Anna Duggar: Why She Won’t Divorce Josh Duggar After He Cheated. Josh Duggar admitted to cheating on his wife Anna Duggar, but it looks like she’s not planning on leaving him, according to a new report. Anna Duggar, 27, is “permanently committed” to her husband, Josh Duggar, 28, regardless of his recent transgressions, a new report claims. Even though he’s admitted to previously molesting his younger siblings and to cheating on his wife, their family is turning to their faith now more than ever — find out more.