"Is that a universal truth, or is it historical? Situational?" It it experience based on historical data. A virus jumping to a new host (species) will be more

"Is that a universal truth, or is it historical? Situational?" It it experience based on historical data. A virus jumping to a new host (species) will be more aggressive in the beginning until it has adopted (mutated) to his new host. While this is not a universal truth, it is experience and could also be backed up mathematically (>host dies to soon, virus can not spread) and by game theory.