How were differential equations for SIR Models calculated?

[Sam Donovan]

Specifically:

 

[fresh_42]

Here's the related Wikipedia entry on the issue:
https://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disease

 

[Sam Donovan]

Here's the related Wikipedia entry on the issue:
https://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disease

Thank you! Do you think there any sites or wiki articles with the math proof for these equations?

 

[fresh_42]

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.