Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument by Siyu Zhang, Fanwei Meng

“…We present new oscillation criteria for the even order neutral delay differential equations with distributed deviating argument [r(t)ψ(x(t))Z(n−1)(t)]′+∫abp(t,ξ)f[x(g(t,ξ))]dσ(ξ)=0,  t≥t0, where Z(t)=x(t)+q(t)x(t−τ). …”
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A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions by Hamid Lmou, Khalid Hilal, Ahmed Kajouni

“…In this paper, we deal with the existence and uniqueness of solution for ψ-Hilfer Langevin fractional pantograph differential equation and inclusion; these types of pantograph equations are a special class of delay differential equations. The existence and uniqueness results are obtained by making use of the Krasnoselskii fixed-point theorem and Banach contraction principle, and for the inclusion version, we use the Martelli fixed-point theorem to get the existence result. …”
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Dynamics of a delay Schistosomiasis model in snail infections by Chunhua Shan, Hongjun Gao, Huaiping Zhu

“…In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. …”
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Global Stability of HIV-1 Infection Model with Two Time Delays by Hui Miao, Xamxinur Abdurahman, Ahmadjan Muhammadhaji

“…We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. …”
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Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions by F. A. Rihan, M. Safan, M. A. Abdeen, D. Abdel Rahman

“…We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. …”
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The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g-Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers by Zhaolin Jiang, Dan Li

“…Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and g-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. …”
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Oscillation Solutions for Nonlinear Second-Order Neutral Differential Equations by Omar Bazighifan, Nawa Alshammari, Faten Aldosari, Loredana Florentina Iambor

“…To demonstrate their practical implications, three illustrative examples are presented, showcasing the applicability and effectiveness of the results in solving real-world problems involving delay differential equations.…”
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Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations by Yunfei Li, Shoufu Li

“…The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. …”
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Noether symmetry of multi-delay Birkhoffian system and its conserved quantity by Xin-Yu Du, Xiang-Hua Zhai

“…The multi-delay differential equations of motion are derived for both Birkhoffian and Hamiltonian models. …”
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The effect of time delay in plant--pathogen interactions with host demography by Bruno Buonomo, Marianna Cerasuolo

“…We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. …”
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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps by Guodong Liu, Xiaohong Wang, Xinzhu Meng, Shujing Gao

“…Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.…”
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Strong Convergence of a New Hybrid Iterative Scheme for Nonexpensive Mappings and Applications by Jie Jia, Khurram Shabbir, Khushdil Ahmad, Nehad Ali Shah, Thongchai Botmart

“…By using the Picard-Thakur hybrid iterative scheme, we can find the solution of delay differential equations and also prove some convergence results for nonexpansive mapping in a uniformly convex Banach space.…”
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Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms by Mingzhu Song, Quanxin Zhu, Hongwei Zhou

“…By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. …”
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Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays by Fulgensia Kamugisha Mbabazi, Joseph Y. T. Mugisha, Mark Kimathi

“…The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio R0 is less than unity and unstable otherwise. …”
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A simple model of carcinogenic mutations with time delay and diffusion by Monika Joanna Piotrowska, Urszula Foryś, Marek Bodnar, Jan Poleszczuk

“…In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. …”
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Positivity of Fundamental Matrix and Exponential Stability of Delay Differential System by Alexander Domoshnitsky, Roman Shklyar, Mikhail Gitman, Valery Stolbov

“…Results on nonnegativity of the Cauchy matrix for system of delay differential equations xi′t+∑j=1n‍pijtxjhijt=fit,   i=1,…,n, which were based on nonpositivity of all diagonal elements, were presented in the previous works. …”
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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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Improving diversification by a hybrid bat-Nelder-Mead algorithm and DDE for rapid convergence to solve global optimization by Enas Suhail, Mahmoud El-Alem, Omar Bazighifan, Ahmed Zekri

“…Delay differential equations and algorithms hold a crucial position in the exploration of some biological systems and several models in real-world applications. …”
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Bifurcation and controller design in a 3D delayed predator-prey model by Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen

“…This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. …”
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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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