From the Guest Editors by Carlos Castillo-Chávez, Christopher Kribs Zaleta, Yang Kuang, Baojun Song

“…Those of us who met the field of mathematical biology as a well-developed,flourishing, and rewarding discipline owe much to those who made it so.This special issue of Mathematical Biosciences and Engineering isdedicated to two such pioneers: Fred Brauer and Karl Hadeler.Since retrospectives of both men have been published in other venues [1, 2], we will only summarize their contributions briefly here.Fred Brauer obtained his Ph.D. from MIT in 1956 under Norman Levinson,and during a long tenure at the University of Wisconsin he co-wrote severaltexts on ordinary differential equations that have become classics.His research entered mathematical biology first through early studies inpredator-prey systems and harvesting, both with and without delays.He then moved into mathematical epidemiology, and the text he co-authoredwith Carlos Castillo-Chavez in both these areas earlier this decade isalready in wide use.For more information please click the “Full Text” above.…”
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Circular thin plates buckling analysis with HRPIM method by Baid Sokayna, Hilali Youssef, Mesmoudi Saïd, Bourihane Oussama

“…The governing partial differential equations are discretized using the Galerkin method and solved by combining a Taylor series expansion with a continuation procedure. …”
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Global Dynamics of Secondary DENV Infection with Diffusion by A. M. Elaiw, A. S. Alofi

“…In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. …”
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Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem by Abdelkrim Salim, Sabri T.M. Thabet, Ava Sh. Rafeeq, Mohammad Esmael Samei, Imed Kedim, Miguel Vivas-Cortez

“…Our study leverages the properties of tempered (κ,ϖ)-Hilfer fractional operators to explore the mathematical underpinnings of the problem, which is characterized by implicit nonlinear fractional differential equations. To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. …”
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Nonlinear Dynamics Modeling and Subharmonic Resonances Analysis of a Laminated Composite Plate by Ting Ma, Xiao Juan Song, Shu Feng Lu

“…The two-degree-of-freedom ordinary differential equations that describe the vibration of the rectangular plate are obtained by the Galerkin method. …”
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AI-assisted discovery of quantitative and formal models in social science by Julia Balla, Sihao Huang, Owen Dugan, Rumen Dangovski, Marin Soljačić

“…By extending neuro-symbolic methods to find compact functions and differential equations in noisy and longitudinal data, we show that our system can be used to discover interpretable models from real-world data in economics and sociology. …”
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Fuzzy Networked Control Systems Design Considering Scheduling Restrictions by H. Benítez-Pérez, A. Benítez-Pérez, J. Ortega-Arjona, O. Esquivel-Flores

“…Therefore, it is necessary to study the behavior of the delays as well as the integration into differential equations of these bounded delays. The related time delays needs to be known a priory but from a dynamic real-time behavior. …”
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A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method by H. T. Cho, A. S. Cornell, Jason Doukas, T.-R. Huang, Wade Naylor

“…We discuss how to obtain black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second-order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. …”
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Elasticity Solutions for Sandwich Arches considering Permeation Effect of Adhesive by Ruili Huo, Yichen Liu, Peng Wu, Hai Fang, Weiqing Liu, Ding Zhou

“…The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. …”
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The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid by S. M. Khaled, Abdelhalim Ebaid, Fahd Al Mutairi

“…The mathematical model is governed by a system of linear and nonlinear partial differential equations with prescribed boundary conditions. …”
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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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Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique by Aliaa Burqan, Mona Khandaqji, Zeyad Al-Zhour, Ahmad El-Ajou, Tasneem Alrahamneh

“…The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. …”
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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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Differential Games of Rechargeable Wireless Sensor Networks against Malicious Programs Based on SILRD Propagation Model by Guiyun Liu, Baihao Peng, Xiaojing Zhong, Xuejing Lan

“…In this paper, nodes are divided into five states according to the residual energy and infection level, and the differential equations are constructed to describe the evolution of nodes. …”
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Qualitative Analysis of the Effect of Weeds Removal in Paddy Ecosystems in Fallow Season by Leru Zhou, Zhigang Liu, Tiejun Zhou

“…In the paper, we introduce a differential equations model of paddy ecosystems in the fallow season to study the effect of weeds removal from the paddy fields. …”
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Conciliating accuracy and efficiency to empower engineering based on performance: a short journey by Chinesta, Francisco, Cueto, Elias

“…The art of modeling for describing the behavior of complex systems from the solution of partial differential equations that are expected to govern their responses. …”
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Prediction of Shear Lag Effect in Thin-Walled Single-Box Multicell Box Girder Based on the Modified Warping Displacement Function by Xiayuan Li, Shui Wan, Kongjian Shen, Peng Zhou, Xiao Wang

“…Based on the principle of minimum potential energy, the governing differential equations are derived and solved with the associated boundary and load conditions. …”
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Dynamic Analysis of Flexible Shaft and Elastic Disk Rotor System Based on the Effect of Alford Force by Wenjun Yang, Huiqun Yuan, Li Hui, Kaifeng Zhang

“…Taken the flexible shaft and elastic disk rotor system as the research object, vibration differential equations are established by the modal synthesis method. …”
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Z2×Z3 Equivariant Bifurcation in Coupled Two Neural Network Rings by Baodong Zheng, Haidong Yin

“…We discuss the spatiotemporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. …”
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Foundational aspects of a new matrix holomorphic structure by Hedi Khedhiri, Taher Mkademi

“…Originality/value – We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. …”
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