= Solution
The <susceptible compartment> retains $S_t$ individuals, gains $B$ recruits per generation and loses $\alpha S_tI_t$ through <infection>. The <mass-action interaction> term represents new infections generated by encounters between susceptible and infectious individuals. Those new cases form the next <infectious compartment>, $I_{t+1}$; the current infectious generation leaves that compartment after one time step.
The initial conditions $S_0,I_0$ specify the starting susceptible and infectious counts. The parameter $\alpha$ is the transmission coefficient in this deterministic approximation, while $B$ supplies new susceptible individuals. This is the <discrete susceptible-infective model with recruitment>.
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