The bigger the evolutionary jump, the more lethal cross-species diseases could be

A disease jumping from a buffalo to a cow is making a short evolutionary jump, and is less likely to be fatal. A disease jumping from a buffalo to a cat involves a larger evolutionary jump and a higher chance of death. Luckily, this lethality may cause the disease to spread poorly amongst its new hosts.

Pneumonic Plague in a Dog and Widespread Potential Human Exposure in a Veterinary Hospital, United States

In December 2017, a dog that had pneumonic plague was brought to a veterinary teaching hospital in northern Colorado. Several factors, including signalment, season, imaging, and laboratory findings, contributed to delayed diagnosis and resulted in potential exposure of >116 persons and 46 concurrently hospitalized animals to Yersinia pestis.