Prediction of hyperglycemia in preterm newborn infants

Many conditions are associated with hyperglycemia in preterm neonates because they are very susceptible to changes in carbohydrate homeostasis. The purpose of this study was to evaluate the occurrence of hyperglycemia in preterm infants undergoing glucose infusion during the first week of life, and to enumerate the main variables predictive of hyperglycemia. This prospective study (during 1994) included 40 preterm neonates (gestational age <37 weeks); 511 determinations of glycemic status were made in these infants (average 12.8/infant), classified by gestational age, birth weight, glucose infusion rate and clinical status at the time of determination (based on clinical and laboratory parameters). The clinical status was classified as stable or unstable, as an indication of the stability or instability of the mechanisms governing glucose homeostasis at the time of determination of blood glucose; 59 episodes of hyperglycemia (11.5%) were identified. A case-control study was used (case = hyperglycemia; control = normoglycemia) to derive a model for predicting glycemia. The risk factors considered were gestational age (<=31 vs. >31 weeks), birth weight (<=1500 vs. >1500 g), glucose infusion rate (<=6 vs. >6 mg/kg/min) and clinical status (stable vs. unstable). Multivariate analysis by logistic regression gave the following mathematical model for predicting the probability of hyperglycemia: 1/exp{-3.1437 + 0.5819(GA) + 0.9234(GIR) + 1.0978(Clinical status)} The main predictive variables in our study, in increasing order of importance, were gestational age, glucose infusion rate and, the clinical status (stable or unstable) of the preterm newborn infant. The probability of hyperglycemia ranged from 4.1% to 36.9%.

Population Dynamics Modeling of Arapaima gigas

Pirarucu (Arapaima gigas) has been of the most important natural fishing resources of the Amazon region. Due to its economic importance, and the necessity to preserve the species hand, field research concerning the habits and behavior of the pirarucu has been increasing for the last 20 years. The aim of this paper is to present a mathematical model for the pirarucu population dynamics considering the species peculiarities, particularly the male parental care over the offspring. The solution of the dynamical systems indicates three possible equilibrium points for the population. The first corresponds to extinction; the third corresponds to a stable population close to the environmental carrying capacity. The second corresponds to an unstable equilibrium located between extinction and full use of the carrying capacity. It is shown that lack of males’ parental care closes the gap between the point corresponding to the unstable equilibrium and the point of stable non-trivial equilibrium. If guarding failure reaches a critical point the two points coincide and the population tends irreversibly to extinction. If some event tends to destabilize the population equilibrium, as for instance inadequate parental care, the model responds in such a way as to restore the trajectory towards the stable equilibrium point avoiding the route to extinction. The parameters introduced to solve the system of equations are partially derived from limited but reliable field data collected at the Mamirauá Sustainable Development Reserve (MSDR) in the Brazilian Amazonian Region.

Contribution to the marine propeller hydrodynamic design for small boats in the Amazon region

ABSTRACTIn the Amazon, river navigation is very important due to the length of navigable rivers and the lack of alternative road networks. Boats usually operate in unfavorable conditions, since there is no hydrodynamic relation among propellers, geometry, and the dimensions of the boat hull. Currently, there is no methodology for propeller hydrodynamic optimization with low computational cost and easy implementation in the region. The aim of this work was to develop a mathematical approach for marine propeller design applied to boats typically found on Amazon rivers. We developed an optimized formulation for the chord and pitch angle distributions, taking into account the classical model of Glauert. A theoretical analysis for the thrust and torque relationships on an annular control volume was performed. The mathematical model used was based on the Blade Element Momentum Theory (BEMT). We concluded that the new methodology proposed in this work demonstrates a good physical behavior when compared with the theory of Glauert and the experimental data of the Wageningen B3-50 propeller.

Sôbre um sistema de equações relativas a um modêlo matemático de populações de Himenópteros endogâmicos

This paper deals with the solution of a system of equations relating with a mathematical model of populations of endogamic Hymenoptera. The Author proves that, unless inequality (5.1) 4R5 + 8R R4 - 4R R³ + 8R² (R -1) R² - A a A a A a a A - R² (4R² + 4R - 1) R +2R³ < 0 a a A a is satisfied, one of the genes is eliminated from the population. He shows that the relative frequencies of different kinds of matings in the population can be obtained when the root R between zero and VRa of equation 2R4 + 2R³ -2R² (RA + Ra) - R(RA +Ra) + 2RA Ra =0 is known. In special, if we let b = RA / Ra > 1 , inequation (5.1) shows that we must have __________________ b³ + 2b² + b + V2b4 + 2b³ - 2b² + 2b Ra < __________________________________ = f(b) 2 (b4 + 2b³ + 2b - 1) The greatest value of f (b) is 0,75 and is obtained for b = 1, that is for RA = Ra.

Economic threshold levels for the velvetbean caterpillar on soybeans in Brazil: the social and the private perspectives

Pest Control is treated as a economic problem. The social and the private perspectives differ due to the consideration of the environmental and social impacts as well as technical aspects such as resistance, resurgence and secondary pests. A mathematical model is developed to determine and compare the social and the private optimum control strategies (which define the Economic Thereshold Levels) for the velvetbean caterpillar on soybeans in Brazil. The crop/pest system incorporates effects of predators and parasites, the soybean natural capacity to compensate for injury and the pesticide effects on both pests and its natural enemies; in the social case, the environmental and social impacts and the effects of pest resistance to the pesticide are incorporated. Consideration of density dependence, weather effects, randomnes of pest attack and risk aversion are discussed. The results can be compared with current control practices and IPM programme recomendations.

The feasibility of forecasting influenza epidemics in Cuba

A large influenza epidemic took place in Havana during the winter of 1988. The epidemiologic surveillance unit of the Pedro Kouri Institute of Tropical Medicine detected the begining of the epidemic wave. The Rvachev-Baroyan mathematical model of the geographic spread of an epidemic was used to forecast this epidemic under routine conditions of the public health system. The expected number of individuals who would attend outpatient services, because of influenza-like illness, was calculated and communicated to the health authorities within enough time to permit the introduction of available control measures. The approximate date of the epidemic peak, the daily expected number of individuals attending medical services, and the approximate time of the end of the epidemic wave were estimated. The prediction error was 12%. The model was sufficienty accurate to warrant its use as a pratical forecasting tool in the Cuban public health system.

The stabilizing effects of the acquired immunity on the schistosomiasis transmission modeling - the sensitivity Analysis

A mathematical model is proposed to analyze the effects of acquired immunity on the transmission of schistosomiasis in the human host. From this model the prevalence curve dependent on four parameters can be obtained. These parameters were estimated fitting the data by the maximum likelihood method. The model showed a good retrieving capacity of real data from two endemic areas of schistosomiasis: Touros, Brazil (Schistosoma mansoni) and Misungwi, Tanzania (S. haematobium). Also, the average worm burden per person and the dispersion of parasite per person in the community can be obtained from the model. In this paper, the stabilizing effects of the acquired immunity assumption in the model are assessed in terms of the epidemiological variables as follows. Regarded to the prevalence curve, we calculate the confidence interval, and related to the average worm burden and the worm dispersion in the community, the sensitivity analysis (the range of the variation) of both variables with respect to their parameters is performed.

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

The risk of acquiring the new influenza A(H1N1) for Brazilian travelers to Chile, Argentina and the USA

We estimate the risk of acquiring the new influenza A(H1N1) for Brazilian travelers to Chile, Argentina and the USA. This is done by a mathematical model that quantifies the intensity of transmission of the new virus in those countries and the probability that one individual has of acquiring the influenza depending on the date of arrival and time spent in the area. The maximum estimated risk reached 7.5 cases per 10,000 visitors to Chile, 17 cases per 10,000 travelers to Argentina and 23 cases per 10,000 travelers to the USA. The estimated number of imported cases until 27 July is 57 ± 9 from Chile, 136 ± 27 from the USA and 301 ± 21 from Argentina, which are in accord with the official figures. Estimating the number of imported cases was particularly important for the moment of the disease introduction into this country, but it will certainly be important again as a tool to calculate the number of future imported cases from northern countries in our next inter-epidemic season, were imported cases can constitute again the majority of the new influenza burden to the Brazilian health services.

Projecting the effectiveness of RotaTeq® against rotavirus-related hospitalisations in Brazil

RotaTeq® (Merck & Company, Inc, Whitehouse Station, NJ, USA) is an oral pentavalent rotavirus vaccine (RV5) that has shown high and consistent efficacy in preventing rotavirus gastroenteritis (RGE) in randomised clinical trials previously conducted in industrialised countries with high medical care resources. To date, the efficacy and effectiveness data for RV5 are available in some Latin American countries, but not Brazil. In this analysis, we projected the effectiveness of RV5 in terms of the percentage reduction in RGE-related hospitalisations among children less than five years of age in four regions of Brazil, using a previously validated mathematical model. The model inputs included hospital-based rotavirus surveillance data from Goiânia, Porto Alegre, Salvador and São Paulo from 2005-2006, which provided the proportions of rotavirus attributable to serotypes G1, G2, G3, G4 and G9, and published rotavirus serotype-specific efficacy from the Rotavirus Efficacy and Safety Trial. The model projected an overall percentage reduction of 93% in RGE-related hospitalisations, with an estimated annual reduction in RGE-related hospitalisations between 42,991-77,383 in the four combined regions of Brazil. These results suggest that RV5 could substantially prevent RGE-related hospitalisations in Brazil.

Potential impact of a presumed increase in the biting activity of dengue-virus-infected Aedes aegypti (Diptera: Culicidae) females on virus transmission dynamics

Recently, we showed that infection with dengue virus increases the locomotor activity of Aedes aegypti females. We speculate that the observed increased locomotor activity could potentially increase the chances of finding a suitable host and, as a consequence, the relative biting rate of infected mosquitoes. We used a mathematical model to investigate the impact of the increased locomotor activity by assuming that this activity translated into an increased biting rate for infected mosquitoes. The results show that the increased biting rate resulted in dengue outbreaks with greater numbers of primary and secondary infections and with more severe biennial epidemics.

Dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus (Diptera, Culicidae) by Bacillus thuringiensis var israelensis, related with temperature, density and concentration of insecticide

The dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus, (Diptera, Culicidae) by Bacillus thuringiensis var israelensis has been related with the temperature, density and concentration of the insecticide. A mathematical model for biological control of Aedes aegypti with Bacillus thuringiensis var israelensis (Bti) was constructed by using data from the literature regarding the biology of the vector. The life cycle was described by differential equations. Lethal concentrations (LC50 and LC95) of Bti were determined in the laboratory under different experimental conditions. Temperature, colony, larvae density and bioinsecticide concentration presented marked differences in the analysis of the whole set of variables; although when analyzed individually, only the temperature and concentration showed changes. The simulations indicated an inverse relationship between temperature and mosquito population, nonetheless, faster growth of populations is reached at higher temperatures. As conclusion, the model suggests the use of integrated control strategies for immature and adult mosquitoes in order to achieve a reduction of Aedes aegypti.

Spatial variability of the chemical, physical and biological properties in lowland cultivated with irrigated rice

In the areas where irrigated rice is grown in the south of Brazil, few studies have been carried out to investigate the spatial variability structure of soil properties and to establish new forms of soil management as well as determine soil corrective and fertilizer applications. In this sense, this study had the objective of evaluating the spatial variability of chemical, physical and biological soil properties in a lowland area under irrigated rice cultivation in the conventional till system. For this purpose, a 10 x 10 m grid of 100 points was established, in an experimental field of the Embrapa Clima Temperado, in the County of Capão do Leão, State of Rio Grande do Sul. The spatial variability structure was evaluated by geostatistical tools and the number of subsamples required to represent each soil property in future studies was calculated using classical statistics. Results showed that the spatial variability structure of sand, silt, SMP index, cation exchange capacity (pH 7.0), Al3+ and total N properties could be detected by geostatistical analysis. A pure nugget effect was observed for the nutrients K, S and B, as well as macroporosity, mean weighted diameter of aggregates, and soil water storage. The cross validation procedure, based on linear regression and the determination coefficient, was more efficient to evaluate the quality of the adjusted mathematical model than the degree of spatial dependence. It was also concluded that the combination of classical with geostatistics can in many cases simplify the soil sampling process without losing information quality.

ORGANIC PHOSPHORUS FRACTIONS IN SOIL FERTILIZED WITH CATTLE MANURE

Inorganic phosphorus (Pi) usually controls the P availability in tropical soils, but the contribution of organic P (Po) should not be neglected, mainly in systems with low P input or management systems that promote organic matter accumulation. The aims of this study were to evaluate the changes in the Po fractions over time in soil fertilized and not fertilized with cattle manure and to correlate Po forms with available P extracted by anion exchange resin. The experiment was carried out under field conditions, in a sandy-clay loam Haplustox. The experimental design was a 2 × 9 randomized complete block factorial design, in which the first factor was manure application (20 t ha-1) or absence, and the second the soil sampling times (3, 7, 14, 21, 28, 49, 70, 91, and 112 days) after manure incorporation. Labile, moderately labile and non-labile Po fractions were determined in the soil material of each sampling. Manure fertilization increased the Po levels in the moderately labile and non-labile fractions and the total organic P, but did not affect the Po fraction proportions in relation to total organic P. On average, 5.1 % of total Po was in the labile, 44.4 % in the moderately labile and 50.5 % in the non-labile fractions. Available P (resin P) was more affected by the manure soluble Pi rather than by the labile Po forms. The labile and non-labile Po fractions varied randomly with no defined trend in relation to the samplings; for this reason, the data did not fit any mathematical model.

Adsorção de íons Cu2+ em latossolo vermelho-amarelo húmico

In environmental studies it is necessary to know the adsorption behavior of metals by soils, since the unfavorable effects of heavy metals and even the micronutrients at high concentrations in the environment are related to these adsorbents' ability to immobilize them. A sample of a humic yellow red oxisol from Araponga region in the State of Minas Gerais, Brazil, was used to verify the adsorption behavior of Cu2+ ions in this substrate. The mathematical model described by Langmuir's adsorption equation in its linearized form was applied and the values of the maximum capacity b and those of the constant related to the bonding energy a were obtained. Aliquots of copper nitrate solutions containing several concentrations of this metal were added to soil samples, the pH being predetermined for developing the adsorption experiments. The chemical and physical characterization of soil sample were performed by determining the organic carbon, nitrogen and phosphorus concentrations, cation exchange capacity (CEC), pH, concentration of metals (Al, Fe, K, Mg, Ca, Zn, Cu, Ni, Cr, Co, Pb, and Cd), granulometric analysis and X-ray diffraction. Langmuir isotherms presented two distinct adsorption regions at both pH 4 and pH 5, showing that the adsorptive phenomenon occurs in two distinct stages. The adsorption sites for the lower part presented greater bonding energy and low adsorption capacity compared with the adsorption sites of the part of the curve corresponding to higher Cu concentrations in the equilibrating solution.