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It might be worth making it more elaborate.
The chance that infected person infects somebody else rises with the time a fter infection, and peaks at the time they start showing symptoms.
The process of being infected and showing symptoms is a number of cycles of a single virus particle infecting a single cell, taking it over and turnin g it into a virus factory until it exhausted and bursts, spreading out of n ew generation of virus particles.
Some the new generation stick around in the original host and infect more c ells, while others escape to infect new hosts. the proportions are going to be same all the way through the process - the virus particles have no info rmation about how many other cells they have infected until the immune syst em response kicks in.
The original host is getting progressively sicker, and their immune system is eventually going to start to churn out anti-bodies and produce fever and so forth.
The number of virus particles generated and shed will rise exponentially un til the immune system kicks in, so most of the infections will happen in th e last stage of the process.