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.

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Mathematical equation correction to spectral and transport interferences in high-resolution continuum source flame atomic absorption spectrometry: determination of lead in phosphoric acid

In this work, a new mathematical equation correction approach for overcoming spectral and transport interferences was proposed. The proposal was applied to eliminate spectral interference caused by PO molecules at the 217.0005 nm Pb line, and the transport interference caused by variations in phosphoric acid concentrations. Correction may be necessary at 217.0005 nm to account for the contribution of PO, since Atotal217.0005 nm = A Pb217.0005 nm + A PO217.0005 nm. This may be easily done by measuring other PO wavelengths (e.g. 217.0458 nm) and calculating the relative contribution of PO absorbance (A PO) to the total absorbance (Atotal) at 217.0005 nm: A Pb217.0005 nm = Atotal217.0005 nm - A PO217.0005 nm = Atotal217.0005 nm - k (A PO217.0458 nm). The correction factor k is calculated from slopes of calibration curves built up for phosphorous (P) standard solutions measured at 217.0005 and 217.0458 nm, i.e. k = (slope217.0005 nm/slope217.0458 nm). For wavelength integrated absorbance of 3 pixels, sample aspiration rate of 5.0 ml min-1, analytical curves in the 0.1 - 1.0 mg L-1 Pb range with linearity better than 0.9990 were consistently obtained. Calibration curves for P at 217.0005 and 217.0458 nm with linearity better than 0.998 were obtained. Relative standard deviations (RSD) of measurements (n = 12) in the range of 1.4 - 4.3% and 2.0 - 6.0% without and with mathematical equation correction approach were obtained respectively. The limit of detection calculated to analytical line at 217.0005 nm was 10 µg L-1 Pb. Recoveries for Pb spikes were in the 97.5 - 100% and 105 - 230% intervals with and without mathematical equation correction approach, respectively.

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.

Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I-100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Mathematical modeling applied to the growth of tilapia in net cages in the sub middle of the São Francisco river

This study aimed to apply mathematical models to the growth of Nile tilapia (Oreochromis niloticus) reared in net cages in the lower São Francisco basin and choose the model(s) that best represents the conditions of rearing for the region. Nonlinear models of Brody, Bertalanffy, Logistic, Gompertz, and Richards were tested. The models were adjusted to the series of weight for age according to the methods of Gauss, Newton, Gradiente and Marquardt. It was used the procedure "NLIN" of the System SAS® (2003) to obtain estimates of the parameters from the available data. The best adjustment of the data were performed by the Bertalanffy, Gompertz and Logistic models which are equivalent to explain the growth of the animals up to 270 days of rearing. From the commercial point of view, it is recommended that commercialization of tilapia from at least 600 g, which is estimated in the Bertalanffy, Gompertz and Logistic models for creating over 183, 181 and 184 days, and up to 1 Kg of mass , it is suggested the suspension of the rearing up to 244, 244 and 243 days, respectively.

Mathematical simulation parameters for drying of cassava starch pellets

Based on experimental tests, it was obtained the equations for drying, equilibrium moisture content, latent heat of vaporization of water contained in the product and the equation of specific heat of cassava starch pellets, essential parameters for realizing modeling and mathematical simulation of mechanical drying of cassava starch for a new technique proposed, consisting of preformed by pelleting and subsequent artificial drying of starch pellets. Drying tests were conducted in an experimental chamber by varying the air temperature, relative humidity, air velocity and product load. The specific heat of starch was determined by differential scanning calorimetry. The generated equations were validated through regression analysis, finding an appropriate correlation of the data, which indicates that by using these equations, can accurately model and simulate the drying process of cassava starch pellets.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

A mathematical framework for group analysis of von Willebrand factor multimeric composition following luminography

The objective of the present study was to establish a method for quantitative analysis of von Willebrand factor (vWF) multimeric composition using a mathematical framework based on curve fitting. Plasma vWF multimers from 15 healthy subjects and 13 patients with advanced pulmonary vascular disease were analyzed by Western immunoblotting followed by luminography. Quantitative analysis of luminographs was carried out by calculating the relative densities of low, intermediate and high molecular weight fractions using laser densitometry. For each densitometric peak (representing a given fraction of vWF multimers) a mean area value was obtained using data from all group subjects (patients and normal individuals) and plotted against the distance between the peak and IgM (950 kDa). Curves were constructed for each group using nonlinear fitting. Results indicated that highly accurate curves could be obtained for healthy controls and patients, with respective coefficients of determination (r²) of 0.9898 and 0.9778. Differences were observed between patients and normal subjects regarding curve shape, coefficients and the region of highest protein concentration. We conclude that the method provides accurate quantitative information on the composition of vWF multimers and may be useful for comparisons between groups and possibly treatments.

Mathematical modeling of electro-rotation spectra of small particles in liquid solutions: Application to human erythrocyte aggregates

Electro-rotation can be used to determine the dielectric properties of cells, as well as to observe dynamic changes in both dielectric and morphological properties. Suspended biological cells and particles respond to alternating-field polarization by moving, deforming or rotating. While in linearly polarized alternating fields the particles are oriented along their axis of highest polarizability, in circularly polarized fields the axis of lowest polarizability aligns perpendicular to the plane of field rotation. Ellipsoidal models for cells are frequently applied, which include, beside sphere-shaped cells, also the limiting cases of rods and disks. Human erythrocyte cells, due to their particular shape, hardly resemble an ellipsoid. The additional effect of rouleaux formation with different numbers of aggregations suggests a model of circular cylinders of variable length. In the present study, the induced dipole moment of short cylinders was calculated and applied to rouleaux of human erythrocytes, which move freely in a suspending conductive medium under the effect of a rotating external field. Electro-rotation torque spectra are calculated for such aggregations of different length. Both the maximum rotation speeds and the peak frequencies of the torque are found to depend clearly on the size of the rouleaux. While the rotation speed grows with rouleaux length, the field frequency nup is lowest for the largest cell aggregations where the torque shows a maximum.

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 ± 2.63 years old) and 16 postmenopausal (57 ± 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg-1 min-1), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg-1 min-1) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (r s = 0.75) and VCO2 (r s = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.