Applications of Delay Differential Equations in Biological Systems

Introduction of time delays in a differential model significantly increases the complexity of the model. [...]studying qualitative behaviors of such models, using stability or bifurcation analysis, is necessary [7]. [...]in view of comparison theorem and limit superior theory, the authors obtain some sufficient conditions for the extinction of this system. In the paper “A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus” by P. S. Shabestari et al., the authors consider that some mathematical models have been presented for glucose and insulin interaction. [6] F. A. Rihan, D. H. Abdel Rahman, S. Lakshmanan, A. S. Alkhajeh, "A time delay model of tumour–immune system interactions: global dynamics, parameter estimation, sensitivity analysis," Applied Mathematics and Computation, vol. 232, pp. 606-623, DOI: 10.1016/j.amc.2014.01.111, 2014.