By B. D. Curti, D. L. Longo (auth.), John A. Adam, Nicola Bellomo (eds.)
Mathematical Modeling and Immunology an incredible volume of human attempt and monetary assets has been directed during this century to the struggle opposed to melanoma. the aim, in fact, has been to discover options to beat this difficult, tough and possible never-ending fight. we will effortlessly think that even larger efforts should be required within the subsequent century. The wish is that finally humanity should be winning; good fortune can have been accomplished while it really is attainable to turn on and keep watch over the immune process in its festival opposed to neoplastic cells. facing the above-mentioned challenge calls for the fullest pos sible cooperation between scientists operating in several fields: biology, im munology, medication, physics and, we think, arithmetic. definitely, bi ologists and immunologists will make the best contribution to the re seek. although, it's now more and more well-known that arithmetic and desktop technological know-how may perhaps in a position to make significant contributions to such prob lems. we won't anticipate mathematicians on my own to resolve basic prob lems in immunology and (in specific) melanoma learn, yet important sup port, in spite of the fact that modest, may be supplied through mathematicians to the study aspirations of biologists and immunologists operating during this field.
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Extra info for A Survey of Models for Tumor-Immune System Dynamics
For completeness, the symmetric two- and three-dimensional versions will be given here also, but it should be noted that in another fundamental paper, with more biologically realistic boundary conditions, Shymko and Glass [SHa] dealt fully with the corresponding three-dimensional problem. Consider a "slab" of slowly growing tissue of width L, centered on the origin, producing growth-inhibitor at a rate P (molecules/unit volume/second) which is depleted or decays at a rate A. This central tissue is embedded in an infinite expanse of non-active tissue.
A. Adam et al. ), A Survey of Models for Tumor-Immune System Dynamics © Birkhäuser Boston 1997 16 A Survey of Models for Tumor-Immune System Dynamics another, they represent formative work or contain significant results that have provided the basis for a better understanding of the processes involved. In a "meta-modeling" sense, it is interesting to note how punctuated the evolutionary track of such models has been! ,--------------------------------- Problem of Interest Simplifications . 1 - Schematic representation of the basic stages of the mathematical modelling process, and their inter-relationships.
1), which is to be contrasted with an empirical approach of inferring mechanisms from a finite (perhaps small) set of observations. While both approaches are prone to error, mathematical models operate in the opposite direction by postulating mechanisms and using mathematics to examine the consequences of those postulates (for a discussion of this in the context of immunology using the notion of rugged landscapes, see [PEa]). Related to these ideas is the question; given a general process (such as neoplasia), are there any general principles or universal features inherent in the process which may be subject to some level of mathematical analysis?
A Survey of Models for Tumor-Immune System Dynamics by B. D. Curti, D. L. Longo (auth.), John A. Adam, Nicola Bellomo (eds.)