# B How were differential equations for SIR Models calculated?

1. Dec 11, 2016

### Sam Donovan

• Member advised to do some research before posting
Specifically:

2. Dec 11, 2016

### Staff: Mentor

3. Dec 11, 2016

### Sam Donovan

4. Dec 11, 2016

### Staff: Mentor

What do you mean by proof?
These models are a method to describe what actually happens. It can only be said to which extend their solutions are proper descriptions of reality or not, i.e. whether a certain choice of parameters and initial conditions lead to such a valid description or not. So a "proof" can only be a comparison with empiric data. SIR models are a class of models, depending on the choice of $\beta, \gamma$ and eventually $N$ plus initial conditions like $\left. \frac{dS}{dt}\right|_{t=0} =S_0$. I would look for the original paper of Reed and Frost or the links on the Wiki page. Also the SARS outbreak in 2002/2003 could provide several data for comparisons.