Numerical bifurcation analysis of immunological models with time delays

DOI10.1016/j.cam.2004.08.019zbMath1072.92025OpenAlexW2063083146MaRDI QIDQ2566208

Dirk Roose, Gennadii A. Bocharov, Tatyana Luzyanina

Publication date: 22 September 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.08.019

zbMATH Keywords

Delay differential equationsModel of HBV infectionNumerical bifurcation analysis

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Medical applications (general) (92C50) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Numerical bifurcation problems (65P30)

Related Items (6)

An SIR epidemic model with partial temporary immunity modeled with delay ⋮ Persistent instability in a nonhomogeneous delay differential equation system of the Valsalva maneuver ⋮ Lie group classification of first-order delay ordinary differential equations ⋮ Existence and convergence of Neimark–Sacker bifurcation for delay differential equations using Runge–Kutta methods ⋮ Observations on evolutionary models with (or without) time lag, and on problematical paradigms ⋮ Stochastic modeling of the impact of random forcing on persistent hepatitis B virus infection

Uses Software

• DKLAG6
• DDE-BIFTOOL
• dde23

Cites Work

• Stability properties of a scheme for the approximate solution of a delay- integro-differential equation
• Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations
• DKLAG6: A code based on continuously imbedded sixth-order Runge-Kutta methods for the solution of state-dependent functional differential equations
• Computing stability of differential equations with bounded distributed delays
• A delay-differential equation model of HIV infection of \(\text{CD}4^+\) T-cells
• Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations
• Stability of Runge-Kutta methods for delay integro-differential equations
• Numerical modelling in biosciences using delay differential equations
• Retarded differential equations
• Age-structured and two-delay models for erythropoiesis
• Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations
• Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations
• Nonlinear Numerics
• COMPUTING FLOQUET MULTIPLIERS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS
• On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations
• Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
• NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY
• Solving DDEs in Matlab
• Numerical bifurcation analysis of delay differential equations arising from physiological modeling
• Low level viral persistence after infection with LCMV: A quantitative insight through numerical bifurcation analysis
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