Related papers: An immune system-tumour interactions model with di…
Upcoming immunotherapies for cancer treatment rely on the ability of the immune system to detect and eliminate tumors in the body. A highly simplified version of this process can be studied in a Petri dish: starting with a random…
Mathematical and computational modelling in oncology has played an increasingly important role in not only understanding the impact of various approaches to treatment on tumour growth, but in optimizing dosing regimens and aiding the…
We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
We propose a multiscale chemo-mechanical model of cancer tumour development in an epithelial tissue. The model is based on transformation of normal cells into the cancerous state triggered by a local failure of spatial synchronisation of…
Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is…
In the field of modeling the dynamics of oncolytic viruses, researchers often face the challenge of using specialized mathematical terms to explain uncertain biological phenomena. This paper introduces a basic framework for an oncolytic…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
It is a well-established fact that tumors up-regulate glucose consumption to meet increasing demands for rapidly available energy by switching to purely glycolytic mode of glucose metabolism. What is often neglected is that cytotoxic cells…
This paper presents a mathematical model for tumour-immune response interactions in the perspective of immunotherapy by immune checkpoint inhibitors ICIs. The model is of the nonlocal integro-differential Lotka-Volterra type, in which…
Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
Tumor-immune interactions are shaped by both antigenic heterogeneity and stochastic perturbations in the tumor microenvironment, yet the mathematical mechanisms underlying immune phase transitions remain poorly understood. We propose a…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
At present it is still quite difficult to match the vast knowledge on the behavior of individual tumor cells with macroscopic measurements on clinical tumors. On the modeling side, we already know how to deal with many molecular pathways…
We analyse the Hamiltonian structure of a system of first-order ordinary differential equations used for modeling the interaction of an oncolytic virus with a tumour cell population. The analysis is based on the existence of a Jacobi Last…
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context…
We consider a model of a population of fixed size N in which each individual gets replaced at rate one and each individual experiences a mutation at rate \mu. We calculate the asymptotic distribution of the time that it takes before there…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the…