Related papers: An immune system-tumour interactions model with di…
We model the interaction between the immune system and tumor cells including a time delay to simulate the time needed by the latter to develop a chemical and cell mediated response to the presence of the tumor. The results are compared with…
We consider the model of interaction between the immune system and tumor cells including a memory function that reflect the influence of the past states, to simulate the time needed by the latter to develop a chemical and cell mediated…
Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors,…
In this paper we consider a free boundary tumor growth model with a time delay in cell proliferation and study how time delay affects the stability and the size of the tumor. The model is a coupled system of an elliptic equation, a…
Understanding cancer cell differentiation is essential for advancing its detection, diagnosis, and treatment. Mathematical models significantly contribute to this by providing a theoretical framework to understand the complex interactions…
Mathematical oncology is a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. Tumor-immune interactions play a…
We introduce a set of ordinary differential equations (ODE) that qualitatively reproduces delayed responses observed in immune checkpoint blockade therapy (e.g. anti-CTLA-4 Ipilimumab). This type of immunotherapy has been at the forefront…
In this paper we consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains wild-type virus and one mutant. A finite response time of the immune system was considered in order which leads…
The main purpose of this paper is to analyze the dynamics of the system of time-delay differential equations (DDEs) \begin{equation*} \begin{split} \dot{T}(t)&=T(t) f(t,T(t))-\gamma E(t)T(t),\\ \dot{E}(t)&=\sigma+…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…
In the tumour microenvironment, cancer cells directly interact with both the immune system and the stroma. It is firmly established that the immune system, historically believed to be a major part of the body's defence against tumour…
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may…
A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune…
We present a spatial hybrid discrete-continuum modelling framework for the interaction dynamics between tumour cells and cytotoxic T cells, which play a pivotal role in the immune response against tumours. In this framework, tumour cells…
Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor…
The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of many kinds of infectious diseases. In the study of mathematical models of infectious diseases it is…
Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally…
This paper investigates dynamic behaviors of the tumor-immune system perturbed by environmental noise. The model describes the response of the cytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The main methods are…
The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T…