Growth of nonnecrotic tumors in the presence and absence of inhibitors

In this article a model for the evolution of a spherically symmetric, nonnecrotic tumor is presented. The effects of nutrients and inhibitors on the existence and stability of time-independent solutions are studied. With a single nutrient and no inhibitors present, the trivial solution, which corresponds to a state in which no tumor is present, persists for all parameter values, whereas the nontrivial solution, which corresponds to a tumor of finite size, exists for only a prescribed range of parameters, which corresponds to a balance between cell proliferation and cell death. Stability analysis, based on a two-timing method, suggests that, where it exists, the nontrivial solution is stable and the trivial solution unstable. Otherwise, the trivial solution is stable. Modification to these characteristic states brought about by the presence of different types of inhibitors are also investigated and shown to have significant effect. Implications of the model for the treatment of cancer are also discussed.