Research

Overview

My research lies at the interface of nonlinear dynamical systems, delay differential equations, and mathematical modeling. My aim is to understand how memory, delay, and coupling reshape stability, bifurcation structure, synchronization, persistence, and control in biological and engineered systems..

I work on both the qualitative theory and the modeling side: proving stability and threshold results, analyzing Hopf and related bifurcations, and building mathematically grounded models motivated by epidemiology, immunology, ecology, neural systems, and networked control.

Interests

Research interests

Mathematical Modeling in Immunology and Infectious Disease Epidemiology
Dynamics and Bifurcations in Neural Networks
Mathematical Ecology and Population Dynamics
Time Delays in Autonomous Vehicle Networks
Applied Analysis, Numerical Methods, and Control Systems

Mathematical Modeling in Immunology and Infectious Disease Epidemiology

This research combines within-host infection and immune-response models with population-level epidemic models. I study how latency, vaccination, asymptomatic carriage, distributed delays, and other biologically meaningful mechanisms alter threshold conditions, persistence, global stability, and intervention outcomes.

Beyond the Threshold: How a Distributed Eclipse-Phase Delay Reshapes Dynamics and Bifurcations in a Within-Host Virus–Interferon Model — Al-Darabsah, I. & Alothman, H. Mathematics, 14(20), 3756. DOI
Global dynamics of a within-host model for immune response with a generic distributed delay — Al-Darabsah, I. Mathematical Methods in the Applied Sciences, 48(12), 12186–12206. DOI
A simple in-host model for COVID-19 with treatments: model prediction and calibration — Al-Darabsah, I., Liao, K. L., & Portet, S. Journal of Mathematical Biology, 86(2), 20. DOI
A time-delayed SVEIR model for imperfect vaccine with a generalized nonmonotone incidence and application to measles — Al-Darabsah, I. Applied Mathematical Modelling, 91, 74–92. DOI
Threshold dynamics of a time-delayed epidemic model for continuous imperfect-vaccine with a generalized nonmonotone incidence rate — Al-Darabsah, I. Nonlinear Dynamics, 101(2), 1281–1300. DOI
A periodic disease transmission model with asymptomatic carriage and latency periods — Al-Darabsah, I. & Yuan, Y. Journal of Mathematical Biology, 77(2), 343–376. DOI
A time-delayed epidemic model for Ebola disease transmission — Al-Darabsah, I. & Yuan, Y. Applied Mathematics and Computation, 290, 307–325. DOI

Dynamics and Bifurcations in Neural Networks

This work focuses on delay-induced oscillations, synchronization, desynchronization, excitability changes, and bifurcations in neural and coupled dynamical systems. A central question is how discrete or distributed delays interact with nonlinear feedback and coupling to reorganize the dynamics.

Influence of large mean delay on distributed delay differential equations dynamics: application to a neural mass model — Al-Darabsah, I., Campbell, S. A., & Rahman, B. Mathematics and Computers in Simulation, 250, 209–233. DOI arXiv:2509.05466
Distributed delay and desynchronization in a neural mass model — Al-Darabsah, I., Campbell, S. A., & Rahman, B. SIAM Journal on Applied Dynamical Systems, 23(4), 3013–3051. DOI
The impact of small time delays on the onset of oscillations and synchrony in brain networks — Al-Darabsah, I., Chen, L., Nicola, W., & Campbell, S. A. Frontiers in Systems Neuroscience, 15, 688517. DOI
M-current induced Bogdanov–Takens bifurcation and switching of neuron excitability class — Al-Darabsah, I. & Campbell, S. A. The Journal of Mathematical Neuroscience, 11(1), 1–26. DOI
A phase model with large time delayed coupling — Al-Darabsah, I. & Campbell, S. A. Physica D: Nonlinear Phenomena, 411, 132559. DOI

Mathematical Ecology and Population Dynamics

This area includes stage-structured populations, predator–prey systems, harvesting, sea-lice dynamics, plant signaling, and delayed population models. The mathematical goals are to characterize persistence, extinction, stability, threshold behavior, and the effects of structure, movement, and biological control.

On the stability of a single-species model with a generic delay distribution kernel — Al-Darabsah, I. Chaos, Solitons & Fractals, 187, 115425. DOI
G protein controls stress readiness by modulating transcriptional and metabolic homeostasis in Arabidopsis thaliana and Marchantia polymorpha — Wu, T. Y., Krishnamoorthi, S., Boonyaves, K., Al-Darabsah, I., Leong, R., Jones, A. M., et al. Molecular Plant, 15(12), 1889–1907. DOI
Dynamic analysis of a biocontrol of sea lice by age-structured model — Al-Darabsah, I. & Yuan, Y. Nonlinear Dynamics, 97(2), 1649–1666. DOI
Global dynamics in sea lice model with stage structure — Tian, Y., Al-Darabsah, I., & Yuan, Y. Nonlinear Analysis: Real World Applications, 44, 283–304. DOI
A stage-structured mathematical model for fish stock with harvesting — Al-Darabsah, I. & Yuan, Y. SIAM Journal on Applied Mathematics, 78(1), 145–170. DOI
A prey-predator model with migrations and delays — Al-Darabsah, I., Tang, X., & Yuan, Y. Discrete & Continuous Dynamical Systems – B, 21(3), 737–761. DOI
Dynamics on a general stage structured N parallel food chains — Al-Darabsah, I. & Yuan, Y. BIOMAT 2013: International Symposium on Mathematical and Computational Biology, 63–84. DOI

Time Delays in Autonomous Vehicle Networks

This research examines how communication and sensing delays affect stability and performance in connected and autonomous vehicle networks. It combines dynamical-systems analysis with cooperative adaptive cruise control, platooning, time-varying communication lags, and data-driven delay compensation.

Validation of an autonomous vehicle platoons model with time-varying communication delays — Al-Darabsah, I., Hsueh, K. F., Khalil, A., Al Janaideh, M., Campbell, S. A., & Kundur, D. Chaos, Solitons & Fractals, 184, 114983. DOI
A deep time delay filter for cooperative adaptive cruise control — Hsueh, K. F., Farnood, A., Al-Darabsah, I., Al Saaideh, M., Al Janaideh, M., & Kundur, D. ACM Transactions on Cyber-Physical Systems, 8(2), 1–24. DOI
Vulnerability of connected autonomous vehicles networks to periodic time-varying communication delays of certain frequency — Al-Darabsah, I., Hsueh, K. F., Al Janaideh, M., Campbell, S. A., & Kundur, D. 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 3452–3457. DOI
Stability of connected autonomous vehicle networks with commensurate time delays — Al-Darabsah, I., Al Janaideh, M., & Campbell, S. A. 2021 American Control Conference (ACC), 3308–3313. DOI
The effect of input signals time-delay on stabilizing traffic with autonomous vehicles — Al-Darabsah, I., Al Janaideh, M., & Campbell, S. A. 2021 IEEE International Conference on Robotics and Automation (ICRA), 12708–12714. DOI

Applied Analysis, Numerical Methods, and Control Systems

This work brings together analytical and numerical methods for differential equations with control-oriented modeling. It includes fractional and integro-differential equations, spectral and Laplace-based methods, soft sensing and modal estimation, and feedback/feedforward compensation of nonlinear actuator behavior.

Generalized sensor-to-sensor transmissibility operators: theory, identification, and applications in soft sensing and modal estimation — Aljanaideh, K. F., Al-Darabsah, I., & Al Janaideh, M. Journal of Sound and Vibration, 628, 119643. DOI
Spectral solutions of nonlinear fractional ADR equations with ABC derivative for groundwater contaminant transport — Al-Khaled, K., Alquran, M., Darweesh, A., Al-Darabsah, I., Ajeel, M. S., Tamimi, S., & Alkhalid, H. K. Modern Physics Letters B, 40(20), 2650155. DOI
Analytical and numerical treatment of evolutionary time-fractional partial integro-differential equations with singular memory kernels — Al-Khaled, K., Al-Darabsah, I., Darweesh, A., & Alshare, A. Fractal and Fractional, 9(6), 392. DOI
Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator — Al Janaideh, M., Rakotondrabe, M., Al-Darabsah, I., & Aljanaideh, O. Control Engineering Practice, 72, 29–41. DOI
A model-based feedforward hysteresis compensator for micropositioning control — Aljanaideh, O., Rakotondrabe, M., Al-Darabsah, I., Aljanaideh, K. F., & Al Janaideh, M. 2017 American Control Conference (ACC), 3506–3511. DOI

Topology and Knot Theory

My earlier work also includes topology, particularly the study of invariants of rational links. This provides a complementary theoretical direction centered on rigorous structure, classification, and geometric properties of knots and links.

The signature of rational links — Qazaqzeh, K., Al-Darabsah, I., & Quraan, A. New York Journal of Mathematics, 20.

Students

I supervise undergraduate projects and graduate theses in mathematical biology, applied dynamical systems, and related areas. Please see the contact page if you are interested in discussing a project or collaboration.