Modelling tumor progression, heterogeneity, and immune competition.
Modelling tumour-immunity interactions with different stimulation functions
Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different...
Modelling within host parasite dynamics of schistosomiasis.
Model-matching-based control of the Beverton-Holt equation in ecology.
Models of interactions between heterotrophic and autotrophic organisms
We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.
Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations
Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare...
Modified step variational iteration method for solving fractional biochemical reaction model.
Modulation of nonlinear waves in a fluid-filled elastic tube with stenosis.
Molecular motors and stochastic networks
Molecular motors are nano- or colloidal machines that keep the living cell in a highly ordered, stationary state far from equilibrium. This self-organized order is sustained by the energy transduction of the motors, which couple exergonic or 'downhill' processes to endergonic or 'uphill' processes. A particularly interesting case is provided by the chemomechanical coupling of cytoskeletal motors which use the chemical energy released during ATP hydrolysis in order to generate mechanical forces and...
Monoids and decay.
Monotone Iterative Methods for Finite Difference System of Reaction-Diffusion Equations.
Monotone scheme for finite difference equations concerning steady-state competing-species interactions
Monotone semiflows generated by neutral equations with different delays in neutral and retarded parts.
Monotonicity of the number of passages in linear chains and of the basis reproduction number in epidemic models.
Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...
Monte Carlo simulation and analytic approximation of epidemic processes on large networks
Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic...
Morphospace: Measurement, Modeling, Mathematics, and Meaning
Artists have long recognized that trees are self-similar across enormous differences in magnitudes; i.e., they share a common fractal structure - a trunk subdivides into branches which subdivide into more branches which eventually terminate in leaves, flowers, fruits, etc. Artistid Lindenmayer (1971, 1975, 1989, 1990) invented a mathematics based on graph grammar rewriting systems to describe such iteratively branching structures; these were named in honor of him and are referred to as L-systems....
Motor control neural models and systems theory
In this paper, we introduce several system theoretic problems brought forward by recent studies on neural models of motor control. We focus our attention on three topics: (i) the cerebellum and adaptive control, (ii) reinforcement learning and the basal ganglia, and (iii) modular control with multiple models. We discuss these subjects from both neuroscience and systems theory viewpoints with the aim of promoting interplay between the two research communities.
Mucus dynamics subject to air and wall motion*
This study presents a numerical investigation of basic interactions between respiratory mucus motion, air circulation and epithelium ciliated cells vibration. One focuses on identification of meaningful rheological parameters, physiological and numerical simulation dimensioning. These preliminary results are crucial before the study of more general configurations of respiratory mucus motion. The numerical study presented in this work aims at providing...
Multi-bump ground states of the Gierer–Meinhardt system in R2