Alejandro B. Engel

An approach to estimating the transmission coefficients for AIDS and for tuberculosis using mathematical models

A mathematical model is presented to simulate the interaction between Human Immunodeficiency Virus (HIV) and Mycobacterium tuberculosis (MTB) infections in a closed environment. The dynamics is formulated through a compartmental system of non-linear ordinary differential equations. The stability of the trivial equilibrium point or absence of infections and the endemic basins are analyzed based on the threshold values for the HIV and MTB transmission coefficients. In order to deal with the estimation of the transmission coefficients of HIV and MTB infections we consider the incarcerated individuals in the Female Penitentiary of São Paulo State, Brazil.

Modelling the effects of temporary immune protection and vaccination against infectious diseases

In this paper, we develop a mathematical model to describe the dynamics of reinfection under the assumption that immune protection may wane over time. As a disease control strategy a schedule of primary and secondary (booster) vaccination is studied, with vaccine induced immunity declining over time. A distinction is made between infection in immunological naive individuals (primary infection) and infection in individuals whose immune system has been primed by vaccination or infection (reinfection). Using the model we analyze the association between prevalence of infection and immunity, induced either by infection or by vaccine. The model shows that eradication depends on vaccination coverage as well as on vaccine efficacy.

Some considerations on a simplified version of Leslie's model

Abstract The present work is based on the analysis of a simplified version of Leslies model retricted to difference equations with two state variables. The model describes the growing of a single species divided in two age classes: the ‘youngs’ and the ‘adults’. We analyse the stability of the system when the reproductive rate of the species varies.

The cybernetics of inertial propulsion

Purpose – The purpose of this paper is to provide a study of inertial propulsion.Design/methodology/approach – In this paper, the theory of inertial propulsion under dry friction and under viscous friction is developed.Findings – As inertia propelled devices do not have any external moving parts; the propelling mechanism is completely enclosed inside the device. For inertial propulsion under dry friction, the equations of movement are explicitly derived and provided in closed form, so that such a device can be designed with its parameters computed exactly. For inertial propulsion under viscous friction, on the other hand, there is no closed form for the equations of movement, its dynamics are provided so that a device can be designed using a computer algebra system, as illustrated in the paper.Originality/value – The paper demonstrates that an inertia propelled device under dry friction moves in the opposite direction than the same device under viscous friction.

A cybernetical strategy for optimal farming: on the growth of Caiman Crocodilus Yacare

Presents an optimal strategy for managing crocodile farms. The strategy is illustrated with the case study of Caiman Crocodilus Yacare of the farm Coocrijapan. However, the strategy can be easily transferred to other farms, once sufficient data on their own crocodile stock is gathered. The main advantage of the ideas developed is that they deal with just one parameter: the break‐even point of the process. The underlying assumption of having a single parameter is that there is no seasonal change in prices; that is, the unitary price of food (say, per kilogram) and the unitary price of crocodile hide (say, per square centimetre) remain approximately constant in some currency. This may or may not be true in the local currency of the country that hosts the farm. With this assumption, dimensionless quantities for profit and return are found.

True parallel processing in artificial neural networks

The area of artificial neural networks, which dates back to the early twentieth century, could only offer positive contributions to technology after the back‐propagation algorithm was proposed in 1986. In this note an alternative algorithm to the gradient descent used in back‐propagation is proposed. This algorithm is based on the discrete central difference. This procedure, as opposed to the back‐propagation algorithm, offers the possibility of true parallel computation.

Biocybernetics : fitting the oxyhaemoglobin dissociation curve

Proposes a modified Hill model for the oxyhaemoglobin dissociation curve. The model fits normal oxyhaemoglobin dissociation experimental data quite accurately, and can easily be adapted to experimental data of subjects suffering haemoglobinopathies when available. Discusses the Adair equation, as well as correcting factors for varying temperature and pH.

Morphosis of the Julia set of the real parameter family of complex quadratic maps

Abstract The present note explores the structure of the interior of Julia sets and of the Mandelbrot set of quadratic maps. These sets usually appear as ‘dark’ regions in the computer generated graphics of iterations of the quadratic map. Two different ways of coloring and probing into these sets are provided.

Testing for normality using neural networks

The most commonly used statistical procedures (t, F, chi-squared, ANOVA, regression) assume that samples have been taken at random from normal populations. In some cases the central limit theorem may provide a satisfactory approximation to normality, but, when samples are small, departures from normality can lead users of these procedures to false conclusions. In the paper on work-in-progress the authors describe the results of training an artificial neural network (ANN) to distinguish normal from non-normal samples for random samples of size 30. With little attempt at fine-tuning, the ANN achieves results comparable to those of the best known tests for normality.<<ETX>>

A mathematical model for spirometry

A model originally designed to fit population growth data was investigated to determine whether it could fit spirometric traces as a function of time in normal and ill humans and in normal rats, obtained, respectively, by spirometer and whole-body plethysmography. The model showed great accuracy when applied to a simple spirometer coupled with an analog-to-digital converter interfaced with a personal computer. It also proved to be a good alternative for the more expensive and less accurate electronic devices, as derivative systems, and may be an attractive method for research and/or diagnostic centers.