Artificial neural networks for stability analysis and simulation of delayed rabies spread models by Ramsha Shafqat, Ateq Alsaadi

“…This study addressed the complexity of rabies spread by integrating two critical delay effects—vaccination efficacy and incubation duration—into a delay differential equations model, capturing more realistic infection patterns between dogs and humans. …”
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Characterization of the dynamic behavior of nonlinear biosystems in the presence of model uncertainty using singular invariance PDEs: Application to immobilized enzyme and... by Nikolaos Kazantzis, Vasiliki Kazantzi

“…The problem of interest is addressed within the context of singular partial differential equations (PDE) theory, and in particular, through a system of singular quasi-linear invariance PDEs for which a general set of conditions for solvability is provided. …”
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Study of COVID-19 cases with real data analysis by Wedad Albalawi, Kottakkaran Sooppy Nisar, Nadir Omer, Adnan Aslam, Takasar Hussain, Muhammad Ozair, Shahid Hussain, Nida Hameed

“…In this work, patients of corona virus disease 2019, known as COVID-19, have been studied in Pakistan and its neighboring countries Iran, India and Afghanistan through the mathematical model in the form of coupled system of five ordinary differential equations. Two types of equilibria, infection free and endemic, are obtained. …”
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Global stability for a mosquito-borne disease model with continuous-time age structure in the susceptible and relapsed host classes by Maria Guadalupe Vazquez-Peña, Cruz Vargas-De-León, Jorge Velázquez-Castro

“…The system of integro-differential equations uses flexible, unspecified functions to represent these dependencies, assuming they are integrable. …”
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Analytical Solutions of Fractional Walter’s B Fluid with Applications by Qasem Al-Mdallal, Kashif Ali Abro, Ilyas Khan

“…By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. …”
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Bat population dynamics: multilevel model based on individuals' energetics by Paula Federico, Dobromir T. Dimitrov, Gary F. McCracken

“…A structured population model based on extended McKendrick-von Foerster partial differential equations integrates those individual dynamics and provides insight into possible regulatory mechanisms of population size as well as conditions of population survival and extinction. …”
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ON THE TECHNIQUE OF MODELING ONTOGENETIC CHANGES IN FISH AND INSECTS LIFECYCLE by A. Yu. Perevaryukha

“…The method has been for submission to decline of generations on the basis of dynamic overriding differential equations with discrete-continuous structure of time. …”
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A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations by Philku Lee, George V. Popescu, Seongjai Kim

“…After a theory of morphogenesis in chemical cells was introduced in the 1950s, much attention had been devoted to the numerical solution of reaction-diffusion (RD) partial differential equations (PDEs). The Crank–Nicolson (CN) method has been a common second-order time-stepping procedure. …”
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EVOLUTION OF THE ROTATIONAL MOTION OF A SATELLITE WITH FLEXIBLE VISCOELASTIC RODS ON THE ELLIPTIC ORBIT by E. V. Sadovnikova, A. V. Shatina

“…We obtain an averaged system of differential equations in the Andoyer variables, which describes the evolution of the satellite's rotational motion. …”
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Analysis of Model Parameters for a Polymer Filtration Simulator by N. Brackett-Rozinsky, S. Mondal, K. R. Fowler, E. W. Jenkins

“…The simulator is a three-dimensional, time-dependent discretization of a coupled system of nonlinear partial differential equations used to model fluid flow and debris transport, along with statistical relationships that define debris distributions and retention probabilities. …”
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Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame by Chunyu Zhao, Qinghua Zhao, Zhaomin Gong, Bangchun Wen

“…Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the disturbance parameters for the angular velocities of the four unbalanced rotors. …”
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Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM by Jifa Jiang, Qiang Liu, Lei Niu

“…By imposing assumptions that the dimerization reactions were fast and dimeric proteins were in rapid equilibrium, they reduced the model to a pair of nonlinear ordinary differential equations of mRNA and total protein concentrations. …”
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A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces by Suguru Arimoto, Morio Yoshida

“…A set of 1st-order differential equations governing rotational motions of each fingertip and the object and updating arc-length parameters should be accompanied with the Euler-Lagrange equations. …”
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Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies by Yustina A. Liana, Mary C. Swai

“…Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. …”
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A Reduced Order Model Based on ANN-POD Algorithm for Steady-State Neutronics and Thermal-Hydraulics Coupling Problem by Hanxing Liu, Han Zhang

“…Due to the high-dimensional partial differential equations (PDEs) derived from the N/TH system, it is usually time consuming to solve such a large-scale nonlinear equation by the traditional numerical solution method of PDEs. …”
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Effects of Thermodiffusion and Chemical Reaction on Magnetohydrodynamic-Radiated Unsteady Flow Past an Exponentially Accelerated Inclined Permeable Plate Embedded in a Porous Mediu... by B. Prabhakar Reddy, M. H. Simba, Alfred Hugo

“…The governing nondimensional set of coupled nonlinear partial differential equations with related initial and boundary conditions are solved numerically by using the accurate and efficient DuFort–Frankel’s explicit finite difference method. …”
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Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform by Nehad Ali Shah, Essam R. El-Zahar, Ali Akgül, Adnan Khan, Jeevan Kafle

“…In fact, when compared to other analytical techniques for solving nonlinear fractional partial differential equations, the present method might be considered one of the finest.…”
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The Feyn-structure of Yangian symmetry by Florian Loebbert, Harshad Mathur

“…Previous applications of the Yangian suggest to employ the resulting differential equations for bootstrapping multi-loop integrals beyond the dual conformal case. …”
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On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations by Peter I. Kogut, Olha P. Kupenko, Rosanna Manzo

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Qualitative Properties of the Solution of a Conjugate Problem of Thermal Convection by A. A. Azanov, E. N. Lemeshkova

“…Thus, the problem was reduced to a system of 10 nonlinear integro-differential equations. Its conjugate and inverse nature is determined by the four functions of time. …”
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