One of the reasons I wanted to take some time before responding is that the answers are not simple.
I cannot find my last book on virology basics. I can't answer right now what the latest sample minimums are in order to set a rate. If I can locate it tomorrow I will respond with the latest. I may call someone as well as it is bugging me now.
Viral growth curves are generally unique to the virus and have not been compared to each other in any real way. There are no real method for there to be an "average" time frame.
Almost all studies around what you are asking, animal to human transmission, relate to HIV. HIV doesn't act like other viruses. It is a very bad virus to use as an example because of how long it takes to cause disease. Other latent viruses include herpes simplex virus (oral and genital herpes), varicella-zoster virus (chickenpox and shingles), and Epstein-Barr virus (mononucleosis) and Hepatitis C virus.
HIV viral loads vs time, while studied extensively, do not behave the same in any 2 individuals.
Interestingly, viral growth curves are also not really curves. They are exponential straight lines as the virus actively infects and replicates, they are not bell shaped curves. For example here is the the growth "curve" for the flu.
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Very few viruses move from animals to humans. The means of transmission are generally not as effective and there are enough differences in cell structure and immune system to limit the transfer ou f hosts. That is why it is an unusual virus that infects both. Most viruses are species specific.
However, host transfer is not unheard of. These transfers involve either increased exposure or the acquisition of variations that allow the virus to overcome barriers to infection of the new hosts. In these cases, devastating outbreaks can result. The most recent being the H1N1 flu. Luckily it was not nearly as effective at spreading itself in humans as it was in birds. If it had been the outbreak would have been devastating.
SARS is another host transfer virus that was quite deadly. Transmission was problematic for the SARS virus because it was not infective until after symptoms started. This enabled us to limit its spread by isolating the sick. Unlike COVID 19 which is infectious long before symptoms start. Making it exceeding good at finding new hosts for itself.
Fortunately for us, most viral host transfers to infect the new hosts cause only single infections or limited outbreaks, and it is rare for a virus to cause an epidemic in a new host.
Does this help or confuse? I feel like I've been rambling. Let me know if I need to clarify.