Modeling the dynamics of innate and adaptive immune response to Parkinson's disease with immunotherapy by Salma M. Al-Tuwairqi, Asma A. Badrah

“…A mathematical model was built using delay differential equations to investigate the effect of active and passive immunotherapies in delaying the progression of Parkinson's Disease. …”
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Analysis of Hopf–Hopf Interactions Induced by Multiple Delays for Inertial Hopfield Neural Models by Juhong Ge

“…The investigation of dynamic behaviors of inertial neural networks depicted by second-order delayed differential equations has received considerable attention. …”
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Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays by Khaled S. Al Noufaey

“…By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. …”
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Modeling biological systems with delays in Bio-PEPA by Giulio Caravagna, Jane Hillston

“…Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. …”
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The effect of temperature on Anopheles mosquito population dynamics and the potential for malaria transmission. by Lindsay M Beck-Johnson, William A Nelson, Krijn P Paaijmans, Andrew F Read, Matthew B Thomas, Ottar N Bjørnstad

“…We developed a temperature-dependent, stage-structured delayed differential equation model to better understand how climate determines risk. …”
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On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems by Andrea Maggiolo-Schettini, Paolo Milazzo, Giulio Caravagna, Roberto Barbuti

“…Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind of differential equations in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. …”
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Investigation of Gyroscopic Effect on the Stability of High Speed Micromilling via Bifurcation Analysis by Rinku K. Mittal, Ramesh K. Singh

“…A numerical scheme based on the linear multistep method is used to solve the time-periodic delay differential equations. The stability limits have been predicted as a function of the spindle speed. …”
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Modeling pulsativity in the hypothalamic–pituitary–adrenal hormonal axis by Alexander N. Churilov, John G. Milton

“…This model takes the form of a system of impulsive time-delay differential equations which include pulsatile release of adrenocorticotropin (ACTH) by the pituitary gland and a time delay for the release of glucocorticoid hormones by the adrenal gland. …”
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On the equilibrium point and Hopf-Bifurcation analysis of GDP-national debt dynamics under the delayed external investment: A new DDE model by Qiliang Chen, Pankaj Kumar, Dipesh, Haci Mehmet Baskonus

“…This mathematical model is based on a system of two non-linear delay differential equations representing GDP (Gross Domestic Product) growth and national debt respectively. …”
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Optimizing the Monotonic Properties of Fourth-Order Neutral Differential Equations and Their Applications by Hend Salah, Osama Moaaz, Sameh S. Askar, Ahmad M. Alshamrani, Elmetwally M. Elabbasy

“…The fourth-order delay differential equations have great practical importance due to their wide applications in civil, mechanical, and aeronautical engineering. …”
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Stability Analysis of Milling Process with Multiple Delays by Yonggang Mei, Rong Mo, Huibin Sun, Bingbing He, Kun Bu

“…Considering the regeneration effect, the dynamics of the milling process with variable pitch cutter is modeled as periodic coefficients delayed differential equations (DDEs) with multiple delays. An adaptive variable-step numerical integration method (AVSNIM) considering the effect of the helix angle is developed firstly, which can discretize the cutting period accurately, thereby improving the calculation accuracy of the stability limit of the milling process. …”
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Integrated chatter avoidance and minimum quantity lubrication conditions for chatter vibration problem in the machining process by Wan Azlan, Wan Mohd Nowalid, A. R., Yusoff

“…The corresponding quasiperiodic solutions of the governing time-periodic delay-differential equations are also identified with some milling experiments in the case of highly intermittent cutting.The predicted stability lobes are compared with the micro-milling force signals transformed into the frequency domain. …”
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Qualitative analysis for a variable delay system of differential equations of second order by Cemil Tunç, Osman Tunç

“…[Stability and boundedness of solutions of certain vector delay differential equations. J Nigerian Math Soc. 2018;37(2):77–87], Theorem 1.1 and Theorem 1.2, under weaker conditions. …”
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Distributed Ledger Technology for Smart Cities, the Sharing Economy, and Social Compliance by Pietro Ferraro, C. King, Robert Shorten

“…In this setting, we propose a set of delay differential equations to describe the dynamical behavior of the Tangle, an IoT-inspired directed acyclic graph designed for the cryptocurrency IOTA. …”
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Computational Sensitivity Analysis on a Mathematical Model of Epileptic Seizures by Karen A Yokley, Andrew F. Fischer, Nicholas S. Luke, Adrienne Rouiller

“…In the current study, a system of ordinary differential equations based on previous modeling is used with distinct biologically reasonable values for membrane capacitance in order to determine model sensitivity to that parameter. Because delay differential equations are used in the model, sensitivity is investigated computationally by examining the variation in output relative to various inputs. …”
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CHOOSING THE MODEL OF BIOLOGICAL NEURAL NETWORK FOR IMAGE SEGMENTATION OF A BIO-LIQUID FACIE by M. E. Semenov, T.Yu. Zablotskaya

“…Also, the mathematical models of biological neural networks that comprise ot only functional nonlinearities but the hysteretic ones are analyzed and the reasons are given for preference of the mathematical model with delay differential equations is chosen providing its applicability for modeling a single neuron and neural network as well.…”
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Viral dynamics of an HIV stochastic model with cell-to-cell infection, CTL immune response and distributed delays by Yan Wang, Tingting Zhao, Jun Liu

“…The stochastic integro-delay differential equations is transformed into a degenerate stochastic differential equations. …”
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Transcription factor competition facilitates self-sustained oscillations in single gene genetic circuits. by Jasper Landman, Sjoerd M Verduyn Lunel, Willem K Kegel

“…The use of delay-differential equations leads to a stability contour that predicts whether a genetic feedback loop will show self-sustained oscillations, even when taking the bursty nature of transcription into account.…”
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Global asymptotic stability of a delayed plant disease model by Yuming Chen, Chongwu Zheng

“…In this paper, we consider the following system of delayed differential equations, \[ \left\{ \begin {array}{rcl} \frac {dS(t)}{dt} & = & \sigma \phi-\beta S(t)I(t-\tau)-\eta S(t), \\ \frac {dI(t)}{dt} & = & \sigma(1-\phi)+\beta S(t)I(t-\tau)-(\eta+\omega)I(t), \end {array} \right. \] which can be used to model plant diseases. …”
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Convergence of solutions in a mean-field model of go-or-grow type with reservation of sites for proliferation and cell cycle delay by Baker, RE, Boldog, P, Rost, G

“…The mean-field model is expressed by a system of delay differential equations and includes variables such as the number of motile cells, proliferating cells, reserved sites and empty sites. …”