We will discuss two approaches for modeling cancer growth. One approach is to employ a deterministic space-independent model that includes separate components to represent specific and non-specific immune function. The other approach employs a spatially dependent hybrid cellular-automata (HCA) model whose rules are driven by cellular metabolic function. For the determinstic model, numerical simulations of mixed chemo-immuno therapy and vaccine therapy using both mouse and human parameters are presented. We illustrate situations for which neither chemotherapy nor immunotherapy alone are sufficient to control tumor growth, but in combination the therapies are able to eliminate the entire tumor burden. The HCA model is in its initial stages of development, and preliminary results will be presented.

We will present several new results about global theorem and asymptotic expansions for the distributions of iid random variables in the domain of attraction of stable laws. Particular attention will be paid to the Cuachy case which exhibits especially interesting features.