confusion about SIR model

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!

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1 Answer
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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.