I would like to calculate the “basic reproduction number” (R0) for a “reaction-diffusion-advection” type epidemic model. I calculated R0 for the ordinary differential equations of my model using the « spectral radius of the next-generation matrix » but I don’t know how to calculate R0 when there are advection and diffusion terms. However, here are some approaches that I found in the literature for calculating R0 from reaction-diffusion epidemic models:
- Variational formula
- Spectral radius of a next-infection operator
- Spectral radius of a resolvent-positive operator
- Spectral radius of a product of four multiplicative operators
Which method should I use? Any advice (or references) would be greatly appreciated.