Special Issue: Applications of delay differential equations in biology

Guest Editor

Prof. Yuming Chen
Wilfrid Laurier University, Canada


Prof. Lin Wang
University of New Brunswick, Canada


Prof. Junjie Wei
Harbin Institute of Technology, China


Manuscript Topics

Delay differential equations (DDEs) are naturally adopted to describe the evolution of a system in which the rate of change of the state variable depends on not only the system's current status but also on its historical status. The study of DDEs has greatly inspired and enhanced the advance in nonlinear analysis and infinite dimensional dynamical systems and provided tremendous new insights on practical applications. This special issue calls for recent advances in application of DDEs in biology. Researchers are encouraged to contribute original research articles as well as surveys that will lead to better understanding of biology. Potential topics include but are not limited to original modeling based on real biological background, epidemiology (between-host and within-host models), and population dynamics.


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Paper Submission

All manuscripts will be peer-reviewed before their acceptance for publication. The deadline for manuscript submission is 01 September 2020

Published Papers(30)

Research article
Asymptotic behaviors of jellyfish model with stage structure
Zin Thu Win Boping Tian Shengqiang Liu
2021, Volume 18, Issue 3: 2508-2526. doi: 10.3934/mbe.2021128
Abstract HTML PDF Cited (2) Viewed (2675)
Research article
Stability and Hopf bifurcations in a competitive tumour-immune system with intrinsic recruitment delay and chemotherapy
Qingfeng Tang Guohong Zhang
2021, Volume 18, Issue 3: 1941-1965. doi: 10.3934/mbe.2021101
Abstract HTML PDF Cited (3) Viewed (3649)
Research article
Global dynamics of an SI epidemic model with nonlinear incidence rate, feedback controls and time delays
Ke Guo Wanbiao Ma
2021, Volume 18, Issue 1: 643-672. doi: 10.3934/mbe.2021035
Abstract HTML PDF Cited (6) Viewed (3358)
Research article
Viral dynamics of a latent HIV infection model with Beddington-DeAngelis incidence function, B-cell immune response and multiple delays
Yan Wang Minmin Lu Daqing Jiang
2021, Volume 18, Issue 1: 274-299. doi: 10.3934/mbe.2021014
Abstract HTML PDF Cited (8) Viewed (3650)
Research article
Modeling and analysis of COVID-19 based on a time delay dynamic model
Cong Yang Yali Yang Zhiwei Li Lisheng Zhang
2021, Volume 18, Issue 1: 154-165. doi: 10.3934/mbe.2021008
Abstract HTML PDF Cited (9) Viewed (6526)
Research article
Mathematical modeling of population structure in bioreactors seeded with light-controllable microbial stem cells
Dane Patey Nikolai Mushnikov Grant Bowman Rongsong Liu
2020, Volume 17, Issue 6: 8182-8201. doi: 10.3934/mbe.2020415
Abstract HTML PDF Viewed (4164)
Research article
Stability and Hopf bifurcation for a delayed diffusive competition model with saturation effect
Changyong Xu Qiang Li Tonghua Zhang Sanling Yuan
2020, Volume 17, Issue 6: 8037-8051. doi: 10.3934/mbe.2020407
Abstract HTML PDF Cited (2) Viewed (3393)
Research article
Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks
Hwayeon Ryu Sue Ann Campbell
2020, Volume 17, Issue 6: 7931-7957. doi: 10.3934/mbe.2020403
Abstract HTML PDF Cited (8) Viewed (4605)
Research article
Impact of variability of reproductive ageing and rate on childhood infectious disease prevention and control: insights from stage-structured population models
Qiuyi Su Jianhong Wu
2020, Volume 17, Issue 6: 7671-7691. doi: 10.3934/mbe.2020390
Abstract HTML PDF Cited (1) Viewed (3527)
Research article
Global stability for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity
Toshikazu Kuniya Tarik Mohammed Touaoula
2020, Volume 17, Issue 6: 7332-7352. doi: 10.3934/mbe.2020375
Abstract HTML PDF Cited (8) Viewed (3736)
Research article
Bifurcation analysis of an age-structured SIRI epidemic model
Xiaohong Tian Rui Xu Ning Bai Jiazhe Lin
2020, Volume 17, Issue 6: 7130-7150. doi: 10.3934/mbe.2020366
Abstract HTML PDF Cited (5) Viewed (4254)
Research article
Traveling waves in delayed reaction-diffusion equations in biology
Sergei Trofimchuk Vitaly Volpert
2020, Volume 17, Issue 6: 6487-6514. doi: 10.3934/mbe.2020339
Abstract HTML PDF Cited (11) Viewed (5404)
Research article
Global analysis and optimal harvesting for a hybrid stochastic phytoplankton-zooplankton-fish model with distributed delays
Yuanpei Xia Weisong Zhou Zhichun Yang
2020, Volume 17, Issue 5: 6149-6180. doi: 10.3934/mbe.2020326
Abstract HTML PDF Cited (7) Viewed (4136)
Research article
Dynamics of an epidemic model with relapse over a two-patch environment
Dongxue Yan Xingfu Zou
2020, Volume 17, Issue 5: 6098-6127. doi: 10.3934/mbe.2020324
Abstract HTML PDF Cited (6) Viewed (4079)
Research article
A consumer-resource competition model with a state-dependent delay and stage-structured consumer species
Yan Wang Xianning Liu Yangjiang Wei
2020, Volume 17, Issue 5: 6064-6084. doi: 10.3934/mbe.2020322
Abstract HTML PDF Cited (1) Viewed (3755)
Research article
Dynamics of a toxin-mediated aquatic population model with delayed toxic responses
Yueping Dong Jianlu Ren Qihua Huang
2020, Volume 17, Issue 5: 5907-5924. doi: 10.3934/mbe.2020315
Abstract HTML PDF Viewed (4047)
Research article
Explicit solution of a Lotka-Sharpe-McKendrick system involving neutral delay differential equations using the r-Lambert W function
Cristeta U. Jamilla Renier G. Mendoza Victoria May P. Mendoza
2020, Volume 17, Issue 5: 5686-5708. doi: 10.3934/mbe.2020306
Abstract HTML PDF Cited (12) Viewed (4645)
Research article
Asymptotic behavior of a stochastic delayed avian influenza model with saturated incidence rate
Yanyan Du Ting Kang Qimin Zhang
2020, Volume 17, Issue 5: 5341-5368. doi: 10.3934/mbe.2020289
Abstract HTML PDF Cited (3) Viewed (4065)
Research article
How fast is the linear chain trick? A rigorous analysis in the context of behavioral epidemiology
Alessia Andò Dimitri Breda Giulia Gava
2020, Volume 17, Issue 5: 5059-5084. doi: 10.3934/mbe.2020273
Abstract HTML PDF Cited (3) Viewed (4799)
Research article
Global dynamics of a delayed diffusive virus infection model with cell-mediated immunity and cell-to-cell transmission
Chunyang Qin Yuming Chen Xia Wang
2020, Volume 17, Issue 5: 4678-4705. doi: 10.3934/mbe.2020257
Abstract HTML PDF Cited (6) Viewed (3931)
Research article
An optimal scheme to boost immunity and suppress viruses for HIV by combining a phased immunotherapy with the sustaining antiviral therapy
Youyi Yang Yongzhen Pei Xiyin Liang Yunfei Lv
2020, Volume 17, Issue 5: 4578-4608. doi: 10.3934/mbe.2020253
Abstract HTML PDF Cited (1) Viewed (4094)
Research article
Global stability for a class of HIV virus-to-cell dynamical model with Beddington-DeAngelis functional response and distributed time delay
Xinran Zhou Long Zhang Tao Zheng Hong-li Li Zhidong Teng
2020, Volume 17, Issue 5: 4527-4543. doi: 10.3934/mbe.2020250
Abstract HTML PDF Cited (3) Viewed (4614)
Research article
Dynamics analysis of Mackey-Glass model with two variable delays
Yanxiang Tan
2020, Volume 17, Issue 5: 4513-4526. doi: 10.3934/mbe.2020249
Abstract HTML PDF Cited (25) Viewed (4637)
Research article
Stability and Hopf bifurcation in a virus model with self-proliferation and delayed activation of immune cells
Huan Kong Guohong Zhang Kaifa Wang
2020, Volume 17, Issue 5: 4384-4405. doi: 10.3934/mbe.2020242
Abstract HTML PDF Cited (2) Viewed (4071)
Research article
Modeling the effect of temperature on dengue virus transmission with periodic delay differential equations
Haitao Song Dan Tian Chunhua Shan
2020, Volume 17, Issue 4: 4147-4164. doi: 10.3934/mbe.2020230
Abstract HTML PDF Cited (14) Viewed (5743)
Research article
Stability analysis and Hopf bifurcation in a diffusive epidemic model with two delays
Huan Dai Yuying Liu Junjie Wei
2020, Volume 17, Issue 4: 4127-4146. doi: 10.3934/mbe.2020229
Abstract HTML PDF Cited (1) Viewed (4309)
Research article
Global asymptotic behavior for mixed vaccination strategy in a delayed epidemic model with interim-immune
Siyu Liu Mingwang Shen Yingjie Bi
2020, Volume 17, Issue 4: 3601-3617. doi: 10.3934/mbe.2020203
Abstract HTML PDF Cited (5) Viewed (4333)
Research article
Stability and bifurcation of a delayed diffusive predator-prey system with food-limited and nonlinear harvesting
Guangxun Sun Binxiang Dai
2020, Volume 17, Issue 4: 3520-3552. doi: 10.3934/mbe.2020199
Abstract HTML PDF Cited (5) Viewed (4532)
Research article
Dynamic properties of VDP-CPG model in rhythmic movement with delay
Liqin Liu Chunrui Zhang
2020, Volume 17, Issue 4: 3190-3202. doi: 10.3934/mbe.2020181
Abstract HTML PDF Cited (6) Viewed (3903)