Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells by Amit Kumar Roy, Priti Kumar Roy, Ellina Grigorieva

“…In this article, we have constructed a set of nonlinear differential equations involving the above cell population for better understanding the impact of cytokines on Psoriasis. …”
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Differential game theory application in models of trade relations of Great Britain with Portugal and Russia with Belarus by I. V. Korolyov

“…The author composes and analyzes a system of four nonlinear ordinary differential equations with parameters, and their (dynamic) variation leads to the improvement of successive approximations of the exact solution, the finding of which is very problematic. …”
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Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System by Z.H. Wang, M. L. Du

“…The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. …”
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What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics? by Aditya S. Khanna, Dobromir T. Dimitrov, Steven M. Goodreau

“…We construct models from each class, usingordinary differential equations and exponential random graph models,respectively. …”
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Radionuclide Transport in Fractured Rock: Numerical Assessment for High Level Waste Repository by Claudia Siqueira da Silveira, Antonio Carlos Marques Alvim, Jose de Jesus Rivero Oliva

“…Transport in the fracture is assumed to obey an advection-diffusion equation, while molecular diffusion is considered the dominant mechanism of transport in porous matrix. The partial differential equations describing the movement of radionuclides were discretized by finite difference methods, namely, fully explicit, fully implicit, and Crank-Nicolson schemes. …”
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Modeling and 1 : 1 Internal Resonance Analysis of Cable-Stayed Shallow Arches by Jiangen Lv, Zhicheng Yang, Xuebin Chen, Quanke Wu, Xiaoxia Zeng

“…Firstly, the Galerkin method is used to discretize the governing nonlinear integral-partial-differential equations. Secondly, the multiple scales method (MSM) is used to derive the modulation equations of the system under external excitation of the shallow arch. …”
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Understanding biofilm--phage interactions in cystic fibrosis patients using mathematical frameworks by Emerenini Blessing O., Hartung Doris, Reyes Grimaldo Ricardo N. G., Canner Claire, Williams Maya, Agyingi Ephraim, Osgood Robert

“…To evaluate the effectiveness of phage therapy against biofilm bacteria, we create a phage-biofilm model with ordinary differential equations and a stochastic model. We considered three possible cases for the stability of disease-free equilibrium; by model simulations and parameter alterations in both models, we investigated the effect of bacteria–phage interactions alongside biofilm bacteria cell detachment from the biofilm phase to the planktonic phase, and how these will affect the efficiency of phage therapy against bacteria. …”
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Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering by Gerasimos G. Rigatos, Efthymia G. Rigatou, Jean Daniel Djida

“…The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. …”
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Water level monitoring by using magnetic optical sensor by Jonatan Daniel Morales Arrieta, Jesus Vargas Ortiz, Jesús Patricio Ordaz Oliver, Juan Carlos González Islas, Omar Samperio Vázquez

“…Firstly, mathematical modeling of the water level measurement in a tank using differential equations is described. This system comprises a printed circuit board (PCB), a novel float mechanism, an optical sensor, a microcontroller, and a visualization stage. …”
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Non-local piezoelasticity to incorporate the influence of small-scale factors on the resonance behavior of the Mindlin piezoelectric polymeric nanoplates by Narinderjit Singh Sawaran Singh, Waqed H. Hassan, Zainab Mоhammed Ameen Ahmed, Younis Mohamed Atiah Al-zahy, Soheil Salahshour, Mostafa Pirmoradian

“…The Galerkin method is utilized to solve the partial differential equations governing the dynamics of the piezoelectric polymeric nanoplate, marking a significant methodological contribution to the field. …”
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The levelized cost of energy in the presence of uncertainty on the offshore wind speed by J. Pablo Arenas-López, Mohamed Badaoui

“…To carry out this task, we employ two techniques based on stochastic differential equations to generate wind power scenarios. Utilizing 40 years of recorded wind speed data sourced from the MERRA-2 reanalysis, we derive the input parameters of the models from fitting to 4-parameter Dagum and Johnson SB probability distributions, which shows that accurate modeling of offshore wind speeds requires dealing with complex mathematical functions that need numerical computation. …”
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On the possibility of controlling the temperature of gases and liquids in a transportation system by local cooling or heating with account salt deposition by Evgeny L. Pankratov

“…The model is based on an analytical solution of partial differential equations with nonlinearity and variation of their coefficients in space and time. …”
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Artificial neural network analysis of Jeffrey hybrid nanofluid with gyrotactic microorganisms for optimizing solar thermal collector efficiency by Anup Kumar, Bhupendra K. Sharma, Bandar Almohsen, Laura M. Pérez, Kamil Urbanowicz

“…The non-similar variables are introduced to the dimensional governing equations to get the non-dimensional ordinary differential equations. The Cash and Carp method is implemented to solve the non-dimensional equations. …”
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Hydromagnetic Flow of Two Immiscible Couple Stress Fluids through Porous Medium in a Cylindrical Pipe with Slip Effect by Punnamchandar Bitla, Yitagesu Daba Kore

“…The resulting differential equations governing the flow in the two regions are converted to nondimensional forms using appropriate dimensionless variables. …”
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Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 by S. V. Bolokhov, V. D. Ivashchuk

“…The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. …”
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Forecasting Crude Oil Consumption in China Using a Grey Prediction Model with an Optimal Fractional-Order Accumulating Operator by Huiming Duan, Guang Rong Lei, Kailiang Shao

“…In this paper, we study the grey-extended SIGM model, which is directly estimated with differential equations. This model has high simulation and prediction accuracies and is one of the important models in grey theory. …”
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Theoretical Analysis and Experimental Validation on Galloping of Iced Transmission Lines in a Moderating Airflow by Bing Huo, Xuliang Li, Fujiang Cui, Shuo Yang

“…Galloping of an iced transmission line subjected to a moderating airflow has been analysed in this study, and a new form of galloping is discovered both theoretically and experimentally. The partial differential equations of the iced transmission line are established based on the Hamilton theory. …”
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Reconstruction of self-oscillating systems with delay time modulation by Ponomarenko, Vladimir Ivanovich, Prokhorov, Mihail Dmitrievich

“…The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. …”
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Computational Role of Autocatalytic Chemical Reaction in the Dynamics of a Ternary Hybrid Nanofluid Past a Rotating Stretching Surface by Shreedevi Madiwal, N. B. Naduvinamani, J. K. Madhukesh, Umair Khan, Anuar Ishak, Raman Kumar, Md Irfanul Haque Siddiqui

“…The governing equations are transformed into the system of ordinary differential equations (ODEs) and numerically tackled with the help of the Runge–Kutta–Fehlberg 4th 5th (RKF45) order scheme. …”
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On optimization of substrate removal in a bioreactor with wall attached and suspended bacteria by Alma Mašić, Hermann J. Eberl

“…In the two-objective optimal control problem, the flow rate between the vessels is selected as the control variable.The treatment reactor is modelled by a system of three ordinary differential equations in which a two-point boundary value problem is embedded. …”
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