Construction of Lyapunov functionals for delay differential equations in virology and epidemiology

DOI10.1016/j.nonrwa.2011.12.011zbMath1257.34053OpenAlexW2087606723MaRDI QIDQ1926158

Yasuhiro Takeuchi, Toru Sasaki, Tsuyoshi Kajiwara

Publication date: 28 December 2012

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2011.12.011

zbMATH Keywords

Lyapunov functionalsdelay differential equationsepidemiologyvirology

Mathematics Subject Classification ID

Epidemiology (92D30) Stability theory of functional-differential equations (34K20) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Medical epidemiology (92C60)

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Cites Work

• Unnamed Item
• Global properties of basic virus dynamics models
• Lyapunov functions and global stability for \(SIR\) and \(SIRS\) epidemiological models with non-linear transmission
• Global stability of an HIV-1 infection model with saturation infection and intracellular delay
• Impact of intracellular delay, immune activation delay and nonlinear incidence on viral dynamics
• Global analysis on delay epidemiological dynamic models with nonlinear incidence
• Stability of differential susceptibility and infectivity epidemic models
• Global dynamics of an in-host viral model with intracellular delay
• Global stability of multi-group epidemic models with distributed delays
• Global-stability problem for coupled systems of differential equations on networks
• Complete global stability for an SIR epidemic model with delay - distributed or discrete
• Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy
• Global stability of an SIR epidemic model with delay and general nonlinear incidence
• Global properties of infectious disease models with nonlinear incidence
• Global stability of epidemiological models with group mixing and nonlinear incidence rates
• Global stability of pathogen-immune dynamics with absorption
• A graph-theoretic approach to the method of global Lyapunov functions
• Lyapunov Functionals for Delay Differential Equations Model of Viral Infections

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