Mathematical modelling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, for example, population dynamics, epidemiology, immunology, physiology, and neural networks. The time-delays/time-lags, in these models, can be related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ODEs, the unknown state and its derivatives are evaluated at the same time instant. However, in DDEs the evolution of the system at a certain time instant depends on the past history/memory. Introduction of such time-delays in a differential model significantly increases the complexity of the model. Therefore, studying qualitative behaviours of such models, using stability or bifurcation analysis, is essential. Parameter identifiability and sensitivity analysis of such models are not adequately investigated in the literature. Also, applications of DDEs with state-dependent delay is a very modern topic in mathematics and might offer the chance for significant steps forward.

This special issue aims at creating a multidisciplinary forum of discussion on recent advances in delay differential equations in biological systems as well as new applications to engineering, physics, medicine, and economics. The accepted papers will show a diversity of new developments in these areas. This issue accepts high quality articles containing original research results and review articles of exceptional merit, and it will let the readers of this journal know more about this fundamental area of mathematics.

Potential topics include but are not limited to the following:

• Dynamics include stability, bifurcation, and chaos
• Qualitative behaviours of biological systems with memory and fractional orders
• Parameter estimations, nonlinearity, and sensitivity analysis
• Neural models and control systems
• Synchronization problems for neural models
• Stability and asymptotic behaviours of neural models
• Optimal control in biological systems and medicine/spread of disease
• Numerical algorithms for DDEs