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Separable transition density in the hybrid model for tumor-immune system competition. (English) Zbl 1234.92026
Summary: A hybrid model of the competition of tumor cells in the immune system is studied under suitable hypotheses. An explicit form for the equations is obtained in the case when the density function of the transition is expressed as the product of separable functions. A concrete application is given starting from a modified Lotka-Volterra system of equations.

92C50Medical applications of mathematical biology
37N25Dynamical systems in biology
Full Text: DOI
[1] N. Bellomo, A. Bellouquid, and M. Delitala, “Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition,” Mathematical Models and Methods in Applied Sciences, vol. 14, no. 11, pp. 1683-1733, 2004. · Zbl 1060.92029 · doi:10.1142/S0218202504003799
[2] N. Bellomo and G. Forni, “Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems,” Mathematical Models and Methods in Applied Sciences, vol. 16, no. 7, pp. 1001-1029, 2006. · Zbl 1093.92002 · doi:10.1142/S0218202506001443
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[17] C. Cattani and A. Ciancio, “Hybrid two scales mathematical tools for active particles modelling complex systems with learning hiding dynamics,” Mathematical Models and Methods in Applied Sciences, vol. 17, no. 2, pp. 171-187, 2007. · Zbl 1142.82019 · doi:10.1142/S0218202507001875
[18] C. Cattani and A. Ciancio, “Third order model for tumor-immune system competition,” in Proceedings of the 4th International Colloquium Mathematics in Engineering and Numerical Physics, pp. 30-37, Bucharest, Romania, 2007. · Zbl 1132.34319
[19] C. Cattani and A. Ciancio, “Qualitative analysis of second-order models of tumor-immune system competition,” Mathematical and Computer Modelling, vol. 47, no. 11-12, pp. 1339-1355, 2008. · Zbl 1145.34303 · doi:10.1016/j.mcm.2007.07.005
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