On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China by Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger

“…In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. …”
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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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Mathematical modeling predicts that endemics by generalist insects are eradicated if nearly all plants produce constitutive defense by Suman Chakraborty, Shalu Dwivedi, Stefan Schuster

“…The objective is addressed by developing deterministic ordinary differential equations under the following conditions: Plants without constitutive defenses are susceptible to oviposition by generalist insects, while they become defended against generalists by storing chemical defenses. …”
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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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Resolvent Positive Operators and Positive Fractional Resolvent Families by Nan-Ding Li, Ru Liu, Miao Li

“…Some examples of positive solutions to fractional differential equations are presented to illustrate our results.…”
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Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme by Afrah M. Almalki, A.A. AlQarni, H.O. Bakodah, A.A. Alshaery, Ahmed H. Arnous, Anjan Biswas

“…This method decomposes both linear and nonlinear differential equations into simpler sub-problems, enabling the extraction of approximate analytical solutions without the need for linearization or perturbation techniques. …”
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Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission by Curtis L. Wesley, Linda J. S. Allen, Michel Langlais

“…Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients and an autonomous system, where the coefficients are taken to be the time-average. …”
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Parallel Simulation of HGMS of Weakly Magnetic Nanoparticles in Irrotational Flow of Inviscid Fluid by Kanok Hournkumnuard, Banpot Dolwithayakul, Chantana Chantrapornchai

“…The two-dimensional problem of particle transport under the influences of magnetic force and fluid flow is considered in an annular domain surrounding the wire with inner radius equal to that of the wire and outer radius equal to various multiples of wire radius. The differential equations governing particle transport are solved numerically as an initial and boundary values problem by using the finite-difference method. …”
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Unstructured Grids and the Multigroup Neutron Diffusion Equation by German Theler

“…It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. …”
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Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations by Meilan Qiu, Liquan Mei, Dewang Li

“…The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations.…”
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Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…Physically existent things utilize partial differential equations as a method of derivation. By using dimensionless variables, the underlying PDEs are dimensionless. …”
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"MoSpec": A customized and integrated system for model development, verification and validation. by Marcello Pompa, Simona Panunzi, Alessandro Borri, Laura D'Orsi, Andrea De Gaetano

“…To facilitate the creation and sharing of such models, the CNR-IASI BioMatLab group developed the "Gemini" (MoSpec/Autocoder) system, a framework allowing researchers with basic mathematical knowledge to quickly and correctly translate biological problems into Ordinary Differential Equations models. The system facilitates the development and computation of mathematical models for the interpretation of medical and biological phenomena, also using data from the clinical setting or laboratory experiments for parameter estimation.…”
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MAC Layer Energy Consumption and Routing Protocol Optimization Algorithm for Mobile Ad Hoc Networks by Yaohua Chen, Waixi Liu

“…In order to solve the problem that the analytic solution of differential equations cannot be obtained in the model, a numerical solution of the optimization algorithm is proposed based on the implicit Runge–Kutta method. …”
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Numerical analysis of ice accretion on an airfoil: A case study by Lucas Farabello, Ana Scarabino, Federico Bacchi

“…The numerical analysis of ice accretion involves differential equations for the resolution of the air velocity field, the transport of droplets, and their icing and melting. …”
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Implementing the Galerkin Method Associated with the Shifted Vieta-Lucas Polynomials for Studying Numerically the Bionanofluid Flow Which Is Saturated by Gyrotactic Microorganisms... by M. M. Khader, M. M. Babatin, Ahmed M. Megahed, A. Eid

“…The shifted Vieta-Lucas polynomials are then used as basis functions on the provided domain to solve the nonlinear system of ordinary differential equations that has been constructed (ODEs). The results are presented in the form of graphs and tables to assess the impact of the problem’s governing parameters. …”
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A Theoretical Model of Listeriosis Driven by Cross Contamination of Ready-to-Eat Food Products by C. W. Chukwu, F. Nyabadza

“…In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. …”
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Mixed Convection in a Double Lid-Driven Wavy Shaped Cavity Filled with Nanofluid Subject to Magnetic Field and Internal Heat Source by Kakali Chowdhury, Md. Abdul Alim

“…The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. …”
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Application of BSDE in Standard Inventory Financing Loan by Hui Zhang, Wenyu Meng, Xiaojie Wang, Jianwei Zhang

“…Applying backward stochastic differential equations (BSDEs), we get the explicit solutions of the models. …”
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Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach by M. B. Almatrafi

“…The outcomes highlight the effectiveness and adaptability of the proposed strategy in resolving fractional nonlinear differential equations and expand our knowledge of fractional-order systems.…”
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Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping by A.M. Yu, Y. Hao

“…Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. …”
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