I searched a lot on the Internet, but I am not clear about the spread of the rabies virus. As I understand, rabies kills any animal it infects—cats, dogs, foxes, bats, humans. If it kills all of its hosts, then where does it stay?
So, if all rabies-infected animals die, but in order to transmit the virus, every rabid animal has to bite some other animal or have rabies without symptoms, must there be some animal that is an asymptomatic carrier?
This is an interesting question, and it's been subject to a fair amount of research. From an epidemiological perspective, most rabies outbreaks have been studied in dogs. Among domestic dogs, the R0, or basic reproduction number, of rabies is usually quite low—estimated to be around 1.2 in rural sub-Saharan Africa, and <2 in most historically observed cases [1] (though a particularly bad epidemic in Osaka had an R0 of ~2.42 [2]). This implies that, among dogs, it's quite possible for rabies to spread faster than it kills its hosts, but can be entirely eliminated in dogs by mass vaccinations (see [1] and [2]).
But your question is still valid—if, say, the virus infects all the dogs in an area, and they all die, shouldn't rabies disappear from that area? There's some debate as to where the virus keeps hanging out. For one, there is some circumstantial evidence [3] that the fatality rate in dogs is not 100%, but actually closer to 85%. However, this doesn't necessarily explain the reemergence of epidemics, since for the virus to spread, it needs to get to the dog's saliva, by which point the dog is likely exhibiting lethal symptoms [4][5]. Dogs sometimes being asymptomatic carriers is a tempting explanation, but remains a "highly speculative" possibility [6].
To answer your question, let's look at a place where rabies outbreaks can cause severe economic losses—the livestock farms of South America and sub-Saharan Africa. Vampire bats, the hematophagic suckers, can bite over half of the animals in at-risk zones [7], which house some 70 million head of cattle. Since bats are very well-known sources of infectious disease—in fact, they're known to be hosts of 10 out of 11 recognized Lyssavirus species, including the rabies virus [8]—they've been a tempting explanation since 1911, when a bat-borne rabies outbreak in Brazil was first diagnosed [9]. [9] continues to say this:
An idea that vampire bats may be asymptomatic rabies carriers, shedding the virus in their saliva for months, was popular during initial studies of vampire bat rabies (16). However, in a well-documented experimental study by Moreno and Baer (17), the disease in vampire bats was similar to rabies observed in other mammals. The bats that developed signs of disease and excreted the virus via saliva soon died, whereas those that survived the inoculation without clinical signs never excreted the virus or had it in the brain as demonstrated upon euthanasia. More recently, the asymptomatic excretion of RABV in the saliva of experimentally infected vampire bats, which survived the challenge during at least 2 years of observation, was documented again (18). Clearly, this phenomenon requires additional investigation.
This is all I've been able to find so far. If I had to bet, I'd put my money on bats being the asymptomatic carrier that you're looking for, with a solid $n=14$ paper to back it up [13]. However, when it comes to established scientific consensus—well, I'm not sure there is one.
