In which of the following diseases do rats NOT act as intermediate hosts?

Rats do not serve as intermediate hosts in amoebic dysentery, as the disease is caused by the protozoan parasite Entamoeba histolytica, which is primarily transmitted through the fecal-oral route, often through contaminated water or food. This means that human infections arise from direct contact with the parasite rather than from an intermediate host like rats.

In contrast, for the other diseases mentioned, rats play a significant role in the transmission cycle. They are known carriers of the bacteria responsible for plague, which is transmitted to humans through fleas that infest the rats. With Weil's disease, which is caused by Leptospira bacteria, rodents, including rats, are important reservoirs, excreting the bacteria in urine that can contaminate water sources. Similarly, rats are associated with endemic typhus, as the disease is transmitted by fleas or lice that infest rats, facilitating the spread of Rickettsia prowazekii.

Thus, the absence of rats in the transmission of amoebic dysentery is what correctly identifies it as the disease for which they do not act as intermediate hosts.