Domestic pet cats generally don't carry rabies virus, because the incubation period of rabies virus in animals is about 1 week, and they will get sick and die in a week. Moreover, dogs with rabies virus will have obvious symptoms, which are easy to distinguish. Therefore, foreign countries will combine observation and injection of rabies vaccine when treating animal scratches or bites. If the bitten dog does not get sick and die within 7 days (conservative 10 days), it means that there is no rabies virus, and the bitten dog can stop injecting the follow-up vaccine. In China, it is a complete course of treatment, so the consumption of rabies vaccine in China is not generally large. In addition, the probability of domestic pets being infected with rabies virus as required is also very small. As for stray dogs, it is hard to say.
As long as you have rabies, cats and dogs have viruses, whether they are sick or not. But it can only be transmitted to others during the onset period, because rabies virus is strictly neurotic, and there is no rabies virus in saliva or peripheral blood of cats and dogs before the onset.