Antonia Vecchio

Kinetics of In Vivo Proliferation and Death of Memory and Naive CD8 T Cells: Parameter Estimation Based on 5-Bromo-2′-Deoxyuridine Incorporation in Spleen, Lymph Nodes, and Bone Marrow

To study naive and memory CD8 T cell turnover, we performed BrdU incorporation experiments in adult thymectomized C57BL/6 mice and analyzed data in a mathematical framework. The following aspects were novel: 1) we examined the bone marrow, in addition to spleen and lymph nodes, and took into account the sum of cells contained in the three organs; 2) to describe both BrdU-labeling and -delabeling phase, we designed a general mathematical model, in which cell populations were distinguished based on the number of divisions; 3) to find parameters, we used the experimentally determined numbers of total and BrdU+ cells and the BrdU-labeling coefficient. We treated mice with BrdU continuously via drinking water for up to 42 days, measured by flow cytometry BrdU incorporation at different times, and calculated the numbers of BrdU+ naive (CD44int/low) and memory (CD44high) CD8 T cells. By fitting the model to data, we determined proliferation and death rates of both subsets. Rates were confirmed using independent sets of data, including the numbers of BrdU+ cells at different times after BrdU withdrawal. We found that both doubling time and half-life of the memory population were ∼9 wk, whereas for the naive subset the doubling time was almost 1 year and the half-life was roughly 7 wk. Our findings suggest that the higher turnover of memory CD8 T cells as compared with naive CD8 T cells is mostly attributable to a higher proliferation rate. Our results have implications for interpreting physiological and abnormal T cell kinetics in humans.

Stability of difference Volterra equations: Direct Liapunov method and numerical procedure

Abstract A procedure to construct Liapunov functionals for discrete Volterra equations is proposed. Using this procedure stability conditions are derived for general Volterra difference equations. Some applications of the proposed procedure for obtaining stability conditions for linear multistep methods for Volterra integro-differential equations are presented.

Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates

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 continuous-time SIR epidemic models. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number , when the infection incidence rate has a suitable monotone property.

A General Discrete Time Model of Population Dynamics in the Presence of an Infection

We present a set of difference equations which generalizes that proposed in the work of G. Izzo and A. Vecchio (2007) and represents the discrete counterpart of a larger class of continuous model concerning the dynamics of an infection in an organism or in a host population. The limiting behavior of this new discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived.

A family of methods for Abel integral equations of the second kind

Abstract A class of methods depending on some parameters are introduced for the numerical solution of the Abel integral equations of the second kind. Some bounds on the parameters are determined so that the corresponding methods have infinite stability intervals.

Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates

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. The model admits a unique endemic equilibrium if and only if the basic reproduction number R0 exceeds one, while the trivial equilibrium and the disease-free equilibrium always exist. First we show that the disease-free equilibrium is globally asymptotically stable if and only if R0 1. Second we show that the model is permanent if and only if R0 > 1. Moreover, using a threshold parameter R0 characterized by the nonlinear incidence function, we establish that the endemic equilibrium is locally asymptotically stable for 1 < R0 R0 and it loses stability as the length of the delay increases past a critical value for 1 < R0 < R0. Our result is an extension of the stability results in (J-J. Wang, J-Z. Zhang, Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonl. Anal. RWA. 11 (2009) 2390-2402).

Stability of discrete volterra equations of hammerstein type

Stability conditions for Volterra equations with discrete time are obtained using direct Liapunov method, without usual assumption of the summability of the series of the coeffcients. Using such conditions, the stability of some numerical methods for second kind Volterra integral equation is analyzed.

Stability analysis of discrete recurrence equations of Volterra type with degenerate kernels

Abstract Stability criteria are derived for difference equations of Volterra type with degenerate kernels. The main tool in this analysis is the use of the new representation formula which allows us to express the solution of discrete Volterra equation with degenerate kernel in terms of the fundamental matrix of the corresponding first-order system of the difference equations.

General linear methods for Volterra integral equations

We investigate the class of general linear methods of order p and stage order q=p for the numerical solution of Volterra integral equations of the second kind. Construction of highly stable methods based on the Schur criterion is described and examples of methods of order one and two which have good stability properties with respect to the basic test equation and the convolution one are given.

Convergence of solutions for two delays Volterra integral equations in the critical case

Abstract In this paper, for the “critical case” with two delays, we establish two relations between any two solutions y ( t ) and y ∗ ( t ) for the Volterra integral equation of non-convolution type y ( t ) = f ( t ) + ∫ t − τ t − δ k ( t , s ) g ( y ( s ) ) d s and a solution z ( t ) of the first order differential equation z ( t ) = β ( t ) [ z ( t − δ ) − z ( t − τ ) ] , and offer a sufficient condition that lim t → + ∞ ( y ( t ) − y ∗ ( t ) ) = 0 .