In regards to the appearance of either the plague or Black Death in Mary Shelley's novel Frankenstein, no mentioning is ever made. You may be referring to a scene in Kenneth Branagh's 1994 filmatic adaption of Shelley's novel --Elizabeth has come to bring Victor home from University given the disease is running rampant. Victor, obsessed by his experimentations, refuses to leave the disease ridden village.
The conflict regarding man (or people) versus infectious disease (Black Death) is an external conflict. External conflicts are defined by any conflict which happens outside of a person/character. These conflicts are defined classically as man versus man, man versus nature and man versus supernatural. In regards to the novel, the conflict can be defined in two very different ways--both man versus nature and man versus man (an individual or society).
In defining the conflict as one which pits man (people) against nature (Black Death), Black Death would be considered an element of nature. Mankind did not create the disease. Given that the disease exists as a result of nature, the conflict would be considered an external conflict of man (people) versus nature.
On the other hand, those infected with Black Death were quarantined. Uninfected people were the ones who were responsible for the mandatory quarantine. In this sense, those who did not have Black Death were fearful of those who did. Given that the people who were infected with the disease were separated from the healthy, the external conflict, under these circumstances, would be considered man (people) versus man (people).