Study of some models in medicine tumor growth and ecology: simple vs complex dynamics

Abstract

newlineIn this thesis I have studied some models of tumor immune system interactions and newlinesome in ecology Both types of models are based on predator prey type interactions newlinePredator prey or consumer resource dynamics is central to ecological complexity The whole thesis is divided into two parts Part I consists of models of tumor growth The model formulation for tumor growth is based on stoichiometric principles Time delay effects in immune system responses are also considered It is found that small delays guarantee stability at the equilibrium level stable focus but the delays greater than a critical value may produce periodic solutions through Hopf bifurcation and larger delays may even lead to chaotic attractors newline