confusion about SIR model

Question

So SIR model is like this:

S(n) - S(n-1) = -alpha*S(n-1)I(n-1);
I(n) - I(n-1) = alpha*S(n-1)I(n-1) - beta*I(n-1);
R(n) - R(n-1) = beta*I(n-1);

so the susceptible number is decreasing because every time there will be a certain portion of susceptible people get infected. The number of infected people is represented by alpha*S(n-1)I(n-1) here. I wonder why it's not just -alpha*S(n-1)??? why we have to multiply the I(n-1)??? Please help me understand, thanks a lot!

Answer 1

Okay, now I finally understand why it's alpha*S(n-1)I(n-1), because the more infected people, the more people get infected so the number of infected people also matters here. It is called law of mass action.