Complexity

Applications of Delay Differential Equations in Biological Systems


Status
Published

1United Arab Emirates University, Al Ain, UAE

2Yuzuncu Yil University, Van, Turkey

3Mansoura University, Mansoura, Egypt

4Deakin University, Geelong, Australia

5Bharathiar University, Coimbatore, India


Applications of Delay Differential Equations in Biological Systems

Description

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

Articles

  • Special Issue
  • - Volume 2018
  • - Article ID 6815190
  • - Research Article

A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus

Payam Sadeghi Shabestari | Karthikeyan Rajagopal | ... | Prakash Duraisamy
  • Special Issue
  • - Volume 2018
  • - Article ID 4584389
  • - Editorial

Applications of Delay Differential Equations in Biological Systems

F. A. Rihan | C. Tunc | ... | R. Rakkiyappan
  • Special Issue
  • - Volume 2018
  • - Article ID 8237634
  • - Research Article

Oscillation Criteria for Delay and Advanced Differential Equations with Nonmonotone Arguments

George E. Chatzarakis | Tongxing Li
  • Special Issue
  • - Volume 2017
  • - Article ID 1409865
  • - Research Article

Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449

Lingling Li | Jianwei Shen
  • Special Issue
  • - Volume 2017
  • - Article ID 6148934
  • - Research Article

Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

Ahmed A. Mahmoud | Sarat C. Dass | ... | Vijanth S. Asirvadam
  • Special Issue
  • - Volume 2017
  • - Article ID 4391587
  • - Research Article

Impact of Time Delay in Perceptual Decision-Making: Neuronal Population Modeling Approach

Urszula Foryś | Natalia Z. Bielczyk | ... | Jan Poleszczuk
  • Special Issue
  • - Volume 2017
  • - Article ID 8197610
  • - Research Article

On Coupled -Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions

Aziz Khan | Yongjin Li | ... | Tahir Saeed Khan
  • Special Issue
  • - Volume 2017
  • - Article ID 4573589
  • - Research Article

Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method

Muhammed I. Syam
  • Special Issue
  • - Volume 2017
  • - Article ID 4654020
  • - Research Article

Hybrid Adaptive Pinning Control for Function Projective Synchronization of Delayed Neural Networks with Mixed Uncertain Couplings

T. Botmart | N. Yotha | ... | W. Weera
  • Special Issue
  • - Volume 2017
  • - Article ID 1047384
  • - Research Article

Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

Nasser Hassan Sweilam | Seham Mahyoub Al-Mekhlafi | Taghreed Abdul Rahman Assiri
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Acceptance rate43%
Submission to final decision64 days
Acceptance to publication35 days
CiteScore3.200
Impact Factor2.462
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