How does Primo Levi's foot get cut?

Keeping this in consideration, how did Primo Levi survive?

Bent on survival, Levi did whatever he could to endure the horrors of Auschwitz. In January 1945, the Red Army liberated Auschwitz and Levi made his journey home. Of the more than 7,000 Italian Jews who had been deported to concentration camps during the war, Levi was among the fewer than 700 who survived.

Beside above, what was Primo Levi's condition during the ten days? Primo Levi had come down with scarlet fever on January 11, 1945 and he had been put into the hospital at Monowitz, so he was not able to join the march out of the camp on January 18, 1945. He wrote that he was being treated in the hospital with sulpha drugs.

Additionally, why did Primo Levi wrote Survival in Auschwitz?

Levi wrote his work as an act of bearing witness to the horrors he had both seen and undergone himself. It's a testimony to both the sheer willpower of perseverance and human strength that emerges when people are stretched to their utter limits, as well as the dark depths to which humanity is capable of sinking.

What illness prevented Primo Levi from being forced into the death march?

After a year in Auschwitz III-Monowitz, Levi was liberated in January 1945 by the Red Army. He was not taken on the final death marches because the Nazis believed he and the others left behind would die of illness, malnutrition and disease before the Red Army arrived.