Soluciones periódicas para un modelo de población celular sujeto a una radiación periódica general

• Autores: Homero Díaz Marín, Carlos Osvaldo Osuna Castro
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 38, Nº. 2, 2020, págs. 81-91
• Idioma: español
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    En este trabajo consideramos modelos con tratamiento de radiación periódico contra el cáncer que describen la dinámica de las poblaciones celulares en un tumor. Establecemos la existencia de órbitas periódicas, utilizando la teoría de los sistemas cooperativos. Damos condiciones suficientes parala unicidad de la solución periódica, también para que esta sea un atractorglobal. Realizamos simulaciones numéricas utilizando funciones de radiación específicas para ilustrar nuestros resultados analíticos.

  • English

    In this work, we considered models with periodic radiation can-cer treatment which describe the dynamics of cell populations in a tumor.This may also be used to consider dynamics of healthy tissue under periodic radiation exposure. We establish the existence of periodic orbits, byusing theory of cooperative systems. We give sufficient conditions for theuniqueness of the periodic solution which then becomes a global attractor.Numerical simulations are performed using specific radiation functions to illustrate our analytical findings.

• Referencias bibliográficas
  • Referencias Benzekry S., et. al. “Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth”,PLOS Computational...
  • Hall E.J. and Giaccia A.J.Radiobiology for the Radiologists, Lippincott Williams & Wilkins(LWW), Philadelphia, 2018.
  • Freedman H. I. and Pinho S. T. R., Persistence and extinction in a mathematical model of cell populations affected by radiation, Period. Math....
  • Gámez M., et. al., “Observation and control in a model of a cell population affected byradiation”,BioSystems96 (2009), No. 2, 172-177. doi:...
  • Greider B.W., Kallman R.F. and Franko A.J, “Recruitment of noncycling tumor Cells into Proliferation by Isoproterenol”, Cancer Research, 43...
  • Korman P., “A periodic model for the dynamics of cell volume”, Annales Polonici Mathe-matici, 116 (2016), 243-249. doi: 10.4064/ap3857-3-2016.
  • Liu Z., et. al., “Permanence, extinction and periodic solutions in a mathematical model ofcell populations affected by periodic radiation”,...
  • Smith H., Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Math. Surveys Monogr., Arizona,...
  • Wallace D.I. and Guo X., “Properties of tumor spheroid growth exhibited by simple mathematical models”, Front Oncol, 3 (2013). doi: 10.3389/fonc.2013.00051.
  • Watanabe Y., et. al., “A mathematical model of tumor growth and its response to single irradiation”, Theoretical Biology and Medical Modeling,...