A minimal mathematical model for the initial molecular interactions of death receptor signalling by Christian Winkel, Simon Neumann, Christina Surulescu, Peter Scheurich

“…We use here a mass action kinetics approach to establish an ordinary differential equations model describing the dynamics of primary ligand/receptor complex formation as a basis for further clustering on the cell membrane. …”
Get full text

The Effect of Delay Techniques on a Lassa Fever Epidemic Model by Ali Raza, Eugenio Rocha, Emad Fadhal, Rashid I. H. Ibrahim, Eman Afkar, Muhammad Bilal

“…By introducing a delay parameter and decay exponential term into the existing model in the literature, we got the system of highly nonlinear delay differential equations (DDEs). The fundamental properties such as positivity, boundedness, existence, and uniqueness are verified for the said model. …”
Get full text

BERT-Residual Quantum Language Model Inspired by ODE Multi-Step Method by Shaohui Liang, Yingkui Wang, Shuxin Chen

“…Therefore, in this paper, we propose the BERT-Residual quantum language model inspired by the multi-step method of ordinary differential equations (ODE), using the density matrix to capture the semantic high-order interaction features missing in the BERT modeling process, and obtain the sentence representation, and perform the first step Residuals. …”
Get full text

Model analysis for an HIV infectious disease using elasticity and sensitivity techniques by Honar J. Hamad, Sarbaz H. A. Khoshnaw, Muhammad Shahzad

“…The model includes a class of nonlinear ordinary differential equations, and has both infection-free and endemic infection equilibrium points. …”
Get full text

SOLUTION OF THE PROBLEM OF OIL-POOL IN-SITU COMBUSTION FRONT PROPAGATION ON THE BASIS OF HEURISTIC HYPOTHESIS REGARDING TEMPERATURE AND CONCENTRATION PROFILES by K. V. Dobrego

“…Simple algebraic and differential equations fordetermination of the temperature and concentration profiles as well as for the front propagation velocity are derived for two cases i.e. the lack of oxidizer and the fuel component fault. …”
Get full text

A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets by Amr Ismail, Mostafa Herajy, Elsayed Atlam, Monika Heiner

“…The traditional approach to construct and simulate 3D models is to build a system of partial differential equations (PDEs). Although this approach may be computationally efficient and has been employed by many researchers over the years, it is not always intuitive since it does not provide a visual depiction of the modelled systems. …”
Get full text

MODELING OF BUSINESS PROCESSES FOR MANAGING INTEGRATIVE DIGITAL DEVELOPMENT OF ENTERPRISES by Оlena V. Vynogradova, Svitlana V. Lehominova, Aliona Yu. Goloborodko, Tetiana I. Nosova

“…The fundamental methods for modeling business process flows using mathematical and analytical tools, specifically a system of differential equations with defined initial conditions, have been substantiated, enabling the integral assessment of enterprise business process modeling. …”
Get full text

A numerical framework for computing steady states of structured population models and their stability by Inom Mirzaev, David M. Bortz

“…In particular, we use the Trotter-Kato Theorem to approximate the infinitesimal generator of an evolution equation on a finite dimensional space, which in turn reduces the evolution equation into a system of ordinary differential equations. Consequently, we approximate and study the asymptotic behavior of stationary solutions. …”
Get full text

Mathematical Modeling of Wax Deposition in Field-Scale Crude Oil Pipeline Systems by Francis Oketch Ochieng, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Phineas Roy Kiogora

“…The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. …”
Get full text

Asymptotic analysis of mathematical model describing a new treatment of breast cancer using AZD9496 and palbociclib by Ophir Nave, Ophir Nave

“…The mathematical model that described the interaction between the cancer cells, the treatment, and the immune system cells includes a system of nonlinear ordinary differential equations of the firs order. In general, dynamic variables of a given system change each at a different rate. …”
Get full text

Physics-Informed Neural Network for modeling and predicting temperature fluctuations in proton exchange membrane electrolysis by Islam Zerrougui, Zhongliang Li, Daniel Hissel

“…This method solves differential equations and estimates the unknown parameters governing the temperature dynamics within the PEM electrolysis system. …”
Get full text

Mathematical Modelling of Cholera Transmission incorporating Media Coverage. by Muhereza, Obed

“…The model was thereafter analyzed using the stability theory of differential equations. The basic reproduction number Ra, was derived using the next generation matrix approach. …”
Get full text

Modeling Highly Buoyant Flows in the Castel Giorgio: Torre Alfina Deep Geothermal Reservoir by Giorgio Volpi, Fabien Magri, Francesca Colucci, Thomas Fisher, Mattia De Caro, Giovanni B. Crosta

“…The open source finite-element code OpenGeoSys is applied to solve the coupled systems of partial differential equations. The commercial software FEFLOW® is also used as additional numerical constraint. …”
Get full text

Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis : Analysis of a spatially nonlocal model by Stephen A. Gourley, Xiulan Lai, Junping Shi, Wendi Wang, Yanyu Xiao, Xingfu Zou

“…The model turns out to be a system of differential equations with a spatially non-local term accounting for the phenomenon that a questing female adult tick that attaches to a deer at one location may later drop to the ground, fully fed, at another location having been transported by the deer. …”
Get full text

An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System by R. Belotti, R. Caracciolo, I. Palomba, D. Richiedei, A. Trevisani

“…This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. …”
Get full text

Computational analysis for efficient thermal transportation of ternary hybrid nanofluid flow across a stretching sheet with Cattaneo-Christov heat flux model by Wei Li, Shan Ali Khan, Muhammad Shafqat, Qamar Abbas, Taseer Muhammad, Muhammad Imran

“…The phenomenon were designed as partial differential equations. These are condensed to system of ODEs via similarity transformations. …”
Get full text

Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate by Usman Khan, Farhad Ali, Ohud A. Alqasem, Maysaa E. A. Elwahab, Ilyas Khan, Ariana Abdul Rahimzai

“…The disease dynamics are first schematically illustrated, and then the law of mass action is applied to obtain nonlinear ordinary differential equations (ODEs). Analysis of the boundedness, positivity, and equilibrium points of the system has been analyzed. …”
Get full text

DyCeModel: a tool for 1D simulation for distribution of plant hormones controlling tissue patterning by D. S. Azarova, N. A. Omelyanchuk, V. V. Mironova, E. V. Zemlyanskaya, V. V. Lavrekha

“…Here, we present DyCeModel, a software tool implemented in MATLAB for one-dimensional simulation of tissue with a dynamic cellular ensemble, where changes in hormone (or other active substance) concentration in the cells are described by ordinary differential equations (ODEs). We applied DyCeModel to simulate cell dynamics in plant meristems with different cellular structures and demonstrated that DyCeModel helps to identify the relationships between hormone concentration and cellular behaviors. …”
Get full text

Novel numerical and artificial neural computing with experimental validation towards unsteady micropolar nanofluid flow across a Riga plate by Muhammad Bilal, F. Maiz, Muhammad Farooq, Hijaz Ahmad, Mohammad Khalid Nasrat, Hassan Ali Ghazwani

“…The fluid flow has been expressed in the form of a nonlinear system of PDEs (partial differential equations), which are reduced into the non-dimensional form of ordinary differential (ODEs) by employing the similarity transformation approach. …”
Get full text

A computational role of blood nanofluid induced by a stenosed artery with porous medium and thermophoretic particle deposition effects by Shivalila Hangaragi, N. Neelima, N. Beemkumar, Ankur Kulshreshta, Umair Khan, Noreen Sher Akbar, Mohammad Kanan, Mona Mahmoud

“…Based on these assumptions, the governing equations are formulated and transformed into a system of ordinary differential equations using appropriate similarity transformations. …”
Get full text