When we discovered the disease, it was already spreading.
We use the word "spread" for diseases like cancer.
"The cancer spread to his brain." (ガンが移動する = metastasize; spread)
We also use the word "progress" to talk about the development of a disease.
ガンのような病気には "spread" という単語が使われます。
"The cancer spread to his brain."(ガンが脳に転移した)
ガンが移動する = metastasize; spread
病気が進行することについては "progress" という単語も使われます。