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Stability analysis of a renewal equation for cell population dynamics with quiescence
(2014-12-31)
We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two subpopulations, and regulation of the ...
Global dynamics of two-compartment models for cell production systems with regulatory mechanisms
(2013-12-31)
We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell ...
Global stability of sirs epidemic models with a class of nonlinear incidence rates and distributed delays
(2012-12-31)
In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed delays. By using ...
Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates
(2012-12-31)
In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays ∫ h 0 p(τ)f(S(t),I(t- τ))dτ under the ...
Global stability for a discrete SIS epidemic model with immigration of infectives
(2012-12-31)
In this paper, we propose a discrete-time SIS epidemic model which is derived from continuous-time SIS epidemic models with immigration of infectives by the backward Euler method. For the discretized model, by applying new ...
Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
(2012-12-31)
In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫ 0 hf(τ)G(I(t-τ))dτ. Applying Lyapunov functional techniques ...
Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates
(2012-12-31)
We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. ...
Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates
(2012-12-31)
In this paper, by applying a variation of the backward Euler method, we propose a discrete-time SIR epidemic model whose discretization scheme preserves the global asymptotic stability of equilibria for a class of corresponding ...
On a generalization of the global attractivity for a periodically forced Pielou's equation
(2012-12-31)
In this paper, we study the global attractivity for a class of periodic difference equation with delay which has a generalized form of Pielou's difference equation. The global dynamics of the equation is characterized by ...
Stability analysis of multi-compartment models for cell production systems
(2012-12-31)
We study two-and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well ...