I know that actual strawberry growers, and serious backyarders, have complex schemes of several different sorts for partly or fully replacing the plants every year or every couple years, generally in a regimented geometric layout and all that.
However, I have to say that my parents' strawberry patch was renovated every 10 years or so but otherwise pretty much left to its own devices, and aside from serious depredations by squirrels and a need for lots and lots of stale beer slug traps, it has always produced Real Well. (Until this past summer -- alas, my parents, who are now in their eighties, decided it was too hard to crawl around picking strawberries every coupla days during strawberry season, and mowing around it the rest of the time, so now it has been returned to lawn -- R.I.P. mom's homemade strawberry preserves with their erratic jelling habits :/ )
Anyhow. If it were me, having been raised as per the foregoing, I would mulch lightly with straw or dried leaves to try to discourage the plants from growing incessantly during the winter. It is probably weakening them. Remove mulch once Real Growing Weather arrives.
If I had had disease or pest problems last year, or if disease or pest problems were common in my area, I would 'deadleaf' all brown or reddish leaves. Otherwise I would probably be lazy and leave them, at least til spring (I'm not saying this is the best thing to do, but at least if you are my parents, you can generally get away with it <g>).
Next summer after strawberries are pretty much over, I would remove any plants that look sad and 'over the hill', and I would encourage runners to take their place. Other than that, I'd just kind of wait and see what happens. If you need to renovate some year, so you need to renovate, why not wait and see what happens first
Mind, I have NO idea how things may be different growing strawberries in Arizona. I suppose you have to keep the javelinas out of the patch, and stuff like that <g>
JME,
Pat