This investigation will continue the study of models of biological and physical systems which are related by the fact that they can be formulated in terms of functional and partial differential equations with nonlocal terms. The main three areas of this study are concerned with: a) the effect of age-structure and other internal variables of a population on the dynamic behavior of epidemic models; d) the effect of the size, shape and compartamental nature of a cell on the critical phenomena that control the cell cycle; c) the formation and stability of spatial patterns in systems of coupled degenerate diffusion equations modeling physical, chemical as well as some population processes. The project will employ both analytical and numerical simulations that will be aimed at fitting the mathematical results to experimental data. Each of the three problems requires the development of new mathematical techniques of analysis that can be applied to broad classes of equations that occur in the analysis of certain biological and physical phenomena. One of problems of general interest that is related to this research is the process of vertical transmission of infectious diseases in populations. Mathematical modeling of this process may help to understand better the process of disease transmission.
