The effects of averaging on the basic reproduction ratio

Authors: F. Adler (1992).

Beautiful paper written by Adler for his thesis at Cornell under the direction of Simon Levin. Ultimately it is a bit of relatively simple matrix analysis. The paper has one theorem, which basically says that, under appropriate modeling assumptions, the largest eigenvalue of one matrix is bigger than that of another.

To Do:

1. Understand the proof on purely mathematical terms (i.e. as a statement about two matrices that live in some relation to one another.)

2. Push the model in some way: allow not just group combinations, but other sorts of distortions (though see next paper.) Joe's ideas: allow differences in susceptibilities, or heterogeneities in the $\gamma$.

3. This paper answers a question about invasability. Is the concept well defined? Can the same techniques be used to answer other questions, perhaps not at a DFE?

4. When do you get equality?

5. Is it possible to get the wrong qualitative answer under aggregation? (i.e. suppose under aggregation $R_0 < 1$, while in fact $R_0 >1$.)