Abstract

Here we use a coupled reaction-diffusion equation to model deep partial thickness wounds in which the interaction of bacteria and normal skin cells is represented by the invasive capacity of bacteria and the phagocytic behavior of normal skin cells. The coupled system is investigated with the assumption that there is a constant consumption rate of bacteria by normal skin cells. The spatially homogenous case is considered obtaining fixed points. Stability analysis was carried out on the steady state solution to determine linear stability. Using biologically appropriate initial conditions numerical solution evolve to form traveling waves and traveling wave analysis was carried out to determine wave velocity. The results of the study reveal that if the wound gets infected, then depending on the model parameters, the wound will either be dominated by bacteria partially healed or totally healed.

Key words: Wound healing, phagocytic, normal skin cell, bacteria.