The National Health Service in the UK spends over £1bn every year treating dermatological conditions such as chronic wounds. These wounds exhibit poor vascularisation prone to polymicrobial infections where slow- or non-healing are typical, and spend prolonged periods in the inflammatory stage. Chronic wounds such as leg and foot ulcers develop in patients with illnesses such as diabetes, where circulation is compromised and regular treatment and monitoring are essential. Many management strategies and new therapies have been introduced to combat chronic wounds and include growth factor therapy and skin substitutes. Although one of the greatest concerns is preventing an acute wound becoming chronic, and retrieving the normal healing before amputations are needed. Other dermatological conditions such as psoriasis affects 2–3% of the UK's population and shares some common traits with the wound healing phenomena, however mathematical models in this area are scarce. The thesis proposes a number of new mathematical models, to describe dermatological skin growth and recovery in both the epidermal and dermal membranes.