An individual-level probabilistic model and solution for control of infectious diseases by Ye Xia

“…The model is related to the work of Fraser et al. on the same topic [1], which provides a population-level model using a combination of differential equations and probabilistic arguments. We show that our individual-level model has certain advantages. …”
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A Qualitative Approach to Universal Numerical Integrators (UNIs) with Computational Application by Paulo M. Tasinaffo, Luiz A. V. Dias, Adilson M. da Cunha

“…The UNIs are used to model non-linear dynamic systems governed by Ordinary Differential Equations (ODEs). Among the main types of UNIs existing in the literature, we can mention (i) The Euler-Type Universal Numerical Integrator (E-TUNI), (ii) The Runge-Kutta Neural Network (RKNN), and (iii) The Non-linear Auto Regressive Moving Average with Exogenous input or NARMAX model. …”
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INFLUENCE OF THE TIME OF DISINHIBITION TO TRANSIENTS AND WEAR OF THE FRICTION LININGS IN AN ASYNCHRONOUS MOTOR by V. V. Solencov, V. V. Brel

“…Calculation of the system of differential equations was fulfilled by the Runge – Kutta method. …”
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Combining robust state estimation with nonlinear model predictive control to regulate the acute inflammatory response to pathogen by Gregory Zitelli, Seddik M. Djouadi, Judy D. Day

“…The inflammatory responseaims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen.In cases of acute systemic inflammation, the possibility of collateral tissuedamage arises, which leads to a necessary down-regulation of the response.A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. …”
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In Silico Evolution of Gene Cooption in Pattern-Forming Gene Networks by Alexander V. Spirov, Marat A. Sabirov, David M. Holloway

“…Finally, we comment on how a differential equations (in contrast to Boolean) approach is necessary for addressing realistic continuous variation in biochemical parameters.…”
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Stability, Bifurcation, and a Pair of Conserved Quantities in a Simple Epidemic System with Reinfection for the Spread of Diseases Caused by Coronaviruses by Jorge Fernando Camacho, Cruz Vargas-De-León

“…In this paper, we study a modified SIRI model without vital dynamics, based on a system of nonlinear ordinary differential equations, for epidemics that exhibit partial immunity after infection, reinfection, and disease-induced death. …”
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A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton by R. Motta Jafelice, C. A. F. Silva, L. C. Barros, R. C. Bassanezi

“…The objective of this research is to study the evolution of CD4+ T lymphocytes infected with HIV in HIV-seropositive individuals under antiretroviral treatment utilizing a mathematical model consisting of a system of delay-differential equations. The infection rate of CD4+ T lymphocytes is a time-dependent parameter with delay. …”
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An in-depth examination of the fuzzy fractional cancer tumor model and its numerical solution by implicit finite difference method. by Hamzeh Zureigat, Saleh Alshammari, Mohammad Alshammari, Mohammed Al-Smadi, M Mossa Al-Sawallah

“…Researchers have employed fractional differential equations to describe these models. In the context of time fractional cancer tumor models, there's a need to introduce fuzzy quantities instead of crisp quantities to accommodate the inherent uncertainty and imprecision in this model, giving rise to a formulation known as fuzzy time fractional cancer tumor models. …”
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Mathematical analysis of a model for glucose regulation by Kimberly Fessel, Jeffrey B. Gaither, Julie K. Bower, Trudy Gaillard, Kwame Osei, Grzegorz A. Rempała

“…Developed by Bergman, Cobelli, and colleagues over three decades ago [7,8], this system of coupled ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test (IVGTT). …”
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Modeling and optimal regulation of erythropoiesis subject to benzene intoxication by H. T. Banks, Cammey E. Cole, Paul M. Schlosser, Hien T. Tran

“…An age-structured model was usedto examine the process of erythropoiesis, the development of red blood cells.This investigation proved the existence and uniqueness of the solution of thesystem of coupled partial and ordinary differential equations. In addition, weformulated an optimal control problem for the control of erythropoiesis andperformed numerical simulations to compare the performance of the optimalfeedback law and another feedback function based on the Hill function.…”
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Numerical and analytical investigation of Jeffrey nanofluid convective flow in magnetic field by FEM and AGM by Mohammad ِDehghan Afifi, Ali Jahangiri, Mohammad Ameri

“…Solving and developing non-linear differential equations is done using finite element method (FEM) and Akbari-Ganji method (AGM). …”
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Evolution-Operator-Based Single-Step Method for Image Processing by Yuhui Sun, Peiru Wu, G. W. Wei, Ge Wang

“…The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. …”
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NONLINEAR CHARACTERISTICS OF HERRINGBONE GEAR FOUR-BRANCHING TRANSMISSION CONSIDERING GEAR BACKLASH EFFECT by DONG Hao, FANG ZongDe, FANG Zhou, ZHAO XiaoLong

“…With herringbone gear loaded tooth contact method of simulation technology,put forward a method for accurate calculation of herringbone gear meshing stiffness excitation; By using the theory of the concentrated parameter,three-dimensional dynamic model of bending torsion coupling of the system is established;Based on the dynamic differential equations are solved with variable step four order Runge-Kutta method,obtained under the influence of backlash in the system without impact,dynamic load coefficient and amplitude of unilateral and bilateral shock state.The results show that Power four branch transmission system has a complex nonlinear characteristic,which is sensitive to the change of the tooth side gap,the influence of the backlash on the nonlinear characteristics is greater,and the system load changes from the side impact to the side impact of the system when the backlash is changed from 0 μm 150 μm; When the tooth gap is greater than a certain critical value,the dynamic characteristics of the system will not change with the increase of the gap of the tooth. …”
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Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators by Syed Tauseef Saeed, Ilyas Khan, Muhammad Bilal Riaz, Syed Muhammad Husnine

“…The mathematical analysis of fractional governing partial differential equations has been established using systematic and powerful techniques of Laplace transform with its numerical inversion algorithms. …”
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Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge by Nazir Umar, Khan Umair, Almujibah Hamad, Gündoğdu Hami

“…The derivation of nonlinear ordinary differential equations (ODEs) is used to characterize momentum, thermal behavior, and fluid motion under these circumstances. …”
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Comment on “Neutrino interaction with matter in a noninertial frame” by R. R. S. Oliveira

“…Next, we use the four-component Dirac spinor and obtain a set/system of four coupled first-order differential equations. From the first two equations with m → 0, we obtain a (compact) second-order differential equation for the last two spinor components. …”
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A novel computational analysis of boundary-driven two-dimensional heat flow with internal heat generation by Muhammad Abid, Madiha Bibi, Nasir Yasin, Muhammad Shahid

“…Accurate numerical solution of parabolic and elliptic partial differential equations governing two-dimensional heat transfer is critical for engineering simulations but computationally challenging.This work employs key numerical techniques finite differences, conjugate gradients, and Crank-Nicolson time stepping to solve the heat diffusion equation and analyze method performance.The Poisson equation is discretized using second-order central finite differences and solved with the conjugate gradient approach to determine the steady state solution. …”
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The Multi-Functional Modelling Shear Lag Method for Accurate Calculation of Static Response and Accordion Effect of Improved Composite Box Girders by Ya-Nan Gan, Zi-Chen Zhang, Gen-Hui Wang

“…Therefore, MFMSL is a method to calculate the static response and accordion effect of the CW-SBS composite box girders. Structural differential equations based on the energy-variation principle present that the MFMSL method effectively improves the calculating accuracy of the CW-SBS box girder static response, which can be verified by both experimental and simulative results. …”
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An Accurate Measurement Method for Tension Force of Short Cable by Additional Mass Block by Shuichang Li, Longlin Wang, Hua Wang, Peihua Shi, Riyan Lan, Changxia Wu, Xirui Wang

“…By attaching an additional mass block to the cable, new parameters are introduced to identify the tension force. Vibration differential equations are established for cable with and without addition mass block, taking new parameters into account, such as equivalent effective length and added mass. …”
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Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands by Yuan Feng, Jongwan Eun, Seunghee Kim, Yong-Rak Kim

“…Recently, physics-informed neural networks (PINNs), which incorporate partial differential equations (PDEs) to solve forward and inverse problems, have attracted increasing attention in machine learning research. …”
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