Persistence of a tumor spheroid with an almost periodic nutrient supply

Homero G. Díaz-Marín; Osvaldo Osuna; Geiser Villavicencio-Pulido

doi:10.56754/0719-0646.2802.363

Authors

Homero G. Díaz-Marín Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana, Ciudad Universitaria, C.P. 58040. Morelia, Michoacán, México. https://orcid.org/0000-0002-2453-9049
Osvaldo Osuna Instituto de Física y Matemáticas, Universidad Michoacana Ciudad Universitaria, C.P. 58040. Morelia, Michoacán, México. https://orcid.org/0000-0002-4698-1321
Geiser Villavicencio-Pulido División de Ciencias Biológicas y de la Salud, Depto. de Ciencias Ambientales, Universidad Autónoma Metropolitana Unidad Lerma, Av. Hidalgo Poniente No. 46, Col. La Estación, 52006 Lerma de Villada, Edo. de México, México. https://orcid.org/0000-0003-1085-8556

DOI:

https://doi.org/10.56754/0719-0646.2802.363

Keywords:

Tumor growth, spheroid tumor, almost periodic function, reaction-diffusion equation

Abstract

We prove that a spherical tumor with free boundary furnished with an almost periodic nutrient supply has a twofold long term time evolution: either it vanishes or it tends towards a persistent tumor which oscillates almost periodically. This is determined by a relation of the mean of the nutrient supply and a threshold value meaning the minimal nutrient supply enabling the tumor to live. In each case, global stability is proved for the almost periodic solution \({(}\sigma_\star(t,x),P_\star(t,x))\) of the corresponding reaction-diffusion equation.

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