Hi Techjobs2k,
I do scientific research using mathematical models and have published some papers, listed on the following link: [login to view URL]
In my most recent publication ([login to view URL]) I used a reaction-diffusion model very similar to the Jalefice et al. (2011) article you shared. I also have some paper under review which uses a system of population-dynamical equations quite similar to the Kang et al. (2011) you also shared.
For starters, let me explain Equation (4) on p. 118 of Kang et al.
1) The first term will be zero if there are no worker ants by definition of the parameter a. That makes sense as the fungi are expected to eventually die in the absence of worker ants to take care of them.
2) The surprising aspect of that model (which is not mentioned in Kang et al.'s article) is that if all ants are workers, the first term (as above mentioned) will also be zero. This seems rather inconsistent with our understanding that fungi are tended by the worker ants.
Those are just among the things we can talk about and discuss if you award me the project.
Do PM me if you decide to hire me. Thank you.