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Dynamic aspects of tumour–immune system interaction under a periodic immunotherapy

Part of: Smooth dynamical systems: general theory Applications - Dynamical systems and ergodic theory Nonlinear operators and their properties Low-dimensional dynamical systems

Published online by Cambridge University Press:  27 May 2021

GLADIS TORRES-ESPINO  and
MANUEL ZAMORA
GLADIS TORRES-ESPINO
Affiliation:
Departamento de Matemática, Universidad del Bío-Bío Grupo de investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Avda. Collao 1202, Casilla 5-C, Concepción, Chile email: gtorres@ubiobio.cl
MANUEL ZAMORA
Affiliation:
Departamento de Matemáticas, Universidad de Oviedo Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA) C/ Federico García Lorca n°18, Oviedo, Spain email: mzamora@uniovi.es
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Abstract

We study a mathematical model proposed in the literature with the aim of describing the interactions between tumor cells and the immune system, when a periodic treatment of immunotherapy is applied. Combining some techniques from non-linear analysis (degree theory, lower and upper solutions, and theory of free-homeomorphisms in the plane), we give a detailed global analysis of the model. We also observe that for certain therapies, the maximum level of aggressiveness of a cancer, for which the treatment works (or does not work), can be computed explicitly. We discuss some strategies for designing therapies. The mathematical analysis is completed with numerical results and conclusions.

Keywords

Tumourimmune systeminteracting populationsperiodic therapiesglobal dynamics

MSC classification

Primary: 37N25: Dynamical systems in biology 37C70: Attractors and repellers, topological structure 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 47H11: Degree theory 37C25: Fixed points, periodic points, fixed-point index theory
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 4 , August 2022 , pp. 606 - 645
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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