How did otto frank survive the concentration camps at the time?

After being discovered with his family in August, 1944 he only stayed in Auschwitz from September, 1944 to January, 1945 when Auschwitz was liberated by Soviet troops. Although that three months had already been long enough to put him in the sick bay, it hadn't been long enough for him to die. His daughter Anne had been transported on to the Bergen-Belsen camp where a typhus epidemy broke out that killed her.