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Joint Applied Math and Probability Seminar
Modeling Tumor Dynamics: An Ecological Perspective
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Many lines of evidence lead to the conclusion that ribosomes (and therefore phosphorus) are important commodities in cancer cells. The population of cancer cells within a given tumor tends to be highly genetically and physiologically varied. Our objective here is to integrate these elements, namely natural selection driven by competition for resources, especially phosphorus, into a mathematical model consisting of delay differential equations. In some of these models, we allow possible mechanisms that may reduce tumor phosphorous uptake or allow the total phosphorus in the organ to vary. Mathematical and numerical analysis of these models show that tumor population growth and ultimate size are more sensitive to total phosphorus amount than their growth rates are. In particular, our results show that if an mechanism (treatment) can cut the phosphorus uptake of tumor cells in half, then it may lead to a three quarter reduction in tumor size, indicating an excellent potential of such a treatment. In general we find that tumors with a relatively high cell death rate are more susceptible to treatments that block phosphorus uptake by tumor cells. Other treatments can also be modeled. |