The Conceprts of Delay Differential Equations and IT’S Application
Adamu Wakili *
Department of Mathematical Sciences, Adamawa State University, Mubi, Adamawa State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
All processes take time to complete. While physical processes such as acceleration and deceleration take little time compared to the times need to travel most distances, the times involved in biological processes such as gestation and maturation can be substantial when compared to the data-collection times in most population studies. Therefore, it is often imperative to explicitly incorporate these process times in mathematical models of population dynamics. These process times are often called delay times, and the model that incorporate such delay times are referred as delay differential equation (DDE) models.
The models will examine some theoretical concepts and their applications to real life situation. The application examines measles and the time it takes to manifest or to its removal or treatment from the system. The solutions of the models will be displayed in graphical forms using MATLAB method. The analysis of the models indicate the times delay and its characteristics.
Keywords: Time delay, maturation, gestation, oscillation, periodic, parameter and dynamics