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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.55 no.1 Bogotá Jan./June 2021 Epub Nov 04, 2021
https://doi.org/10.15446/recolma.v55n1.99096
Original articles
Periodic solutions for a model of tumor volume with anti-angiogenic periodic treatment
Soluciones periódicas para un modelo del volumen de un tumor con tratamiento periódico
1 Universidad Michoacana, Morelia, México
In this work, we consider the dynamics of a model for tumor volume growth under a drug periodic treatment targeting the process of angiogenesis within the vascularized cancer tissue. We give suffcient conditions for the existence and uniqueness of a global attractor consisting of a periodic solution. This conditions happen to be satisfied by values of the parameters tested for realistic experimental data. Numerical simulations are provided illustrating our findings.
Keywords: Cancer treatment modelling; cooperative systems; periodic orbits; tumor development; angiogenesis
En este trabajo, consideramos la dinámica de un modelo para el crecimiento del volumen de un tumor bajo un tratamiento periódico de medicamentos dirigido al proceso de angiogénesis dentro del tejido vascularizado del cáncer. Damos condiciones suficientes para la existencia y la unicidad de una solución periódica la cual es globalmente atractora. Estas condiciones se cumplen con los valores de los parámetros probados en datos experimentales reales. Se proporcionan simulaciones numéricas que ilustran nuestros resultados.
Palabras clave: Angiogénesis; Modelos de tratamiento de tumores de cancer; sistemas cooperativos; órbitas periódicas
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Received: June 06, 2020; Accepted: September 16, 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
