Related papers: A stochastic model for tumor growth with immunizat…
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…
In a previous work, we presented a model that integrates cancer cell differentiation and immunotherapy, analysing a particular therapy against cancer stem cells by cytotoxic cell vaccines. As every biological system is exposed to random…
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…
We consider a three-state model comprising tumor cells, effector cells and tumor detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress…
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…
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…
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…
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…
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…
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 deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into…
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 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…
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 this work, we present and analyze a system of PDEs, which models tumor growth by considering chemotaxis, active transport, and random effects. The stochasticity of the system is modelled by random initial data and Wiener noises that…
We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the…
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…
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…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…