I understand that the majority of people were illiterate but surely a few people wrote about it.
I summarized the basic time lines of the outbreak as well as the chief primary sources for a while in: How do we know about the Black Death and it’s timeline?
In short, there are some chronicles and diaries, either contemporary and near-contemporary (i.e. written in the generation after the outbreak), that record the visit of the outbreak in the region where the author lived mainly in the Mediterranean.
In addition to some examples I introduced in the question thread above like Gabrielle de Mussis and Michele da Piazza, Giovanni Villanni, Florentine merchant, and his Chronicle (Chronica) is worth mentioning, since Giovanni himself died of the plague during the first wave of the outbreak in Italy in 1348, and his family members took over the continuation of the work. The Chronicle is also one of the most important contemporary sources on the 14th century Italy as well as the Italian merchants [also out of Italian Peninsula].
While different excerpts of these texts, originally written in Latin, in diverse European vernacular languages in addition to even in Arabic, are now translated into English and easily accessible in form of two primary source collections (see Aberth ed. 2016 & Horrox ed. 1994 in the linked thread above), AFAIK there is unfortunately no complete English translation of these works.
On the other hand, it is rather difficult to find the reliable contemporary account north to the Alps so that we have some difficulty in the exact timeline of the Black Death especially in Germany and in Northern Europe. Nevertheless, we can make use of some correspondences of the town councils and merchants even there.
If you specify the region/ country out of Italy you'd like to know, I'm willing to check additional information on the contemporary primary texts of the Black Death.
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