Richards Model Research Articles

Descripción de la curva de crecimiento de pavos locales usando modelos no lineales

Objetivo. Determinar el modelo no lineal que mejor ajuste la curva de crecimiento de pavos locales criados en confinamiento. Material y métodos. Veinticuatro y 43 pavos hembras y machos, respectivamente, criados en confinamiento fueron alimentados con dietas comerciales. Cada animal se pesó desde el nacimiento hasta la semana 29 de edad. Los modelos de Gompertz, Brody, Richards, von Bertalanffy y Logístico fueron elegidos para describir la relación edad-peso. El mejor modelo se seleccionó con base en el coeficiente de determinación (R2), el criterio de información de Akaike (AIC) y el análisis visual de las curvas observadas y predichas. Resultados. El mejor ajuste (machos y hembras) correspondió al modelo von Bertalanffy. El más alto valor del parámetro A (edad a la madurez), para hembras y machos correspondió al modelo von Bertalanffy, seguido de Gompertz y Logístico. El estimador A fue mayor para machos que hembras. El mayor valor del parámetro k (tasa de madurez), para hembras y machos, variaron según el modelo utilizado. Los valores de k fueron más altos para hembras que para machos. La edad al punto de inflexión (TI) y peso vivo al punto de inflexión (WI) también variaron de un modelo a otro. Los valores más altos de TI y WI correspondieron al modelo Logístico. Entre sexos, los valores mayores de TI y WI correspondieron a los machos. Conclusiones. El mejor modelo que describió la curva de crecimiento de los pavos locales fue el de von Bertalanffy.

Morphometric Models of Growth in Ornate Box Turtles (Terrapene ornata ornata) as Related to Growth Rings

Few studies document early growth of hatchling turtles. We fit growth models to 606 carapace length (CL) measurements of ornate box turtles (Terrapene ornata ornata) for 231 males, 226 females, and 53 individuals of undetermined sex. We used the Richards model to fit 95% confidence bands and 95% prediction bands on the best-fit curves for males and females. We also computed Spearman's rho correlation relating growth ring counts to CL and plotted change in CL for 131 recaptured individuals (45 males, 57 females, and 29 individuals of undetermined sex) for which we had two or more measurements from different years. There was a strong correlation between CL and number of growth rings. Using the properties of the derivative of Richards growth model, juvenile 1, juvenile 2, subadult, and adult stages were defined for male and female growth. Our overall growth models were similar to those for studies of ornate box turtles in Kansas and South Dakota and the desert box turtle (T. o. luteola) in New Mexico; however, our growth stages were defined by smaller turtles. Unlike a previous study in South Dakota, our adult males were larger than adult females. Prior to a CL of approximately 86 mm and 8 growth rings, the carapace grew faster than the plastron, after which the plastron grew faster than the carapace. Five hatchlings' plastra grew an average of 26% (SD = 14%) the first year and the carapace grew an average of 15% (SD = 7%). During the first 3 yrs, most individuals developed only one growth ring per year. If major growth rings approximate age, size can be used to estimate age in ornate box turtles up to 60–90 mm (about 8 growth rings). Between 8 and 12 growth rings, size and age are also correlated, but accuracy of age estimates decreases. Life-history traits such as age at reproductive maturation and size at which individuals are vulnerable to predation are important to assess long-term viability of a population; therefore, understanding environmental impacts on individual growth is important for conservation planning and management of this threatened species in Iowa.

Modelling and genetic evaluation of Markhoz goat growth curve parameters

The objectives of our study were to compare different non-linear mixed effect models (Brody, Von Bertalanffy, Richards, Gompertz and Logistic) for best description the growth patterns of Markhoz kids, evaluate the influence of environmental (fixed) effects on growth curve parameters of the best-fit growth model and finally estimate the genetic parameters for growth curve characteristics. Live weights of 3678 individuals from the historical archives of the Markhoz Goat Performance Testing Station (in Sanandaj), which were collected from birth to 365 days of age during 1992 to 2015, were used in the analysis. Models were fitted according to the stochastic approximation expectation-maximization (SAEM) procedure implemented in R package SAEMIX. All studied mixed models described the growth pattern in Markhoz goat, except Richards model. However, the Brody model best fit the data. The analysis of variance on the growth curve parameters (at the individual level) showed that among the fixed effects (i.e., sex, birth type, age of dam and year of birth) for the Brody model, only age of dam had no effect on any of the growth parameters. Estimates of heritability for growth curve parameters were low, with 0.067 ± 0.011, 0.063 ± 0.010 and 0.044 ± 0.001 for mature weight (a), constant of integration (b) and rate of maturing (k), respectively. Low heritability estimates suggest that the environment is not favorable for expression of genetic potential of Markhoz kids. The negative genetic (−0.866 ± 0.000) and phenotypic (−0.723 ± 0.008) correlations between the parameters a and k indicates that animals with lower growth rates are more likely to reach higher weight values when adults.

The Effect of Religion Intervention on Life Satisfaction and Depression in Elderly with Heart Failure.

The elderly suffering from heart failure is facing with some problems such as lowering of life satisfaction and depression. Regarding a lack of information in this issue, the current study was conducted to determine the effect of religion intervention on life satisfaction and depression in the elderly with heart failure, in Ilam-Iran. In a clinical trial study conducted on the elderly with heart failure disease in Ilam-Iran, the patients were randomly allocated into two experimental (46) and control (47) groups. The used instruments were a demographic checklist, life satisfaction questionnaire of LSI-Z and Beck depression inventory. The intervention done for test group was a religion-spiritual program designed based on the Richards and Bergin model, and according to Islam and Shia regulations and conducted during six sessions, each 30-45min. The tools were completed before and after intervention. Gathered data were entered into SPSS software and analyzed by descriptive (mean and standard deviation) and inferential (independent t test and ANOVA) statistics. The results showed that there was no significant difference between the mean (SD) of life satisfaction in the experimental group [5.47 (3.37)] and control [5.85 (3.92)] before the intervention (P = 0.62) but after the intervention. The mean (SD) of life satisfaction of the test group [8.08 (4.36)] was higher than that of the control group [5.55 (3.96)] (P = 0.006). Also, no significant difference between the mean (SD) of depression in the experimental group [47.80 (10.48)] and control [49.87 (11.40)] before the intervention (P = 0.62) but after the intervention. The mean (SD) of depression of the test group [28.28 (14.78)] was lower than that of the control group [50.44 (14.02)] (P = 0.006). Regarding the positive effect of religion-spiritual program in depression and life satisfaction of the elderly with heart failure, it is suggested this program will be educated to these patients by health-care workers.

Modelling of growth alteration in Japanese quail after a selection experiment for body weight at 4 weeks of age

AbstractThe current study investigated the influence of selection for body weight (BW) on growth curve parameters in two lines of Japanese quail through a mixed model approach. Live BWs of 1400 Japanese quail were recorded at 3-day intervals from hatching to 42 days of age. Birds were distributed equally across lines (selected and control) and sexes (male and female). The asymptotic weight parameter (β0) values were always higher in Gompertz than Richards models in both lines. The values ofβ0were higher in the selected than control lines and in females than males across models. Differences were found in the inflection point for age and weight across lines and sexes. Values of the growth rate parameter (β2) ranged from 0.06 to 0.10 in both models, favouring males over females in both lines. Lower weights at the inflection point of both models were observed in the control line. Determination coefficient (R2) of both models in different genetic groups and sexes was similar. Mean square error (MSE) values of the Gompertz model were lower for females in selectedv.control lines. In contrast, MSE values of the Richards model were lower for selected malesv.control males. According to the criteria of choice (highestR2and lowest MSE, Akaike information criterion and Bayesian information criterion), the Richards model was considered the best fitting model for the growth data of males, while the Gompertz model was the best for growth data of female quails in both lines.

An existence result for a constrained two-phase transition model with metastable phase for vehicular traffic

In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called metastable phase. The model is given by the Lighthill–Whitham–Richards model in the free-flow phase and by the Aw–Rascle–Zhang model in the congested phase. In particular, we study the existence of solutions to Cauchy problems satisfying a local point constraint on the density flux. We prove that if the constraint F is higher than the minimal flux \(f_\mathrm{c}^-\) of the metastable phase, then constrained Cauchy problems with initial data of bounded total variation admit globally defined solutions. We also provide sufficient conditions on the initial data that guarantee the global existence of solutions also in the case \(F < f_\mathrm{c}^-\). These results are obtained by applying the wave-front tracking technique.

Evaluation of Model Concepts to Describe Water Transport in Shallow Subsurface Soil and Across the Soil\u2013Air Interface

Soil water evaporation plays a critical role in mass and energy exchanges across the land–atmosphere interface. Although much is known about this process, there is no agreement on the best modeling approaches to determine soil water evaporation due to the complexity of the numerical modeling scenarios and lack of experimental data available to validate such models. Existing studies show numerical and experimental discrepancies in the evaporation behavior and soil water distribution in soils at various scales, driving us to revisit the key process representation in subsurface soil. Therefore, the goal of this work is to test different mathematical formulations used to estimate evaporation from bare soils to critically evaluate the model formulations, assumptions and surface boundary conditions. This comparison required the development of three numerical models at the REV scale that vary in their complexity in characterizing water flow and evaporation, using the same modeling platform. The performance of the models was evaluated by comparing with experimental data generated from a soil tank/boundary layer wind tunnel experimental apparatus equipped with a sensor network to continuously monitor water–temperature–humidity variables. A series of experiments were performed in which the soil tank was packed with different soil types. Results demonstrate that the approaches vary in their ability to capture different stages of evaporation and no one approach can be deemed most appropriate for every scenario. When a proper top boundary condition and space discretization are defined, the Richards equation-based models (Richards model and Richards vapor model) can generally capture the evaporation behaviors across the entire range of soil saturations, comparing well with the experimental data. The simulation results of the non-equilibrium two-component two-phase model which considers vapor transport as an independent process generally agree well with the observations in terms of evaporation behavior and soil water dynamics. Certain differences in simulation results can be observed between equilibrium and non-equilibrium approaches. Comparisons of the models and the boundary layer formulations highlight the need to revisit key assumptions that influence evaporation behavior, highlighting the need to further understand water and vapor transport processes in soil to improve model accuracy.

The influence of sample distribution on growth model output for a highly-exploited marine fish, the Gulf Corvina (Cynoscion othonopterus).

Estimating the growth of fishes is critical to understanding their life history and conducting fisheries assessments. It is imperative to sufficiently sample each size and age class of fishes to construct models that accurately reflect biological growth patterns, but this may be a challenging endeavor for highly-exploited species in which older fish are rare. Here, we use the Gulf Corvina (Cynoscion othonopterus), a vulnerable marine fish that has been persistently overfished for two decades, as a model species to compare the performance of several growth models. We fit the von Bertalanffy, Gompertz, logistic, Schnute, and Schnute–Richards growth models to length-at-age data by nonlinear least squares regression and used simple indicators to reveal biased data and ensure our results were biologically feasible. We then explored the consequences of selecting a biased growth model with a per-recruit model that estimated female spawning-stock-biomass-per-recruit and yield-per-recruit. Based on statistics alone, we found that the Schnute–Richards model described our data best. However, it was evident that our data were biased by a bimodal distribution of samples and underrepresentation of large, old individuals, and we found the Schnute–Richards model output to be biologically implausible. By simulating an equal distribution of samples across all age classes, we found that sample distribution distinctly influenced model output for all growth models tested. Consequently, we determined that the growth pattern of the Gulf Corvina was best described by the von Bertalanffy growth model, which was the most robust to biased data, comparable across studies, and statistically comparable to the Schnute–Richards model. Growth model selection had important consequences for assessment, as the per-recruit model employing the Schnute–Richards model fit to raw data predicted the stock to be in a much healthier state than per-recruit models employing other growth models. Our results serve as a reminder of the importance of complete sampling of all size and age classes when possible and transparent identification of biased data when complete sampling is not possible.

Comparative Studies on the Behaviour of Copper in Various Electrically Insulating Fluids

This paper presents an exhaustive study regarding the behaviour of copper in various insulating fluids when exposed to 1100C for 1000 hours in closed systems, with no access to atmospheric oxygen. Following the analysis carried out, it was found that the variation of oxygen concentration in the investigated oil samples, during the thermal treatment, may be best described using an exponential decrease versus time. Moreover, from the gas chromatography determinations with respect to the evolution of the CO and CO2 content in the oils during the thermal treatment one found out that these fit very well the Richards model, which corroborated with all the other analysis confirms the fact that the copper films undergo consistent morphological changes only when exposed to mineral oils, so that it is of paramount importance that, taking into account this aggressive character, the equipment placed in direct contact with these oils should be carefully inspected on a periodical basis. This behaviour is thought to be a direct consequence of the sulphur compounds contents for these oils, the secondary oxidation products of these compounds increasing their corrosive aggressiveness.

Kinetics and modeling of cell growth for potential anthocyanin induction in cultures of Taraxacum officinale G.H. Weber ex Wiggers (Dandelion) in vitro

Background: Taraxacum officinale G.H. Weber ex Wiggers is a wild plant used in folk medicine to treat several diseases owing to bioactive secondary metabolites present in its tissue. The accumulation of such molecules in plant cells can occur as a response against abiotic stress, but these metabolites are often deposited in low concentrations. For this reason, the use of a biotechnological approach to improve the yields of technologically interesting bioactive compounds such as anthocyanins is a compelling option. This work focuses on investigating the potential of in vitro T. officinale cultures as an anthocyanin source. Results: To demonstrate the suitability of anthocyanin induction and accumulation in calluses under specific conditions, anthocyanin was induced in the T. officinale callus. A specific medium of 5.5% sucrose supplemented with 6-benzylaminopurine /1-naphthaleneacetic acid in a 10:1 ratio was used to produce an anthocyanin yield of 1.23 mg g-1 fw. An in vitro dandelion callus line was established from this experiment. Five mathematical models were then used to objectively and predictably explain the growth of anthocyanin-induced calluses from T. officinale. Of these models, the Richards model offered the most suitable representation of anthocyanin callus growth in a solid medium and permitted the calculation of the corresponding kinetic parameters. Conclusions: The findings demonstrate the potential of an in vitro anthocyanin-induced callus line from T. officinale as an industrial anthocyanin source.

Ethanol production in a biofilm reactor with non-sterile carob extract media and its modeling

ABSTRACTModeling is gain importance to knowledge about kinetic-metabolic nature of fermentations. In this study, Modified Richards Model (MRM) was applied to model ethanol fermentation in a biofilm reactor with non-sterile carob extract (NSCE). Results indicated that MRM showed its generality to fit cell growth, ethanol production, and sugar consumption curves in non-sterile enriched (NSE) and non-sterile non-enriched (NSNE) media. For NSE medium, MRM successfully predicted the biomass and ethanol production and sugar consumption. Nonetheless, MRM victoriously forecasted all sigmoid curves related to fermentation of NSNE medium. Consequently, MRM predictions satisfactorily fitted the experimental data based on the model evaluation results.

Generalized logistic functions in modelling emergence of Brassica napus L.

The objective of this study was to determine whether generalized logistic functions (Richards model with time shift) may be used to predict emergence of winter rapeseed (Brassica napus L.) after its seed treatment with plant extracts from Taraxacum officinale roots under controlled environment conditions. Emergence analyses were conducted for winter rape whose seeds were treated with a plant extract and for the non-treated seeds sown to the soil at the site of earlier point application of the extract. Curves were plotted for experimental data by minimizing the square sum of differences between the experimental data and the mathematical model. To evaluate model fit, the mean squared error was divided into four factors. Computing modelling efficiency coefficients were also introduced to enable complete analysis. Results of simulation research demonstrate that the determined parameters of curves (e.g. values of growth parameters, time shift or the upper limit of population) describing the number of seedlings in the function of time stayed compliant to the interpretation with regard to the biology of the analyzed processes. The proposed mathematical description based on generalized logistic functions showed extraordinary fit (r = 0.999) to the experimental data, which makes it highly useful in predictive control of rapeseed emergence. In addition, the study enabled concluding that plant extracts application to the soil allowed achieving a higher maximal emergence rate compared to the control sample. The application of the plant extracts increased the final population of rapeseed and significantly accelerated the occurrence of the maximal emergence rate.

Nonlinear models of Brazilian sheep in adjustment of growth curves

Growth curves of the Morada Nova sheep males and females were described using nonlinear models and the relationships between body weight and thoracic circumference were evaluated. Altogether 1516 repeated measures of body weight and thoracic circumference of the Morada Nova sheep (668 males and 848 females) taken since birth till 730 days of age were used. The Brody, Richards, von Bertalanffy, Gompertz, and Logistic models have been tested. The Fisher’s test (F) was used to verify the differences (P &amp;lt; 0.05) in growth curves between males and females. The Gompertz model presented a significant difference (P &amp;lt; 0.001) for growth curve parameters between males (asymptotic weight (A) = 40.5 kg and maturing rate (k) = 0.0043 kg/day) and females (A = 36.44 kg and k = 0.0028 kg/day). The relationships between body weight and thoracic circumference presented R&lt;sup&gt;2&lt;/sup&gt; above 0.7 and a high significance (P &amp;lt; 0.0001) for all categories, showing that the thoracic circumference may be a good indicator of body weight. In addition, a significant effect (P &amp;lt; 0.05) of the relationship between thoracic circumference and prediction of animal’s body weight was verified using the models of linear, quadratic, and cubic regression. Among the models studied, the Gompertz model presented the best fit and biological interpretation. Furthermore, the Gompertz model indicated the need to separate animals by sex in order to properly meet nutritional requirements and determine adequate slaughter age. Thoracic circumference can be used to predict animal body weight with a high accuracy.

Comparison of Non-linear Growth Models to Describe the Growth Behaviour of Deccani Sheep

The present study was carried out to determine the most suitable of the six frequently used non-linear growth models, viz. Brody, Von Bertalanffy, Richards, logistic, Gompertz and negative exponential, to describe the growth curve of 146 Deccani male and female sheep maintained at ICAR—Network Project on Sheep Improvement, MPKV, Rahuri (India). The monthly body weights were collected from birth to 18 months of age for the period of January 2014 to June 2016. Sex-wise modelling of growth curve showed that females had lower maturity weights, but reached maturity earlier than males. The Brody model provided highest adjusted R2 value and the lowest value of the root means square error, Akaike’s information criterion and Bayesian information criterion as compared to other models. The Richards model showed the closeness in results of goodness of fit criteria with Brody model; however, Brody model was preferred as it was simpler (three parameters compared to four of Richards).

Models to optimise bioengineering of banana wastes to animal feeds and fertilisers

Microbial growth models are usually employed to describe the growth kinetics of microorganisms under optimised operational conditions. Much time and resources are involved in running central composite or Box–Behnken full factorial designs of the experiment (DoEs) before the optimum conditions are attained. In this study, a Taguchi model (two-level) was used for DoEs and kinetic parameters derived from the mathematical models were used for process optimisation. This resulted in running less ‘robust’ anaerobic digestion experiments for the varying selected parameters – that is, pH and temperature. Chapman–Richards model results were considered to represent experimental data and were compared with the kinetic parameters derived from the Bergter, Andrews and Contois models. Also, a pure population of Saccharomyces cerevisiae (Saf-instant) was used, unlike in many studies where mixed populations are employed for anaerobic digestion. From the model results, a pH of 4·6–5·6 and a temperature of 25–30°C were considered optimum for S. cerevisiae anaerobic growth on banana waste. Chemical characterisation of the digested banana wastes under optimised conditions indicated an increase in proteins and lipids by 7 and 5%, respectively, and an approximately 8% mineral content increase was also noted. The waste could also be used as a nutrient-rich fertiliser and chicken feed supplement.

Rehabilitation reliability of the road pavement structure with recycled base course with foamed bitumen

This article presents a new approach to reliability assessment of the road structure in which the base layer will be constructed in the process of cold deep recycling with foamed bitumen. In order to properly assess the reliability of the structure with the recycled base, it is necessary to determine the distribution of stress and strain in typical pavement layer systems. The true stress and strain values were established for particular structural layers using the complex modulus (E*) determined based on the master curves. The complex modulus was determined by the direct tension-compression test on cylindrical specimens (DTC-CY) at five temperatures (-7°C, 5°C, 13°C, 25°C, 40°C) and six loading times (0.1 Hz, 0.3 Hz, 1 Hz, 3 Hz, 10 Hz, 20 Hz) in accordance with EN 12697-26 in the linear viscoelasticity (LVE) range for small strains ranging from 25 to 50 με. The master curves of the complex modulus were constructed using the Richards model for the mixtures typically incorporated in structural layers, i.e., SMA11, AC16W, AC22P and MCAS. The values of the modulus characterizing particular layers were determined with temperature distribution in the structure taken into account, when the surface temperature was 40°C. The stress distribution was established for those calculation models. The stress values were used to evaluate the fatigue life under controlled stress conditions (IT-FT). This evaluation, with the controlled stress corresponding to that in the structure, facilitated the quality assessment of the rehabilitated recycled base course. Results showed that the recycled base mixtures having the indirect tensile strength (ITSDRY) similar to the stress in the structure under analysis needed an additional fatigue life evaluation in the indirect tensile test ITT. This approach to the recycled base quality assessment will allow eliminating the damage induced by overloading.

Growth of Mongolian pine in Zhanggutai of Liaoning Province.

The aim is to summarize the growth process for first generation Mongolian pine (Pinus sylvestris var.mongolica) on sandy land, where its life cycle ends after about 60 years, and to provide a theoretical basis for promotion, regeneration, and management of a Mongolian pine plantation. 11 trees were selected for analysis, chosen from standard plots of 11 Mongolian pine plantation stands (> 30 a) with different site conditions in Zhanggutai of Liaoning Province. Then parameters for Richards model were solved and the goodness-of-fit was tested. To reveal the growth process of Mongolian pine, eigenvalues of Mongolian pine trees were used in Richards Equation. Results of height, diameter at breast height (DBH), and volume of Mongolian pine were simulated by Richards model with the parameter estimated values of 14.179, 0.084, and 2.803 for height; 19.379, 0.075, and 1.712 for DBH; and 0.296, 0.062, and 5.926 for volume. For tree height growth of first generation Mongolian pine introduced to Zhanggutai, the relative growth rate reached its maximum of 0.54 m·a-1 at year 12.3, and the average growth rate achieved its peak at year 21.4 with 0.39 m·a-1. Growth of DBH for trees started at year 6.6 with the relative growth rate reaching its maximum of 0.77 cm·a-1 at year 14.0 and the average growth rate achieving its peak at year 26.0 with 0.47 cm·a-1. Volume growth was very slow before age 12.0 with the relative growth rate reaching its maximum of 0.007 4 m3·a-1 at 29.0 years, the average growth rate achieving its peak at year 47.0 with 0.004 5 m3·a-1. The quantitative maturity age, when the maximum of average growth rate of volume appears, was 47.0 years of Mongolian pine in Zhanggutai. We drew a conclusion that the maximum of relative growth rate of height, DBH and volume of Mongolian pine appear at the age of 12.3 a, 14.0 a and 29.0 a, respectively. The maximum of average growth rate of height, DBH and volume appear at the age of 21.4, 26.0 and 47.0 years, respectively. The quantitative maturity appears in the 47th year after planting.

Influence of sulfuric acid concentration on biohydrogen production from rice mill wastewater using pure and coculture of Enterobacter aerogenes and Citrobacter freundii

We report a concise study on the influence of sulfuric acid concentration used in the hydrolysis of rice mill wastewater on biohydrogen production using pure as well as co-culture of Enterobacter aerogenes and Citrobacter freundii. A higher total reducing sugar release of 14.2 g/L was obtained with 1.5% sulfuric acid (v/v). The effect of pH on cumulative biohydrogen production from 1.5% acid hydrolyzed rice mill wastewater was investigated using pure and coculture of Enterobacter aerogenes and Citrobacter ferundii. The fermentative hydrogen production using mixed culture showed a maximum hydrogen yield of 1.61 mol/mol sugar. In addition, about 70% reduction in chemical oxygen demand (COD) and higher volatile fatty acids (VFA) production were observed. Modified Logistic, Gompertz and Richards models were used to fit cumulative hydrogen production data whereas Logistic equation was used fit growth data. Richards model showed best fit and Logistic equation gave least error in predicting maximum hydrogen producing potential.

Use of modified Richards model to predict isothermal and non-isothermal microbial growth

Mathematical models are often used to predict microbial growth in food products. An important class of these models involves the adaptation of classical sigmoid functions, such as the Gompertz and logistic functions. This study aimed to validate the use of the modified Richards model in various situations, which have not previously been tested. The model was obtained through solving a system of two differential equations and could be applied to both isothermal and non-isothermal environments. To test and validate this model, we used published datasets containing data for the growth of Pseudomonas spp. in fish products. The results obtained after fitting the model showed that it could be effectively used to describe and predict the Pseudomonas growth curves under various temperature regimens. However, the influence of the shape parameter on the growth curve is an issue that needs further evaluation.

Spatial and Temporal Characteristics of 2014 Dengue Outbreak in Guangdong, China

The record-breaking number of dengue cases reported in Guangdong, China in 2014 has been topic for many studies. However, the spatial and temporal characteristics of this unexpectedly explosive outbreak are still poorly understood. We adopt an integrated approach to ascertain the spatial-temporal progression of the outbreak in each city in Guangdong as well as in each district in Guangzhou, where the majority of cases occurred. We utilize the Richards model, which determines the waves of reported cases at each location and identifies the turning point for each wave, in combination with a spatial association analysis conducted by computing the standardized G* statistic that measures the degree of spatial autocorrelation of a set of geo-referenced data from a local perspective. We found that Yuexiu district in Guangzhou was the initial hot spot for the outbreak, subsequently spreading to its neighboring districts in Guangzhou and other cities in Guangdong province. Hospital isolation of cases during early stage of outbreak in neighboring Zhongshan (in effort to prevent disease transmission to the vectors) might have played an important role in the timely mitigation of the disease. Integration of modeling approach and spatial association analysis allows us to pinpoint waves that spread the disease to communities beyond the borders of the initially affected regions.