On estimating the basic reproduction number in distinct stages of a contagious disease spreading

In epidemiology, the basic reproduction number R-0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition. R-0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R-0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R-0 >1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable: when R-0 <1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R-0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptibleinfective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R-0 obtained from both approaches are compared, showing good agreement. (C) 2012 Elsevier B.V. All rights reserved.

Coupling collective modes in a trapped superfluid

We consider a superfluid cloud composed of a Bose-Einstein condensate oscillating within a magnetic trap (dipole mode) where, due to the existence of a Feshbach resonance, an effective periodic time-dependent modulation in the scattering length is introduced. Under this condition, collective excitations such as the quadrupole mode can take place. We approach this problem by employing both the Gaussian and the Thomas-Fermi variational Ansatze. The resulting dynamic equations are analyzed by considering both linear approximations and numerical solutions, where we observe coupling between dipole and quadrupole modes. Aspects of this coupling related to the variation of the dipole oscillation amplitude are analyzed. This may be a relevant effect in situations where oscillation in a magnetic field in the presence of a bias field B takes place, and should be considered in the interpretation of experimental results.

A novel self consistent calculation approach for the capacitance-voltage characteristics of semiconductor quantum wire transistors based on a split-gate configuration

Purpose - The purpose of this paper is to develop an efficient numerical algorithm for the self-consistent solution of Schrodinger and Poisson equations in one-dimensional systems. The goal is to compute the charge-control and capacitance-voltage characteristics of quantum wire transistors. Design/methodology/approach - The paper presents a numerical formulation employing a non-uniform finite difference discretization scheme, in which the wavefunctions and electronic energy levels are obtained by solving the Schrodinger equation through the split-operator method while a relaxation method in the FTCS scheme ("Forward Time Centered Space") is used to solve the two-dimensional Poisson equation. Findings - The numerical model is validated by taking previously published results as a benchmark and then applying them to yield the charge-control characteristics and the capacitance-voltage relationship for a split-gate quantum wire device. Originality/value - The paper helps to fulfill the need for C-V models of quantum wire device. To do so, the authors implemented a straightforward calculation method for the two-dimensional electronic carrier density n(x,y). The formulation reduces the computational procedure to a much simpler problem, similar to the one-dimensional quantization case, significantly diminishing running time.

Periodic averaging theorems for various types of equations

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.