What determines the rate at which people leave the first "compartment" (susceptibles) to enter the second one (infected and infectious cases)?

The "mass action principle" states that this rate is a function of the number susceptible individuals in the population, i.e.:

C_t+1/C_t = f (S_t), where C is the number of infected cases, S the number of susceptibles, t a given time period, t+1 the next time period.

This can also be expressed as:

C_t+1 = S_t C_t r, where r is a transmission parameter.

(The latter expression explains the name of the "mass action principle", which was given by analogy to the "law of mass action" in chemistry, according to which the velocity of a chemical reaction is a function of the concentrations of the initial reagents.)

The "mass action principle" is actually the theoretical basis of the phenomenon of herd immunity. It was introduced in the 1900’s and helped understand the dynamics of epidemics of diseases like measles: as the infection spreads during an epidemic, the number of infected cases in each successive time period initially increases while the number of susceptibles in the population decreases; therefore, there will be a point when susceptibles become sparse and the number of new cases in each successive time period decreases; and, finally, susceptibles are so scarce that there is no more than one new case for each case in the previous time period, and the epidemic fades out although a number of susceptibles have not been infected.