order in English - it just does not sound right and is probably grammatically incorrect. You can say "have now been infected" or "have been infected now."