How do the Franks, the Van Danns, and Dussel die?

Otto was the only survivor.

Mr. van Daan does in the gas chambers as Auschwitz, and Mrs. van Daan died in transit to the camps.

Anne and her sister died at the Bergen-Belsen camp, Peter at the Mauthausen concentration camp.

Mrs. Frank died of starvation while interred at Auschwitz-Birkenau.

Fritz Pfeffer (known as Albert Dussel in the diary) died on 20 December 1944 in Neuengamme concentration camp.