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The mathematics of these models for the "normalized" (i.e., proportional) formulation of the model are potentially confusing. In these formulations the infection rate beta is usually considered to be a constant, regardless of population density, etc., unless a specific formula for this relationship is specified. For this to be true, all compartments in the model (S,I, etc.) must sum to one. The introduction of the mu_i term into the model destroys this relationship, making the meaning of beta unclear. Given, if s,i, are renormalized at each time step (as they are by the use of an updating population term in the actual implementation) then this formulation is correct. The documentation should be specific on this point or contain a more standard formulation. Additionally, which values are constants and which values are recalculated per time step is not well specified in the documentation, hence it is not initially clear if the equations are correct. I propose that all time dependent values be indicated with a (t) for clarity. E.g., S becomes S(t).
The code faithfully implements the computations documented in the Javadoc. Is there something missing there?
I hope there is not a problem in the implementation. I think the problem with the documentation is that: 1 - It is not clear when normalization is taking place 2 - It is not clear which variables are time varying and which are not. (essentially the same as 1) I decided to open this because it took me a long time to figure out what was going on when I was doing a mathematics double check.
I see. I remember it taking forever to write all the Javadoc, but I did it because it was absolutely necessary for the integrity and acceptance of the system. So, I'm in full agreement to fully documenting and clarifying the model, and adjusting it as necessary. I'm at a loss as to how to prioritize this however. On one hand, there a significant interface and usability issues that need attention, while on the other, the math/models should be correct and accepted by the community. Does it make sense to use what we have for the moment and make progress on the other issues?
resassigning to Stefan
can this be closed?
Yes, Models have all been redone. New documentation is available on the wiki.
resolved
closed
