There is no replacing Vince Wilfork. There's no player quite like him in the NFL, much less on New England's roster. You can't just find 350-pound run stoppers "on the street" who take up multiple blockers.
Patriots coach Bill Belichick is good at adapting. Belichick values versatility above all else. He could ask Chandler Jones to move inside to defensive tackle, like the Patriots did during Sunday's 30-23 win over the Atlanta Falcons. That would hurt New England's pass rush. The team also has CFL import Armond Armstead on the reserve/non-football injury list. He can return to practice after Week 6.
Wilfork was struggling through the worst start to a season of his career before tearing his Achilles, and the Patriots still are 4-0 with the sixth-ranked scoring defense in the league. NBC's Cris Collinsworth hinted that Wilfork previously was struggling with a foot issue. The Patriots primarily use a four-man defensive line, which makes finding a true nose tackle to replace Wilfork less important.