**Preface**

Differential equations naturally arise when modeling a large number of phenomena in optics, radiophysics, biology, medicine, economics, and sociology.

It is well known that, for the adequate mathematical modeling of the dynamics of many processes in various areas of science, it is crucial to take into account the influence of lags. That is why delay differential equations play an important role in mathematical modeling. For example, they are able to model gene networks, information transmission systems, population size, and infectious diseases.

Qualitative properties of solutions to equations with delay are also of great interest.

The present book contains the 11 articles accepted for publication out of the 31 manuscripts submitted to the Special Issue "Advances in Delay Differential Equations" of the MDPI journal *Mathematics*.

The 11 articles cover a wide range of topics connected to the theory of differential equations with delay. These topics include, among others, the construction of solutions and analytical and numerical methods for; dynamical properties of; and applications of DDE to the mathematical modeling of various phenomena and processes in physics, biology, ecology, and medicine.

It is hoped that the book will be interesting and useful for those working in the area of differential equations with delays and nonlinear dynamics, as well as for those with the proper mathematical background who are willing to become familiar with recent advances in mathematical modelling.

As the Guest Editor of the Special Issue, I am grateful to the authors of the papers for their quality contributions, to the reviewers for their valuable comments towards the improvement of the submitted manuscripts, and to the administrative staff of MDPI for the support needed to complete this project. Special thanks are due to the Managing Editor of the Special Issue, Dr. Syna Mu, for excellent collaboration and valuable assistance.

> **Alexandra Kashchenko** *Editor*
