相关论文: Spatiotemporal Noise Triggering Infiltrative Tumor…

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…

We investigate noise-induced pattern formation in a model of cancer growth based on Michaelis-Menten kinetics, subject to additive and multiplicative noises. We analyse stability properties of the system and discuss the role of diffusion…

We studied the effect of additive and multiplicative noises on the growth of a tumor based on a logistic growth model. The steady-state probability distribution and the average population of the tumor cells were given to explain the…

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…

Stochastic resonance induced by external factor is considering to investigate the complex dynamics of tumor. The surrounding environment and the treatment effects on the tumor growth are considered as additive and multiplicative noises in…

We studied the single-variable dynamics model of the tumor growth. A first-order phase transition induced by an additive noise is shown to reproduce the main features of tumor growth under immune surveillance. The critical average cells…

In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting…

We study a spatially inhomogeneous model of cancer growth based on Michaelis--Menten kinetics, subjected to additive Gaussian noise and multiplicative dichotomous noise. In presence of the latter, we can observe a transition between two…

Multiplicative noise is found to divide the growth law of tumors into two parts in a logistic model, which is driven by additive and multiplicative noises simultaneously. The Fokker-Planck equation was also derived to explain the fact that…

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…

This paper explores fluctuations and noise in various facets of cancer development. The three areas of particular focus are the stochastic progression of cells to cancer, fluctuations of the tumor size during treatment, and noise in cancer…

Cancer results from a sequence of genetic and epigenetic changes which lead to a variety of abnormal phenotypes including increased proliferation and survival of somatic cells, and thus, to a selective advantage of pre-cancerous cells. The…

The influence of random fluctuations on the recruitment of effector cells towards a tumor is studied by means of a stochastic mathematical model. Aggressively growing tumors are confronted against varying intensities of the cell-mediated…

Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division.…

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…

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…

We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term…

Analysis of invasion front has been widely used to decipher biological properties, as well as the growth dynamics of the corresponding populations. Likewise, the invasion front of tumors has been investigated, from which insights into the…

In this work we explore the temporal dynamics of spatial heterogeneity during the process of tumorigenesis from healthy tissue. We utilize a spatial stochastic process model of mutation accumulation and clonal expansion in a structured…

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,…