Dengue disease, basic reproduction number and control

Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of Dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: This is a preprint of a paper whose final and definitive form has appeared in International Journal of Computer Mathematics (2011), DOI: 10.1080/00207160.2011.55454

Generating functions for generalized binomial distributions

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties: the constraints of nonnegativeness are automatically fulfilled, a complete characterization in terms of generating functions is given and a large number of analytical examples becomes available.Comment: PDFLaTex, 27 pages, 5 figure

Optimal control strategies for tuberculosis treatment: a case study in Angola

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions. Numerical simulations are given using data from Angola.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

The Formation of Large Galactic Disks: Revival or Survival?

Using the deepest and the most complete set of observations of distant galaxies, we investigate how extended disks could have formed. Observations include spatially-resolved kinematics, detailed morphologies and photometry from UV to mid-IR. Six billion years ago, half of the present-day spiral progenitors had anomalous kinematics and morphologies, as well as relatively high gas fractions. We argue that gas-rich major mergers, i.e., fusions between gas-rich disk galaxies of similar mass, can be the likeliest driver for such strong peculiarities. This suggests a new channel of disk formation, e.g. many disks could be reformed after gas-rich mergers. This is found to be in perfect agreement with predictions from the state-of-the-art LCDM semi-empirical models: due to our sensitivity in detecting mergers at all phases, from pairs to relaxed post-mergers, we find a more accurate merger rate. The scenario can be finally confronted to properties of nearby galaxies, including M31 and galaxies showing ultra-faint, gigantic structures in their haloes.Comment: Proceedings of the annual meeting of the French Astronomical Society, 2011, 6 pages, 1 Figur

On the Formation of Copper Linear Atomic Suspended Chains

We report high resolution transmission electron microscopy and classical molecular dynamics simulation results of mechanically stretching copper nanowires conducting to linear atomic suspended chains (LACs) formation. In contrast with some previous experimental and theoretical work in literature that stated that the formation of LACs for copper should not exist our results showed the existence of LAC for the [111], [110], and [100] crystallographic directions, being thus the sequence of most probable occurence.Comment: 4 pages, 3 figure