A class of competing models with discrete delay
A delayed chemostat model with impulsive diffusion and input on nutrients.
A delayed epidemic model with pulse vaccination.
A delayed mathematical model for testosterone secretion with feedback control mechanism.
A general framework for stability analysis of gene regulatory networks with delay.
A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation
In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability...
A predator-prey Gompertz model with time delay and impulsive perturbations on the prey.
A predator-prey model in the chemostat with time delay.
Almost periodic solution of a diffusive mixed system with time delay and type III functional response.
Analysis of a delayed SIR model with nonlinear incidence rate.
Analysis of a nonautonomous delayed predator-prey system with a stage structure for the predator in a polluted environment.
Analysis of immunotherapy models in the context of cancer dynamics
A basic mathematical model of the immune response when cancer cells are recognized is proposed. The model consists of six ordinary differential equations. It is extended by taking into account two types of immunotherapy: active immunotherapy and adoptive immunotherapy. An analysis of the corresponding models is made to answer the question which of the presented methods of immunotherapy is better. The analysis is completed by numerical simulations which show that the method of adoptive immunotherapy...
Asymptotic properties of a hepatitis B virus infection model with time delay.
Bifurcation analysis for a delayed predator-prey system with stage structure.
Bifurcation analysis of a Kaldor-Kalecki model of business cycle with time delay.
Bifurcation analysis on a delayed SIS epidemic model with stage structure.
Bifurcations of FitzHugh-Nagumo excitable systems with chemical delayed coupling
Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch
A nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the...
Delays induced in population dynamics
This paper provides an introduction to delay differential equations together with a short survey on state-dependent delay differential equations arising in population dynamics. Our main goal is to examine how the delays emerge from inner mechanisms in the model, how they induce oscillations and stability switches in the system and how the qualitative behaviour of a biological model depends on the form of the delay.
Distributed delayed competing predators