Following a couple of textbooks for an example, Brauer 2019 Models in Epidemiology, and in whichever paper i read regarding Next-generation-matrices they have defined, R0 as the spectral radius of the NGM.
Now having tried finding a proof for sometime I found papers such as Diekmann, which IMO had no rigorous proof towards the claim.
I wonder if anyone has any knowledge or idea of where i can find such a proof, or construct it. Thanks
EDIT: So this is within the field of epidemiology, where Next-generation matrices is a type of matrix within heterogeneous modelling, R0 is simply the famous reproductive number, i.e expected number of people that one infected individual infects. https://en.wikipedia.org/wiki/Next-generation_matrix Basically the last row on Wikipedia is what i would like to see.
There's no proof of R0 = spectral radius of NGM because it is just one way to define R0.
Now the reason why everyone uses this definition is that it guarantees the global asymptotic stability of the point with no disease (I(0) = 0) for many models. That fact does require proof and it can be found in the original paper that proposed this definition. https://doi.org/10.1016/S0025-5564(02)00108-6