Related papers: Levy model of cancer
Effects of non-Gaussian $\alpha-$stable L\'evy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density from inside a safe or benign domain. The mean exit…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
The analysis of glioblastoma (GB) cell locomotion and its modeling inspired by Levy random walks is presented herein. We study such walks occurring on a two-dimensional plane where the walk is similar to the motion of a bird flying with a…
An endogenous molecular-cellular network for both normal and abnormal functions is assumed to exist. This endogenous network forms a nonlinear stochastic dynamical system, with many stable attractors in its functional landscape. Normal or…
Tumor development is an evolutionary process in which a heterogeneous population of cells with differential growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to…
The meaning of public messages such as "One in x people gets cancer" or "One in y people gets cancer by age z" can be improved. One assumption commonly invoked is that there is no other cause of death, a confusing assumption. We develop a…
The dynamical evolution of a tumor growth model, under immune surveillance and subject to asymmetric non-Gaussian $\alpha$-stableL\'evy noise, is explored. The lifetime of a tumor staying in the range between the tumor-free state and the…
Development of resistance limits efficiency of present anticancer therapies and preventing it remains big challenge in cancer research. It is accepted, at intuitive level, that the resistance emerges as a consequence of cancer cells…
Angiogenesis is a key process in the tumoral growth which allows the cancerous tissue to impact on its vasculature in order to improve the nutrient's supply and the metastatic process. In this paper, we introduce a model for the density of…
The transformation of the regular vasculature in normal tissue into a highly inhomogeneous tumor specific capillary network is described by a theoretical model incorporating tumor growth, vessel cooption, neo-vascularization, vessel…
We introduce a superstatistical model for the progression statistics of malignant cancer cells. The metastatic cascade is modeled as a complex nonequilibrium system with several macroscopic pathways and inverse-chi-square distributed…
Survival of living tumor cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell…
This paper is devoted to exploring the effects of non-Gaussian fluctuations on dynamical evolution of a tumor growth model with immunization, subject to non-Gaussian {\alpha}-stable type L\'evy noise. The corresponding deterministic model…
Lung cancer is a leading cause of cancer-related deaths worldwide. The spread of the disease from its primary site to other parts of the lungs, known as metastasis, significantly impacts the course of treatment. Early identification of…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
We have analyzed gene expression data from 3 different kinds of samples: normal human tissues, human cancer cell lines and leukemic cells from lymphoid and myeloid leukemia pediatric patients. We have searched for genes that are over…
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…
Assuming that there is feedback between an expanding cancer system and its organ-typical microenvironment, we argue here that such local tumor growth is guided by co-existence rather than competition with the surrounding tissue. We then…
In this paper we propose an ecological resilience point of view on cancer. This view is based on the analysis of a simple ODE model for the interactions between cancer and normal cells. The model presents two regimes for tumor growth. In…
Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as…