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Parametric inference for mixed models defined by stochastic differential equations

Sophie Donnet, Adeline Samson (2008)

ESAIM: Probability and Statistics

Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...

Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement

Papáček, Štěpán, Lynnyk, Volodymyr, Rehák, Branislav (2021)

Programs and Algorithms of Numerical Mathematics

The common goal of systems pharmacology, i.e. systems biology applied to the field of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system...

Simulating Kinetic Processes in Time and Space on a Lattice

J. P. Gill, K. M. Shaw, B. L. Rountree, C. E. Kehl, H. J. Chiel (2011)

Mathematical Modelling of Natural Phenomena

We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...

Spatial Dynamics of Contact-Activated Fibrin Clot Formation in vitro and in silico in Haemophilia B: Effects of Severity and Ahemphil B Treatment

A. A. Tokarev, Yu. V. Krasotkina, M. V. Ovanesov, M. A. Panteleev, M. A. Azhigirova, V. A. Volpert, F. I. Ataullakhanov, A. A. Butilin (2010)

Mathematical Modelling of Natural Phenomena

Spatial dynamics of fibrin clot formation in non-stirred system activated by glass surface was studied as a function of FIX activity. Haemophilia B plasma was obtained from untreated patients with different levels of FIX deficiency and from severe haemophilia B patient treated with FIX concentrate (Ahemphil B) during its clearance with half-life t1/2=12 hours. As reported previously (Ataullakhanov et al. Biochim Biophys Acta 1998; 1425: 453-468), clot growth in space showed two distinct phases:...

Stationary solutions of aerotaxis equations

Piotr Knosalla, Tadeusz Nadzieja (2015)

Applicationes Mathematicae

We study the existence and uniqueness of the steady state in a model describing the evolution of density of bacteria and oxygen dissolved in water filling a capillary. The steady state is a stationary solution of a nonlinear and nonlocal problem which depends on the energy function and contains two parameters: the total mass of the colony of bacteria and the concentration (or flux) of oxygen at the end of the capillary. The existence and uniqueness of solutions depend on relations between these...

Testing the method of multiple scales and the averaging principle for model parameter estimation of quasiperiodic two time-scale models

Papáček, Štěpán, Matonoha, Ctirad (2023)

Programs and Algorithms of Numerical Mathematics

Some dynamical systems are characterized by more than one time-scale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of...

Transport in a molecular motor system

Michel Chipot, Stuart Hastings, David Kinderlehrer (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.

Transport in a molecular motor system

Michel Chipot, Stuart Hastings, David Kinderlehrer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.

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