How old is Luke at the end of the story?

Margaret Peterson Haddix is the author of the novel Among the Hidden, which is a part of a series of books in the Shadow Children sequence.
In chapter seven, dialogue reveals that Luke, the third child born in a society where it is only legal to have two children in a family, is twelve years old. From that chapter until chapter twelve, the text mentions harvest time and late October. So readers could infer that the novel begins in summer, and has spanned about three to four months at this point. In chapter nineteen, November is referenced. Luke's father is playing cards with him on Luke's bed because there is no work for him to do.

"'Again?' Dad asked, shuffling the cards.
'If you don't have any work you've got to do.'
'In November? With no livestock? Only work I've got now is figuring out how we're going to pay our bills once the hog money runs out.'"

Chapter twenty is set in mid-January, and chapter twenty-one begins in mid-February. Chapter twenty-two begins with April rain. The next chapters span the remainder of that month. Chapter twenty-six opens a week and a half after the rally, which is probably the beginning of May.
I couldn't find any other definite time markers longer than a day or two from chapter twenty-six to the end of the book, chapter thirty. So, we can infer that Luke is still twelve, and the events of the novel take place in just under a year's time.