Mathematical models to describe the growth curves of Vietnamese Ri chicken

Ri chicken is the most popular backyard chicken breed in Vietnam, but little is known about the growth curve of this breed. This study compared the performances of models with three parameters (Gompertz, Brody, and Logistic) and models containing four parameters (Richards, Bridges, and Janoschek) for describing the growth of Ri chicken. The bodyweight of Ri chicken was recorded weekly from week 1 to week 19. Growth models were fitted using minpack.lm package in R software and Akaike’s information criterion (AIC), Bayesian information criterion (BIC), and root mean square error (RMSE) were used for model comparison. Based on these criteria, the models having four parameters showed better performance than the ones with three parameters, and the Richards model was the best one for males and females. The lowest and highest value of asymmetric weights (α) were obtained by Bridges and Brody models for each of sexes, respectively. Age and weight estimated by the Richard model were 8.46 and 7.51 weeks and 696.88 and 487.58 g for males and for females, respectively. Differences in the growth curves were observed between males and female chicken. Overall, the results suggested using the Richards model for describing the growth curve of Ri chickens. Further studies on the genetics and genomics of the obtained growth parameters are required before using them for the genetic improvement of Ri chickens.

An investigation of spatial-temporal patterns and predictions of the COVID-19 pandemic in Colombia, 2020-2021

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 4,240,982 cases and 106,544 deaths as of June 30, 2021. This motivates an investigation of the SARS-CoV-2 transmission dynamics at the national and regional level using case incidence data. Mathematical models are employed to estimate the transmission potential and perform short-term forecasts of the COVID-19 epidemic trajectory in Colombia. Furthermore, geographic heterogeneity of COVID-19 in Colombia is examined along with the analysis of mobility and social media trends, showing that the increase in mobility in July 2020 and January 2021 were correlated with surges in case incidence. The estimation of national and regional reproduction numbers shows sustained disease transmission during the early phase of the pandemic, exhibiting sub-exponential growth dynamics. Moreover, most recent estimates of reproduction number are >1.0 at the national and regional levels as of May 30, 2021. Further, the 30-day ahead short-term forecasts obtained from Richards model present a sustained decline in case counts in contrast to the sub-epidemic and GLM model. Nevertheless, our spatial analysis in Colombia shows distinct variations in incidence rate patterns across different departments that can be grouped into four distinct clusters. Lastly, the correlation of social media trends and adherence to social distancing measures is observed by the fact that a spike in the number of tweets indicating the stay-at-home orders was observed in November 2020 when the case incidence had already plateaued.

Forecasting COVID-19 Epidemic in Spain and Italy Using A Generalized Richards Model with Quantified Uncertainty

The Richards model and its generalized version are deterministic models that are often implemented to fit and forecast the cumulative number of infective cases in an epidemic outbreak. In this paper we employ a generalized Richards model to predict the cumulative number of COVID-19 cases in Spain and Italy, based on available epidemiological data. To quantify uncertainty in the parameter estimation, we use a parametric bootstrapping approach to construct a 95% confidence interval estimation for the parameter model. Here we assume that the time series data follow a Poisson distribution. It is found that the 95% confidence interval of each parameter becomes narrow with the increasing number of data. All in all, the model predicts daily new cases of COVID-19 reasonably well during calibration periods. However, the model fails to produce good forecasts when the amount of data used for parameter estimations is not sufficient. Based on our parameter estimates, it is found that the early stages of COVID-19 epidemic, both in Spain and in Italy, followed an almost exponentially growth. The epidemic peak in Spain and Italy is respectively on 2 April 2020 and 28 March 2020. The final sizes of cumulative number of COVID-19 cases in Spain and Italy are forecasted to be at 293220 and 237010, respectively.

Stochastic perturbation of the Lighthill–Whitham–Richards model via the method of stochastic characteristics

In this paper we apply the method of stochastic characteristics to a Lighthill–Whitham–Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation perturbed by a standard Brownian motion and the geometric Brownian motion without drift.

Bertalanffy-Pütter models for avian growth

This paper explores the ratio of the mass in the inflection point over asymptotic mass for 81 nestlings of blue tits and great tits from an urban parkland in Warsaw, Poland (growth data from literature). We computed the ratios using the Bertalanffy-Pütter model, because this model was more flexible with respect to the ratios than the traditional models. For them, there were a-priori restrictions on the possible range of the ratios. (Further, as the Bertalanffy-Pütter model generalizes the traditional models, its fit to the data was necessarily better.) For six birds there was no inflection point (we set the ratio to 0), for 19 birds the ratio was between 0 and 0.368 (lowest ratio attainable for the Richards model), for 48 birds it was above 0.5 (fixed ratio of logistic growth), and for the remaining eight birds it was in between; the maximal observed ratio was 0.835. With these ratios we were able to detect small variations in avian growth due to slight differences in the environment: Our results indicate that blue tits grew more slowly (had a lower ratio) in the presence of light pollution and modified impervious substrate, a finding that would not have been possible had we used traditional growth curve analysis.

Genetic and phenotypic parameters for body weights, harvest length, and growth curve parameters in American mink

Understanding the genetics underlying growth curve is important for selection of animals with better growth potential, but little is known about the genetics of growth curve parameters in mink. This study estimated the genetic parameters for body weights (BW), harvest length (HL) and growth parameters derived from the Richards model. For this purpose, individual BW of 1,088 mink measured seven times in three-week intervals (week 13 to week 31 of life) were used for growth curve modeling using the Richards model. The BW traits included body weight at week 13 (BW13), 16 (BW16), 19 (BW19), 22 (BW22), 25 (BW25), 28 (BW28), and 31 (BW31). Univariate analyses indicated that sex and birth-year had significant effects (P < 0.05) on BW, HL, asymptotic weight (α), growth rate at mature (k), shape parameter (m), weight at the inflection point (WIP), and age at the inflection point (AIP). In contrast, the color type had only a significant effect (P < 0.05) on BW31 and HL. Estimated heritabilities (±SE) were ranged from 0.36±0.13 (BW13) to 0.46±0.10 (BW22) for BW and were 0.51±0.09, 0.29±0.09, 0.30±0.09, 0.33±0.1, 0.44±0.10, and 0.47±0.10 for HL, α, k, m, WIP and AIP, respectively. The parameter α had non-significant (P > 0.05) genetic correlations (±SE) with k (-0.21±0.23) and m (-0.10±0.22), suggesting that changing in shape parameters (k and m) will not influence asymptotic weight (α). Strong significant (P < 0.05) phenotypic (from 0.46±0.03 to 0.60±0.03) and genetic (0.70±0.13 to 0.88±0.09) correlations were observed between HL and different BW measures. The α, AIP, and WIP parameters had significant (P < 0.05) genetic correlations, and HL indicated that selection for higher α, AIP, and WIP values would increase HL. Parameters k and m had non-significant (P > 0.05) genetic correlations with HL, indicating the change of the curve shape could not influence HL. Overall, the results suggest that growth curve parameters are heritable and can respond to genetic or genomic selection for optimizing the performance in mink.

Modelling growth in seven chicken genotypes

Three non-linear growth models were used to fit weight-age data for seven chicken genotypes: Comparisons were made among these models for goodness of fit, biological interpretability and computational case. Monomolecular and Richards Models overestimated body weight at the early phases of growth. All the three models underestimated the asymptotic mature weight but Gumpertz function gave a better estimate than the other two. Maturing rates were also variable and Richards Model gave the best estimate of K. Using these three non-linear models to describe growth rate of chest girth of the seven chicken genotypes yields a different result from that of the body weight. The point of inflection ranged from - 3 56 for FINA (F/Na) genotype to 28.26 for frizzled (Frx Fr) genotype. Genetic variations in rates of gain, maluring rute und mature size were observed.

Phenomenological and mechanistic models for predicting early transmission data of COVID-19

<abstract> <p>Forecasting future epidemics helps inform policy decisions regarding interventions. During the early coronavirus disease 2019 epidemic period in January–February 2020, limited information was available, and it was too challenging to build detailed mechanistic models reflecting population behavior. This study compared the performance of phenomenological and mechanistic models for forecasting epidemics. For the former, we employed the Richards model and the approximate solution of the susceptible–infected–recovered (SIR) model. For the latter, we examined the exponential growth (with lockdown) model and SIR model with lockdown. The phenomenological models yielded higher root mean square error (RMSE) values than the mechanistic models. When using the numbers from reported data for February 1 and 5, the Richards model had the highest RMSE, whereas when using the February 9 data, the SIR approximation model was the highest. The exponential model with a lockdown effect had the lowest RMSE, except when using the February 9 data. Once interventions or other factors that influence transmission patterns are identified, they should be additionally taken into account to improve forecasting.</p> </abstract>