Application of mathematical models for the prediction of adsorption isotherms in solid mixture for mango powder refreshment

Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.

Mathematical models to describe the volumetric shrinkage rate of red beans during drying

The present study aimed to determine the volumetric shrinkage rate of bean (Phaseolus vulgaris L.) seeds during air-drying under different conditions of air, temperature and relative humidity, and to adjust several mathematical models to the empiric values observed, and select the one that best represents the phenomenon. Six mathematical models were adjusted to the experimental values to represent the phenomenon. It was determined the degree of adjustment of each model from the value of the coefficient of determination, the behavior of the distribution of the residuals, and the magnitude of the average relative and estimated errors. The rate of volumetric shrinkage that occurred in bean seeds during drying is between 25 and 37%. It basically depends on the final moisture content, regardless of the air conditions during drying. The Modified Bala & Woods' model best represented the process.

Extraction of soil water by plants: development and validation of a model

A quantitative model of water movement within the immediate vicinity of an individual root is developed and results of an experiment to validate the model are presented. The model is based on the assumption that the amount of water transpired by a plant in a certain period is replaced by an equal volume entering its root system during the same time. The model is based on the Darcy-Buckingham equation to calculate the soil water matric potential at any distance from a plant root as a function of parameters related to crop, soil and atmospheric conditions. The model output is compared against measurements of soil water depletion by rice roots monitored using γ-beam attenuation in a greenhouse of the Escola Superior de Agricultura "Luiz de Queiroz"/Universidade de São Paulo(ESALQ/USP) in Piracicaba, State of São Paulo, Brazil, in 1993. The experimental results are in agreement with the output from the model. Model simulations show that a single plant root is able to withdraw water from more than 0.1 m away within a few days. We therefore can assume that root distribution is a less important factor for soil water extraction efficiency.

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Models and applications for risk assessment and prediction of Asian soybean rust epidemics

Asian rust of soybean [Glycine max (L.) Merril] is one of the most important fungal diseases of this crop worldwide. The recent introduction of Phakopsora pachyrhizi Syd. & P. Syd in the Americas represents a major threat to soybean production in the main growing regions, and significant losses have already been reported. P. pachyrhizi is extremely aggressive under favorable weather conditions, causing rapid plant defoliation. Epidemiological studies, under both controlled and natural environmental conditions, have been done for several decades with the aim of elucidating factors that affect the disease cycle as a basis for disease modeling. The recent spread of Asian soybean rust to major production regions in the world has promoted new development, testing and application of mathematical models to assess the risk and predict the disease. These efforts have included the integration of new data, epidemiological knowledge, statistical methods, and advances in computer simulation to develop models and systems with different spatial and temporal scales, objectives and audience. In this review, we present a comprehensive discussion on the models and systems that have been tested to predict and assess the risk of Asian soybean rust. Limitations, uncertainties and challenges for modelers are also discussed.

Growth and development of honey weed based on days or thermal units

This work was carried out with the objective of evaluating the growth and development of honey weed (Leonurus sibiricus) based on days or thermal units (growing degree days). Thus, two independent trials were developed to quantify the phenological development and total dry mass accumulation in increasing or decreasing photoperiod conditions. Considering only one growing season, honey weed phenological development was perfectly fit to day scale or growing degree days, but with no equivalence between seasons, with the plants developing faster at increasing photoperiods, and flowering 100 days after seeding. Even day-time scale or thermal units were not able to estimate general honey weed phenology during the different seasons of the year. In any growing condition, honey weed plants were able to accumulate a total dry mass of over 50 g per plant. Dry mass accumulation was adequately fit to the growing degree days, with highlights to a base temperature of 10 ºC. Therefore, a higher environmental influence on species phenology and a lower environmental influence on growth (dry mass) were observed, showing thereby that other variables, such as the photoperiod, may potentially complement the mathematical models.

Initial growth and development of southern sandbur based on thermal units

Availability of basic information on weed biology is an essential tool for designing integrated management programs for agricultural systems. Thus, this study was carried out in order to calculate the base temperature (Tb) of southern sandbur (Cenchrus echinatus), as well as fit the initial growth and development of the species to accumulated thermal units (growing degree days - GDD). For that purpose, experimental populations were sown six times in summer/autumn conditions (decreasing photoperiod) and six times in winter/spring condition (increasing photoperiod). Southern sandbur phenological evaluations were carried out, on alternate days, and total dry matter was measured when plants reached the flowering stage. All the growth and development fits were performed based on thermal units by assessing five base temperatures, as well as the absence of it. Southern sandbur development was best fit with Tb = 12 ºC, with equation y = 0,0993x, where y is the scale of phenological stage and x is the GDD. On average, flowering was reached at 518 GDD. Southern sandbur phenology may be predicted by using mathematical models based on accumulated thermal units, adopting Tb = 12 ºC. However, other environmental variables may also interfere with species development, particularly photoperiod.

Growth and development of sourgrass based on days or thermal units

This work was carried out with the objective of evaluating growth and development of sourgrass (Digitaris insularis) based on days or thermal units (growing degree days - GDD). Two independent trials were developed aiming to quantify the species' phenological development and total dry matter accumulation in increasing or decreasing photoperiod conditions. Plants were grown in 4 L plastic pots, filled with commercial substrate, adequately fertilized. In each trial, nine growth evaluations were carried out, with three replicates. Phenological development of sourgrass was correctly fit to time scale in days or GDD, through linear equation of first degree. Sourgrass has slow initial growth, followed by exponential dry matter accumulation, in increasing photoperiod condition. Maximum total dry matter was 75 and 6 g per plant for increasing and decreasing photoperiod conditions, respectively. Thus, phenological development of sourgrass may be predicted by mathematical models based on days or GDD; however, it should be noted that other environmental variables interfere on the species' growth (mass accumulation), especially photoperiod.

Experimental results and modeling of poultry carcass cooling by water immersion

Poultry carcasses have to be chilled to reduce the central breast temperatures from approximately 40 to 4 °C, which is crucial to ensure safe products. This work investigated the cooling of poultry carcasses by water immersion. Poultry carcasses were taken directly from an industrial processing plant and cooled in a pilot chiller, which was built to investigate the influence of the method and the water stirring intensity on the carcasses cooling. A simplified empiric mathematical model was used to represent the experimental results. These results indicated clearly that the understanding and quantification of heat transfer between the carcass and the cooling water is crucial to improve processes and equipment. The proposed mathematical model is a useful tool to represent the dynamics of carcasses cooling, and it can be used to compare different chiller operational conditions in industrial plants. Therefore, this study reports data and a simple mathematical tool to handle an industrial problem with little information available in the literature.

Drying kinetics of jatropha seeds

Given the necessity of developing jatropha cultivation equipment, this work adjusted different mathematical models to experimental data obtained from the drying of jatropha seeds submitted to different drying conditions and selected the best model to describe the drying process. The experiment was carried out at the Federal Institute of Goiás - Rio Verde Campus. Seeds with initial moisture content of approximately 0.50 (kg water/kg dry matter) were dried in a forced air-ventilated oven, at temperatures of 45, 60, 75, 90 and 105°C to moisture content of 0.10 ± 0.005 (kg water/kg dry matter). The experimental data were adjusted to 11 mathematical models to represent the drying process of agricultural products. The models were compared using the coefficient of determination, chi-square test, relative mean error, estimated mean error and residual distribution. It was found that the increase in the air temperature caused a reduction in the drying time of seeds. The models Midilli and Two Terms were suitable to represent the drying process of Jatropha seeds and between them the use of the Midili model is recommended due to its greater simplicity.

Dengue and the risk of urban yellow fever reintroduction in São Paulo State, Brazil

OBJECTIVE: To propose a mathematical method for the estimation of the Basic Reproduction Number, R0, of urban yellow fever in a dengue-infested area. METHODS: The method is based on the assumption that, as the same vector (Aedes aegypti) causes both infections, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic, could be applied to yellow fever dynamics. It is demonstrated that R0 for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period. RESULTS: In this study the analysis was expanded to the epidemiological situation of dengue in São Paulo in the year 2001. The total number of dengue cases increased from 3,582 in 2000 to 51,348 in 2001. It was then calculated R0 for yellow fever for every city which have shown R0 of dengue greater than 1. It was also estimated the total number of unprotected people living in highly risky areas for urban yellow fever. CONCLUSIONS: Currently there is a great number of non-vaccinated people living in Aedes aegypti infested area in the state of São Paulo.

Pertussis booster vaccine for adolescents and young adults in São Paulo, Brazil

OBJECTIVE: To develop a model to assess different strategies of pertussis booster vaccination in the city of São Paulo. METHODS: A dynamic stationary age-dependent compartmental model with waning immunity was developed. The "Who Acquires Infection from Whom" matrix was used to modeling age-dependent transmission rates. There were tested different strategies including vaccine boosters to the current vaccination schedule and three of them were reported: (i) 35% coverage at age 12, or (ii) 70% coverage at age 12, and (iii) 35% coverage at age 12 and 70% coverage at age 20 at the same time. RESULTS: The strategy (i) achieved a 59% reduction of pertussis occurrence and a 53% reduction in infants while strategy (ii) produced 76% and 63% reduction and strategy (iii) 62% and 54%, respectively. CONCLUSION: Pertussis booster vaccination at age 12 proved to be the best strategy among those tested in this study as it achieves the highest overall reduction and the greatest impact among infants who are more susceptible to pertussis complications.

Toxicological and toxicogenetic effects of plants used in popular medicine and in cattle food

Toxicological and toxicogenetic effects of aqueous (tea) and hexanica fruit extract of Indigofera suffruticosa Mill, and hydroalcoholic root extract od Solanum agrarium Stendt. Were evaluated in Balb C male mice intraperitoneally exposed. A hepatotoxic effect was observed just for animals treated with aqueous fruit extract of I. suffruticosa. In relation to the toxicogenetic effect, just the group trreated with 12.5% of toxic dose of aqueous fruit extract of I. suffruticosa showed a statistically significant increase in the frequency of cells with chromosome aberrations (cytogenetic effect), although a slight increase was also observed for the highest dose (25% of LF50_ of hydroalcoholic root extract of S. agrarium. The results obtanied show that before S. agrarium is used as medicine and before the wide use of I. suffruticosa in cattle food, careful evaluation must be done.

Pharmacological screening of plants recommended by folk medicine as anti-snake venom: I. Analgesic and anti-inflammatory activities

We have observed that several plants used popularly as anti-snake venom show anti-inflammatory activity. From the list prepared by Rizzini, Mors and Pereira some species have been selected and tested for analgesic activity (number of contortions) and anti-inflammatory activity (Evans blue dye diffusion - 1% solution) according to Whittle's technique (intraperitoneal administration of 0.1 N-acetic acid 0.1 ml/10 g) in mice. Previous oral administration of a 10% infusion (dry plant) or 20% (fresh plant) corresponding to 1 or 2 g/Kg of Apuleia leiocarpa, Casearia sylvestris, Brunfelsia uniflora, Chiococca brachiata, Cynara scolymus, Dorstenia brasiliensis, Elephantopus scaber, Marsypianthes chamaedrys, Mikania glomerata and Trianosperma tayuya demonstrated analgesic and/or anti-inflammatory activities of varied intensity