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 inhibitor s on the existence and stability of time-independent solutions are stu died. With a single nutrient and no inhibitors present, the trivial so lution, which corresponds to a state in which no tumor is present, per sists for all parameter values, whereas the nontrivial solution, which corresponds to a tumor of finite size, exists for only a prescribed r ange of parameters, which corresponds to a balance between cell prolif eration and cell death. Stability analysis, based on a two-timing meth od, 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 t he presence of different types of inhibitors are also investigated and shown to have significant effect. Implications of the model for the t reatment of cancer are also discussed.