While it will certainly be hard to contain, there are historical precedents for containing disease outbreaks where small mammals are the vectors. A notable case is the Bolivian hemorrhagic fever, caused by the Machupo virus, where an outbreak in 1966 was largely extinguished after two weeks by extensive trapping of the rodent vector[1]. Of course the effectiveness of trapping depends on many factors, and it is not always feasible. Studies like the ones being conducted by the CDC are essential for understanding these diseases and inform strategies on how to contain them.

If you’re interested in reading about the initial cases of various emerging diseases (or rather, emerging diagnoses), Laurie Garrett‘s book, The Coming Plague, is a good read.

1. https://wwwnc.cdc.gov/eid/article/1/3/95-0308_article