A stochastic spatially structured epidemic model with diffusive processes

We developed a stochastic lattice model to describe the vector-borne disease (like yellow fever or dengue). The model is spatially structured and its dynamical rules take into account the diffusion of vectors. We consider a bipartite lattice, forming a sub-lattice of human and another occupied by mosquitoes. At each site of lattice we associate a stochastic variable that describes the occupation and the health state of a single individual (mosquito or human). The process of disease transmission in the human population follows a similar dynamic of the Susceptible-Infected-Recovered model (SIR), while the disease transmission in the mosquito population has an analogous dynamic of the Susceptible-Infected-Susceptible model (SIS) with mosquitos diffusion. The occurrence of an epidemic is directly related to the conditional probability of occurrence of infected mosquitoes (human) in the presence of susceptible human (mosquitoes) on neighborhood. The probability of diffusion of mosquitoes can facilitate the formation of pairs Susceptible-Infected enabling an increase in the size of the epidemic. Using an asynchronous dynamic update, we study the disease transmission in a population initially formed by susceptible individuals due to the introduction of a single mosquito (human) infected. We find that this model exhibits a continuous phase transition related to the existence or non-existence of an epidemic. By means of mean field approximations and Monte Carlo simulations we investigate the epidemic threshold and the phase diagram in terms of the diffusion probability and the infection probability.

Experiencias virtuales, una herramienta para enseñar mecanica.

Apresentação oral em palestra semiplenaria do trabalho "Experiencias virtuales, una herramienta para enseñar mecanica".

Regional and socioeconomic distribution of household food availability in Brazil, in 2008-2009

OBJECTIVE: To describe the regional and socioeconomic distribution of household food availability in Brazil. METHODS: Data from the 2008-2009 Household Budget Survey on food and beverage acquisition for household consumption, conducted by the Instituto Brasileiro de Geografia e Estatistica (Brazilian Institute of Geography and Statistics), were analyzed. The amounts of foods, recorded during seven consecutive days in the 55,970 sample households, were converted into calories and nutrients. Food quality indicators were constructed and analyzed according to the regional and socioeconomic strata of the Brazilian population. RESULTS: The amount of energy from protein was adequate in all regional and socioeconomic strata. On the other hand, an excess of free sugars and fats was observed in all regions of the country, especially in the Southern and Southeastern regions. The proportion of saturated fats was high in urban areas and consistent with the greater contribution of animal-derived products. Limited availability of fruits and vegetables was found in all regions. An increase in the fat content and reduction in carbohydrate content of the diet were observed with the increase in income. CONCLUSIONS: The negative characteristics of the Brazilian diet observed at the end of the first decade of the 21(st) century indicate the need to prioritize public policies for the promotion of healthy eating.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

Influence of Goertler vortices spanwise wavelength on heat transfer rates

The boundary layer over concave surfaces can be unstable due to centrifugal forces, giving rise to Goertler vortices. These vortices create two regions in the spanwise direction—the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer toward the wall, increasing the heat transfer rate. The upwash region does the opposite. In the nonlinear development of the Goertler vortices, it can be observed that the upwash region becomes narrow and the spanwise–average heat transfer rate is higher than that for a Blasius boundary layer. This paper analyzes the influence of the spanwise wavelength of the Goertler the heat transfer. The equation is written in vorticity-velocity formulation. The time integration is done via a classical fourth-order Runge-Kutta method. The spatial derivatives are calculated using high-order compact finite difference and spectral methods. Three different wavelengths are analyzed. The results show that steady Goertler flow can increase the heat transfer rates to values close to the values of turbulence, without the existence of a secondary instability. The geometry (and computation domain) are presented

Pair approximation for a model of vertical and horizontal transmission of parasites.

We apply Stochastic Dynamics method for a differential equations model, proposed by Marc Lipsitch and collaborators (Proc. R. Soc. Lond. B 260, 321, 1995), for which the transmission dynamics of parasites occurs from a parent to its offspring (vertical transmission), and by contact with infected host (horizontal transmission). Herpes, Hepatitis and AIDS are examples of diseases for which both horizontal and vertical transmission occur simultaneously during the virus spreading. Understanding the role of each type of transmission in the infection prevalence on a susceptible host population may provide some information about the factors that contribute for the eradication and/or control of those diseases. We present a pair mean-field approximation obtained from the master equation of the model. The pair approximation is formed by the differential equations of the susceptible and infected population densities and the differential equations of pairs that contribute to the former ones. In terms of the model parameters, we obtain the conditions that lead to the disease eradication, and set up the phase diagram based on the local stability analysis of fixed points. We also perform Monte Carlo simulations of the model on complete graphs and Erdös-Rényi graphs in order to investigate the influence of population size and neighborhood on the previous mean-field results; by this way, we also expect to evaluate the contribution of vertical and horizontal transmission on the elimination of parasite. Pair Approximation for a Model of Vertical and Horizontal Transmission of Parasites.

The role of asymmetries in rock-paper-scissors biodiversity models.

The maintenance of biodiversity is a long standing puzzle in ecology. It is a classical result that if the interactions of the species in an ecosystem are chosen in a random way, then complex ecosystems can't sustain themselves, meaning that the structure of the interactions between the species must be a central component on the preservation of biodiversity and on the stability of ecosystems. The rock-paper-scissors model is one of the paradigmatic models that study how biodiversity is maintained. In this model 3 species dominate each other in a cyclic way (mimicking a trophic cycle), that is, rock dominates scissors, that dominates paper, that dominates rock. In the original version of this model, this dominance obeys a 'Z IND 3' symmetry, in the sense that the strength of dominance is always the same. In this work, we break this symmetry, studying the effects of the addition of an asymmetry parameter. In the usual model, in a two dimensional lattice, the species distribute themselves according to spiral patterns, that can be explained by the complex Landau-Guinzburg equation. With the addition of asymmetry, new spatial patterns appear during the transient and the system either ends in a state with spirals, similar to the ones of the original model, or in a state where unstable spatial patterns dominate or in a state where only one species survives (and biodiversity is lost).