Related papers: Towards a Field Theoretical Stochastic Model for D…
Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m.…
Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are…
The topology of gene expression space for a set of 12 cancer types is studied by means of an entropy-like magnitude, which allows the characterization of the regions occupied by tumor and normal samples. The comparison indicates that the…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…
We are interested in describing the infected size of the SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size $M$; the size is kept constant by…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…
A mathematical analysis of local and nonlocal phase-field models of tumor growth is presented that includes time-dependent Darcy-Forchheimer-Brinkman models of convective velocity fields and models of long-range cell interactions. A…
In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply, and chemotherapy. The subdiffusion of the system…
In this study, we provide a dynamical systems perspective to the modelling of pathological states induced by tumors or infection. A unified disease model is established using the innate immune system as the reference point. We propose a…
Understanding the untreated tumor growth kinetics and its intrinsic findings is interesting and intriguing. The aim of this study is to propose an approximate analytical expression that allows to simulate changes in surface charge density…
Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells…
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…
We propose a method to accurately obtain the ratio of tumor cells over an entire histological slide. We use deep fully convolutional neural network models trained to detect and classify cells on images of H&E-stained tissue sections.…
In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…
Mathematical models (MMs) are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use 5 MMs with an increasing number of parameters to explore how certain (often…
Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…
A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing to extract a deterministic…
The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and…