A PDE approach for the dynamics of the inflammatory stage in diabetic wound healing
Wound healing is an extremely complicated process and still not fully understood, moreover when diabetis mellitus is present. The inflammatory phase, the first one of this process, is where there exists a major difference between diabetic and nondiabetic wound healing. Here, we present a work in progress related with the modeling and analysis of the dynamics of some of the main agents involved in this first phase.
We propose a reaction-diffusion system as a model for these dynamics. This model aims at generalizing the previous existing approach of J.Sherratt and H.Waugh, where an ODE system (only taking into account the time variable) is proposed as a simplified model for this situation.
After obtaining this PDE approach, the well-posedness of the problem will be stated (both in a mathematical and a biological sense) and we will present some results related with the equilibria of the system. Finally, we will show some numerical simulations to illustrate the previous results.
This is a joint work with Neus Consul (Universitat Politecnica de Catalunya) and Sergio M. Oliva (Universidade de Sao Paulo).