Modeling with delay differential equations (DDEs) is widely used in various areas of life sciences, including population dynamics, epidemiology, immunology, physiology, and neural networks. In these models, time-delays/time-lags are related to hidden processes like the stages of the life cycle, the time between infection and the generation of new viruses, the infectious period, the immune period, etc. ODEs evaluate the unknown state and its derivatives at the same time.

However, in DDEs, the evolution of the system at a certain time instant is determined by the past. The introduction of such time delays significantly increases the complexity of a differential model. Therefore, stability and bifurcation analysis of these models are essential for studying their qualitative behavior. These models haven't been properly investigated for parameter identifiability or sensitivity analysis. The application of DDEs with state-dependent delays is a very recent topic in mathematics that might result in significant advances.

The aim of this Special Issue is to create a forum for discussion of recent developments in delay differential equations, and new applications to engineering, physics, medicine, and economics. Accepted papers will present a variety of new developments in these areas. The purpose of this Issue is to publish original research and review articles to enable the readers of this journal to understand more about this fundamental area of mathematics.

Potential topics include but are not limited to the following:

• Qualitative behaviors of DDEs
• Numerical methods for DDEs
• Dynamics include stability, bifurcation, and chaos of DDEs
• Fractional-order DDEs and applications
• Parameter estimations with DDEs
• Nonlinearity and sensitivity analysis
• Neural models and control systems
• Synchronization problems for neural models
• Optimal control in biological systems, medicine/spread of disease
• Numerical algorithms for DDEs