Jim, you might take a look at the graph theoretic concepts of maximum flow,
independent paths, minimum cutsets, and particularly Menger's theorem.
----- Original Message -----
From: "Jim "GrimJim" W Lai" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, July 24, 2001 4:11 PM
Subject: Re: network topology of the AIDS epidemic
> On Mon, 23 Jul 2001, Valdis wrote:
> > Can we stop the AIDS epidemic by focusing on the high degree Hubs in the
> > network?
> I agree with the others who have followed up. We must be careful not to
> let the constraints or focus of a model overly constrain our possible
> avenues of attack.
> I hope this isn't inappropriate, but off the cuff I see value in a
> physical analogy of networks. I have no URLs to cite, sadly.
> Networks - corresponds to pipes, interconnected between nodes.
> Infection - corresponds to fluid transported by pipes.
> Fluid flow volume over time through a node is trivially as follows:
> cross-section X velocity X density
> cross-section = proportionate to connectivity
> velocity = proportionate to frequency of transmission
> density = proprotionate to effectiveness of transmission
> The model suggests three points of attack to stem flow, aside from the
> elimination of nodes in the network.
> minimize cross-section: high connectivity hubs
> minimize velocity: numerically common vectors
> minimize density: high risk infectivity vectors
> Prevention efforts should attack all three, depending on which is most
> effective. There is no a priori one best attack mode from this model.
> From the model, one should be able to demonstrate the effectiveness of
> each method of attack individually, but a combined picture gives a more
> accurate assessment of the situation.
> Jim Lai