A non-standard numerical scheme for an age-of-infection epidemic model

We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the equation. The study of convergence properties and the analysis of the qualitative behavior of the numerical solution show that it preserves all the basic properties of the continuous model with no restrictive conditions on the step-length $h$ of integration and that it recovers the continuous dynamic as $h$ tends to zero.Comment: 17 pages, 3 figure

Global stability condition for collocation methods for Volterra integral equations of the second kind

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H9c2 Cardiomyocytes under Hypoxic Stress: Biological Effects Mediated by Sentinel Downstream Targets

The association between diabetes and cardiovascular diseases is well known. Related diabetes macro- and microangiopathies frequently induce hypoxia and consequently energy failure to satisfy the jeopardized myocardium basal needs. Additionally, it is widely accepted that diabetes impairs endothelial nitric oxide synthase (eNOS) activity, resulting in diminished nitric oxide (NO) bioavailability and consequent endothelial cell dysfunction. In this study, we analyzed the embryonic heart-derived H9c2 cell response to hypoxic stress after administration of a high glucose concentration to reproduce a condition often observed in diabetes. We observed that 24 h hypoxia exposure of H9c2 cells reduced cell viability compared to cells grown in normoxic conditions. Cytotoxicity and early apoptosis were increased after exposure to high glucose administration. In addition, hypoxia induced a RhoA upregulation and a Bcl-2 downregulation and lowered the ERK activation observed in normoxia at both glucose concentrations. Furthermore, a significant cell proliferation rate increases after the 1400W iNOS inhibitor administration was observed. Again, hypoxia increased the expression level of myogenin, a marker of skeletal muscle cell differentiation. The cardiomyocyte gene expression profiles and morphology changes observed in response to pathological stimuli, as hypoxia, could lead to improper ventricular remodeling responsible for heart failure. Therefore, understanding cell signaling events that regulate cardiac response to hypoxia could be useful for the discovery of novel therapeutic approaches able to prevent heart diseases

Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity

On the Solution of a Class of Nonlinear Systems Governed by an -Matrix

We consider a weakly nonlinear system of the form (+())=, where () is a real function of the unknown vector , and (+()) is an -matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (+())+1=, =0,1,…. The global convergence is proved by considering a related fixed-point problem

Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity