Related papers: An immune system-tumour interactions model with di…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
Advances in healthcare and in the quality of life significantly increase human life expectancy. With the ageing of populations, new un-faced challenges are brought to science. The human body is naturally selected to be well-functioning…
Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the…
Real-world processes often exhibit temporal separation between actions and reactions - a characteristic frequently ignored in many modelling frameworks. Adding temporal aspects, like time delays, introduces a higher complexity of problems…
The tumour microenvironment plays a fundamental role in understanding the development and progression of cancer. This paper proposes a novel spatial point process model that accounts for inhomogeneity and interaction to flexibly model a…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
Immunotherapy constitutes a paradigm shift in cancer treatment. Its FDA approval for several indications has yielded improved prognosis for cases where traditional therapy has shown limited efficiencey. However, many patients still fail to…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of…
A virus dynamics model with intracellular state-dependent delay and nonlinear infection rate of Beddington-DeAngelis functional response is studied. The technique of Lyapunov functionals is used to analyze stability of an interior infection…
Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the…
In this paper, a reaction-diffusion system modeling injection of a chemotherapeutic drug on the surface of a living tissue during a treatment for cancer patients is studied. The system describes the interaction of the chemotherapeutic drug…
In oncology, phase II or multiple expansion cohort trials are crucial for clinical development plans. This is because they aid in identifying potent agents with sufficient activity to continue development and confirm the proof of concept.…
In this paper, we adapt a two-species agent-based cancer model that describes the interaction between cancer cells and healthy cells on a uniform grid to include the interaction with a third species -- namely immune cells. We run six…
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires…
The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…
Previously we showed how delay communication between globally coupled self-propelled agents causes new spatio-temporal patterns to arise when the delay coupling is fixed among all agents \cite{Forgoston08}. In this paper, we show how…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
We report on a simple model of spatial extend anti-tumor system with a fluctuation in growth rate, which can undergo a nonequilibrium phase transition. Three states as excited, sub-excited and non-excited states of a tumor are defined to…