Richards Model Research Articles

Parameters Estimation of Generalized Richards Model for COVID-19 Cases in Indonesia Using Genetic Algorithm

In this research, genetic algorithm was implemented to estimate parameters in generalized Richards model by adjusting COVID-19 case data in Indonesia. Data collected were the daily new cases and cumulative number of COVID-19 case in Indonesia from early March to early June 2020, that was reported by databoks.katadata.co.id. The best pair of parameters was selected based on the lowest cost function value, determined from the distance between data with estimated model and real data. Next, model with estimated parameters is used to predict new cases and cumulative cases for upcoming days. Numerical simulations were carried out so that the peaks and ends of the COVID-19 pandemic can be seen easily.

Optimal location problem for variable speed limit application areas

Some studies consider variable speed limit (VSL) control as a viable option to prevent traffic breakdown at bottlenecks by limiting the mainline flow with reduced speed limits. However, few studies consider the location of the application area as a design variable of the problem. This paper explains why the location of a VSL control area is crucial to prevent the capacity drop phenomenon at lane drop bottlenecks. We first define two types of stationary states, congested and uncongested, inside a lane drop bottleneck assuming the Lighthill-Whitham Richards model with bounded acceleration. In particular, the characteristics of these stationary states and their admissible conditions are discussed thoroughly. If the speed limit imposed is low enough, the location of the VSL application area is irrelevant to ensure an uncongested stationary state inside the bottleneck. However, for a given range of speed limits, the location of the VSL application area should be designed carefully to allow for uncongested stationary states and prevent the occurrence of the capacity drop. We formulate an optimization problem and show that, contrary to the general belief, the larger the speed limit, the farther the VSL application area should be from the bottleneck. Finally, the results are extended to other types of bottlenecks, such as sag or tunnel bottlenecks. To the best of our knowledge, this is the first study to analytically identify, formulate, and solve the optimal location problem for variable speed limit application areas. It makes fundamental contributions to both traffic flow theory (by analyzing the stationary states for VSL-controlled bottlenecks) and traffic control (by determining the optimal location of a VSL application area). Moreover, the results presented are of practical relevance because they can help to establish some guidelines for practitioners to implement VSL control strategies.

Growth and development of the brush-tailed rabbit-rat (

Knowledge of life history can reveal much about phylogeny, behaviour and ecology, all of which are essential for managing threatened species. Conilurus penicillatus has declined over its range and there is little information on its biology, including growth and development. Weight and four body measurements were recorded using 87 progeny of Mitchell Plateau stock, from birth to >150 days. Developmental features were recorded in animals less than 3 months old. Morgan–Mercer–Flodin, 4-Parameter Richards and Exponential growth models were applied to metric data. Neonatal development was rapid (pinnae were unfolded at birth, ears opened at 7–10 days, eyes opened at 11–14 days). An almost-complete juvenile pelage developed by 14 days. Weaning occurred at 23–40 days and adult size was attained by 100 days. At birth, males were significantly heavier than females but this difference was not evident in adults (mean = 168 g, combined sexes), when only head length was greater. Lack of sexual size dimorphism may be associated with a monogamous social structure. Conilurus penicillatus is more precocial but grows more slowly than the closely related Mesembriomys gouldii. Variation in growth and development strategies among tree-rats may be related to differences in diet, habitat and other life-history characteristics.

Moral Dilemmas—An Introduction

Moral Dilemmas—An Introduction George Kateb (bio) we should be struck by the title of our panel, "moral dilemmas." At first sight it should seem odd that discussion of a particular disease lends itself to worry about moral dilemmas. After all, we usually expect that the only issue about a disease is medical: how to treat it. But as we know all too keenly, AIDS is no ordinary disease; it is not even an ordinary fatal disease. It is, rather, a disease that is contracted because of two kinds of intense pleasure: sex and drugs. This fact, by itself, would guarantee that society would take either a puritanical or a prurient interest in the disease and thus infect discussion of it with all sorts of nonmedical considerations. Whenever pleasures figure, one can also be sure that religious ideologists will take their pleasure in denouncing pleasure, and find an even greater pleasure in the fact that pleasures of a certain sort can lead to premature death. The height of religious inanity was reached by a Catholic spokesman, who said (as quoted by Robert Suro in the New York Times), that the church could not condone the public provision of condoms because the greatest physical harm is less important than the smallest moral harm. (This inanity, by the way, has its sources in the past, and can count Cardinal Newman as one of its authorities.) Not all the religions reach this height, but many climb quite far. The subject of AIDS, if it does nothing else, exposes the intimate connection between religion and sex (to leave aside drugs). There is something almost uncanny in the devious ways by which religion despises sex, guards it, inflames it, contorts it, sullies it, and sanctifies it. In some moods one may think that sex is all that religion is about. [End Page 431] The matter is yet more complicated. Because of a quirk of fortune, AIDS, in the West, turns out to have struck two groups that society dislikes and despises, male homosexuals and heroin addicts. The moral dilemmas arise because those who suffer from the disease see that even when some people in society want to understand the disease in order to help them, others, in their religious or nonreligious puritanical or prurient hostility, want to use the procedures needed to study AIDS and help those sick from it as devices of humiliation and punishment. The sick and those who may one day become sick are driven to cooperate with those who want to help them, and driven also to resist them. The sick are in a dilemma and so are those who want to help them. Our three papers sensitively explore the main dilemma as well as other aspects of this torn situation. I would just like to point out moments in the three papers that may repay further thinking. David Richards provides an eloquent defense of the constitutional right of homosexuals to express their sexual nature without fear of legal or social punishment. The basis of his position is the idea of human dignity, the basis of all rights, including privacy. In the course of establishing his argument, he may, however, give too large a role to "authentic feelings of affection, attachment, and mutual love." Richards's model relationship is the faithful loving couple, whether heterosexual or homosexual. His standards may be too strict. Eros is not worshiped only by faithful and loving couples. There are desires that cannot be slaked monogamously; indeed, that cannot be slaked at all, because their object is symbolic or phantasmal. Yet they are human desires, intrinsic to countless personalities, and deserve constitutional protection just as much as monogamously satisfiable desires. Not all personal integrity is monogamous. The human dignity of some people is quite compatible with, say, casual sex, or so-called promiscuity. Despite the overall decent good sense of Anthony Quinton's paper, it has one chilling moment, and one hasty generalization. The chill is at the beginning, when he says that "I, like most of my reflective [End Page 432] compatriots except for Locke, do not really believe in rights in the abstract … but only in legal rights and, in a more qualified fashion...

Approaches to Daily Monitoring of the SARS-CoV-2 Outbreak in Northern Italy.

Italy was the first European country affected by the Sars-Cov-2 pandemic, with the first autochthonous case identified on Feb 21st. Specific control measures restricting social contacts were introduced by the Italian government starting from the beginning of March. In the current study we analyzed public data from the four most affected Italian regions. We (i) estimated the time-varying reproduction number (Rt), the average number of secondary cases that each infected individual would infect at time t, to monitor the positive impact of restriction measures; (ii) applied the generalized logistic and the modified Richards models to describe the epidemic pattern and obtain short-term forecasts. We observed a monotonic decrease of Rt over time in all regions, and the peak of incident cases ~2 weeks after the implementation of the first strict containment measures. Our results show that phenomenological approaches may be useful to monitor the epidemic growth in its initial phases and suggest that costly and disruptive public health controls might have had a positive impact in limiting the Sars-Cov-2 spread in Northern Italy.

Quickstart for SIRD Modeling of the COVID-19 Outbreak

Overview: There are a number of different methodologies that one can employ in order to model the outbreak of an infectious disease, in this case the novel 2019 coronavirus (COVID-19). Some, like generalized logistic models or Richards models rely on the expectation of a logistic pattern of growth in cumulative cases and clasically do not incorporate such complex dynamics as isolation of infected individuals, shelter-in-place orders for the general population (as instituted in New York City), or other change in public health policy over time. Here we present an implementation of a Susceptible-Infected-Recovered-Deceased (SIRD) model, with parameter fitting to real-world data, which can assist in projecting the overall trajectory of an outbreak in response to such complex changes in the environment. Our methodology is contained in a freely available IPython notebook, with the goal of providing a good starting point for other citizen scientists interested in exploring and forecasting the COVID-19 outbreak. Methodology: While a great deal can be learned from the simpler style of models mentioned above, the SIRD model allows for a great deal of nuance in forecasting because it attempts to approximate real-world dynamics, namely the flux of individuals between compartments in the outbreak; for example, susceptible people become infected at a specific rate, and those infected people then recover or die at specific rates. Our implementation of this model utilizes a system of ordinary differential equations (ODEs) inspired by the work of Diego Caccavo [1]. Typically we model the rate of infection as a constant β multiplied by the overall proportion of infected people and by the # of susceptible people. In our methodology, we have instead modeled this β value as a function of time β(t). In this way, we can account for changes in infection rate, for example a decrease due to a lockdown at timepoint t_lockdown (with shelter-in-place, for example) or an increase due to the lifting of such a lockdown at timepoint t_lift (Fig C). After establishing the equations which will dictate the dynamics of the model, we fit the parameters (β, 𝜏_𝛽, 𝛾, 𝛿) using non-linear least-squares regression via a function provided by the SciPy package. Results: We demonstrate a functional IPython Notebook which allows for fitting of SIRD model parameters to real-world datasets. Additionally, we can form rudimentary projections of potential outbreak trajectories in response to real-world changes in the environment in which an outbreak is occuring by modifying the system of ODEs. For example, we show the effect of changing the date on which shelter-in-place measures are lifted on a simulated New York City (NYC). We first fit the parameters of the SIRD model (Fig C) using real-world outbreak data from NYC provided by the NY Times. We then run the model, demonstrating that lifting shelter-in-place public health measures after only a month causes a rebound and second peak in cases in the simulated New York City (Fig A). On the other hand, lifting the shelter-in-place orders after two months allows the outbreak in the simulated city to die down without a second spike in cases (Fig B). Conclusions: Overall, we believe that there is a great deal of predictive and explanatory power provided by SIRD-type models. We hope that other researchers in the field can use our work as a basis for further customization and tailoring of the system of ODEs, allowing these models to be fit to a variety of different cities, states, or other regions. That said, we also want to urge caution to those hoping to utilize these models to exactly predict the course of an outbreak or develop specific timing of public policies. These models are simply projections, and are highly limited by the overall limited availability and quality of data at this point in the COVID-19 outbreak.

Comparing traditional estimators and the estimators of (PSO) algorithm for some growth models of gross domestic product in Iraq

Growth models are considered to be one of the most important statistical means that is widely used in the study of the behaviors of different phenomena throughout time, and the estimation of the parameters of these models is considered to be the key element that plays a major role in the inference about these models. In this paper, this problem will be discussed briefly. The aim of the paper is to compare the estimators of some traditional methods and the estimators of the Particle Swarm Optimization (PSO) algorithm for estimating the parameters of some growth models as well as building the best growth model for the Gross Domestic Product (GDP) in Iraq. The growth models that are used in this paper will include three linear models which are Polynomials of order (1, 3, and 5) as well as three nonlinear models which are (The Logistic Model, The Gompertz Model, and The Richards Model). It was concluded that the (PSO) algorithm was better than the traditional methods in estimating the parameters of the growth models, also the fifth degree polynomial was the best model to describe the (GDP) data in Iraq.

Strain Variability of Listeria monocytogenes under NaCl Stress Elucidated by a High-Throughput Microbial Growth Data Assembly and Analysis Protocol.

Listeria monocytogenes causes the severe foodborne illness listeriosis and survives in food-associated environments due to its high stress tolerance. A data assembly and analysis protocol for microbial growth experiments was compiled to elucidate the strain variability of L. monocytogenes stress tolerance. The protocol includes measurement of growth ability under stress (step 1), selection of a suitable method for growth parameter calculation (step 2), comparison of growth patterns between strains (step 3), and biological interpretation of the discovered differences (step 4). In step 1, L. monocytogenes strains (n = 388) of various serovars and origins grown on media with 9.0% NaCl were measured using a Bioscreen C microbiology reader. Technical variability of the growth measurements was assessed and eliminated. In step 2, the growth parameters determined by Gompertz, modified-Gompertz, logistic, and Richards models and model-free splines were compared, illustrating differences in the suitability of these methods to describe the experimental data. In step 3, hierarchical clustering was used to describe the NaCl tolerance of L. monocytogenes measured by strain-specific variation in growth ability; tolerant strains had higher growth rates and maximum optical densities and shorter lag phases than susceptible strains. The spline parameter area under the curve best classified "poor," "average," and "good" growers. In step 4, the tested L. monocytogenes lineage I strains (serovars 4b and 1/2b) proved to be significantly more tolerant toward 9.0% NaCl than lineage II strains (serovars 1/2a, 1/2c, and 3a). Our protocol provides systematic tools to gain comparable data for investigating strain-specific variation of bacterial growth under stress.IMPORTANCE The pathogen Listeria monocytogenes causes the foodborne disease listeriosis, which can be fatal in immunocompromised individuals. L. monocytogenes tolerates several environmental stressors and can persist in food-processing environments and grow in foodstuffs despite traditional control measures such as high salt content. Nonetheless, L. monocytogenes strains differ in their ability to withstand stressors. Elucidating the intraspecies strain variability of L. monocytogenes stress tolerance is crucial for the identification of particularly tolerant strains. To enhance reliable identification of variability in bacterial stress tolerance phenotypes, we compiled a large-scale protocol for the entire data assembly and analysis of microbial growth experiments, providing a systematic approach and checklist for experiments on strain-specific growth ability. Our study illustrated the diversity and strain-specific variation of L. monocytogenes stress tolerance with an unprecedented scope and discovered biologically relevant serovar- and lineage-dependent phenotypes of NaCl tolerance.

Comparison of four nonlinear growth models in Creole chickens of Mexico

Animal growth is a complex and dynamic process that involves physiological and morphological changes from hatching to maturity. It is defined as the increase in body size per time unit. Mathematical functions, called growth models, have been used to explain growth patterns. The aim of this study was to compare the Gompertz-Laird, logistic, Richards, and Von Bertalanffy growth models to determine which best fits the data of the Creole chickens (CC). Three hundred forty-seven CC were individually weighed from hatching until 177 D of age. Birds were fed a starter diet (0–18 D of age; 19% crude protein (CP) and 3,000 kcal of ME/kg) and grower diet (19–177 D of age; 18% CP and 2,800 kcal of ME/kg). Data were analyzed using PROC NLIN to fit the nonlinear growth curve. The coefficient of determination (R2), Akaike information criteria (AIC), and Bayesian information criteria (BIC) were used to compare the goodness of fit of the models. The Von Bertalanffy (R2: 0.9382, 0.9415; AIC: 2,224.1, 2,424.8; BIC: 2,233.5, 2,434.3, for females and males, respectively) was the model that best explained growth of the birds. On the other hand, both the Gompertz-Laird and logistic models overestimated hatching BW and underestimated the final BW of CC. Females reached age of maximum growth faster than males. The asymptotic weight was higher in males (3,011 g) than in females (2,011 g). Body weight at inflection point was 892 g at 64 D of age for males and 596 g at 54 D for females. In conclusion, the best fit of the data was obtained with the Von Bertalanffy growth model; the information is intended to serve as the basis for utilizing CC.

Implementation of flexible models to bioethanol production from carob extract–based media in a biofilm reactor

In the present study, eleven flexible models were employed to describe the effect of different medium compositions (DMC) on ethanol fermentation in repeated-batch biofilm reactors with carob extract. Residual-sum of square, root-mean-square-error, mean-absolute-error, determination coefficient, bias factor, accuracy factor, F test, and objective function were used to compare the models. Findings indicated that corresponding with the prediction of the experimental data of substrate concentration (S), the best-selected models were the Baranyi model (media A and C), Weibull model (medium B), and re-modified Gompertz model (R-MGM) (medium D). It was also found that in the estimation of the observed biomass concentration (X) data, Baranyi model (medium A), Weibull model (medium B), and Stannard model (media C and D) gave well-directed results according to the model comparison, validation, and fitting results. As related to ethanol concentration (P), the predicted data with the re-modified Richards model (R-MRM) (media A and B), re-modified logistic model (R-MLM) (medium C), and Baranyi model (medium D) were showed good agreement with the experimental p values. To validate the best-selected models, an independent set of the experimental data for each medium was used and it was found that the independent experimental values were highly compatible with the selected models. Consequently, the best-selected models can serve as universal equations to fit satisfactorily the experimental S, X, and P curves. These models can also be used for further improvement of the carob extract–based bioethanol production process.

Adequacy of Logistic models for describing the dynamics of COVID-19 pandemic.

Logistic models have been widely used for modelling the ongoing COVID-19 pandemic. This study used the data for Kuwait to assess the adequacy of the two most commonly used logistic models (Verhulst and Richards models) for describing the dynamics COVID-19. Specifically, the study assessed the predictive performance of these two models and the practical identifiability of their parameters. Two model calibration approaches were adopted. In the first approach, all the data was used to fit the models as per the heuristic model fitting method. In the second approach, only the first half of the data was used for calibrating the models, while the other half was left for validating the models. Analysis of the obtained calibration and validation results have indicated that parameters of the two models cannot be identified with high certainty from COVID-19 data. Further, the models shown to have structural problems as they could not predict reasonably the validation data. Therefore, they should not be used for long-term predictions of COVID-19. Suggestion have been made for improving the performances of the models.

Stable Day-to-Day Dynamics for Departure Time Choice

All existing day-to-day dynamics of departure time choice at a single bottleneck are unstable, and this has led to doubt over the existence of a stable user equilibrium in the real world. However, empirical observations and our personal driving experience suggest stable stationary congestion patterns during a peak period. In this paper, we attempt to reconcile the discrepancy by presenting a stable day-to-day dynamical system for drivers’ departure time choice at a single bottleneck. In our model, the decision variable in the execution stage is still drivers’ departure times on the next day, but in the planning stage before the execution stage, drivers determine their departure times in order to arrive at the destination at better times with lower scheduling costs. We first define within-day traffic dynamics with the point queue model, costs, the departure time user equilibrium (DTUE), and the arrival time user equilibrium (ATUE). We then identify three behavioral principles in the planning stage: (i) drivers choose their departure and arrival times in a backward fashion (backward choice principle); (ii) after choosing the arrival times, they update their departure times to balance the total costs (cost-balancing principle); (iii) they choose their arrival times to reduce their scheduling costs or gain their scheduling payoffs (scheduling cost–reducing or scheduling payoff–gaining principle). In this sense, drivers’ departure and arrival time choices are driven by their scheduling payoff choice. With a single tube or imaginary road model, we convert the nonlocal day-to-day arrival time shifting problem to a local scheduling payoff shifting problem. After introducing a new variable for the imaginary density, we apply the Lighthill–Whitham–Richards (LWR) model to describe the day-to-day dynamics of scheduling payoff choice and present splitting and cost-balancing schemes to determine arrival and departure flow rates accordingly. We define the scheduling payoff user equilibrium (SPUE) as the stationary state of the LWR model, formulate a new optimization problem for the SPUE, and prove the global stability of the SPUE and, therefore, ATUE and DTUE by using Lyapunov’s second method in which the objective function in the optimization formulation is the potential function. We also develop the corresponding discrete models for numerical solutions and use one numerical example to demonstrate the effectiveness and stability of the new day-to-day dynamical model. Different from existing ones, the new adjustment mechanism leads to stable day-to-day departure time choice dynamics by guaranteeing that drivers have better choices of departure/arrival times with larger scheduling payoffs on the next day, and such better choices are not over-chosen because of the constraint imposed by the single tube’s cross-section area, which is equal to the jam density in the LWR model. This study is the first step for understanding stable day-to-day dynamics for departure time choice, and many follow-up studies are possible and warranted.

Effects of cadmium toxicity on sesame seed germination explained by various nonlinear growth models

This experiment was conducted to evaluate the effects of cadmium toxicity on the seed germination properties of sesame cultivars (Halil, Nazok Shakhei, Oltan, and Yellow White) using non-linear growth models. Seeds were germinated in petri dishes (90 mm diameter), with a double layered of filter paper soaked in distilled water as control treatment or cadmium (CdSO4) solutions in concentrations of 0, 100, 200, 400, 600, 800 and 1000 ppm. Each treatment was replicated four times and included 50 seeds in each petri dishes. Hyperbolastic growth models for the description of seed germination data were compared to Richards, Weibull, Logistic and Gompertz models. Our results revealed that all studied cultivars were germinated at the cadmium-polluted germination medium to a maximum of 200 ppm without reduction in germination fraction, while seed germination rate was decreased at this concentration compared to 0 and 100 ppm. Increasing cadmium concentration resulted in the germination fraction reduction from 1 to 0.4 at the 400 ppm. The recommended hyperbolastic growth model was type III or (H3) as it provided the best model with the lowest Corrected Akaike Information Criterion for cv. Halil (AICc = −14.6) and cv. Nazok Shakhei, (AICc = −14.2).

Large-scale Lassa fever outbreaks in Nigeria: quantifying the association between disease reproduction number and local rainfall.

Lassa fever (LF) is increasingly recognised as an important rodent-borne viral haemorrhagic fever presenting a severe public health threat to sub-Saharan West Africa. In 2017-18, LF caused an unprecedented epidemic in Nigeria and the situation was worsening in 2018-19. This work aims to study the epidemiological features of epidemics in different Nigerian regions and quantify the association between reproduction number (R) and state rainfall. We quantify the infectivity of LF by the reproduction numbers estimated from four different growth models: the Richards, three-parameter logistic, Gompertz and Weibull growth models. LF surveillance data are used to fit the growth models and estimate the Rs and epidemic turning points (τ) in different regions at different time periods. Cochran's Q test is further applied to test the spatial heterogeneity of the LF epidemics. A linear random-effect regression model is adopted to quantify the association between R and state rainfall with various lag terms. Our estimated Rs for 2017-18 (1.33 with 95% CI 1.29-1.37) was significantly higher than those for 2016-17 (1.23 with 95% CI: (1.22, 1.24)) and 2018-19 (ranged from 1.08 to 1.36). We report spatial heterogeneity in the Rs for epidemics in different Nigerian regions. We find that a one-unit (mm) increase in average monthly rainfall over the past 7 months could cause a 0.62% (95% CI 0.20%-1.05%)) rise in R. There is significant spatial heterogeneity in the LF epidemics in different Nigerian regions. We report clear evidence of rainfall impacts on LF epidemics in Nigeria and quantify the impact.

Stochastic LWR model with heterogeneous vehicles: Theory and application for autonomous vehicles

The introduction of autonomous vehicles (AV) will increase the vehicle heterogeneity on our roads. It is claimed that these vehicles will be able to achieve lower spacings for the same speed than human driven ones. Therefore, a good understanding of the influence of heterogeneous driver behavior on macroscopic traffic flow characteristics is crucial. This paper presents a stochastic Lighthill-Whitham Richards model by introducing heterogeneous, i.e., vehicle dependent, jam densities. The model is solved in Lagrangian coordinates, and the nature of the model allows for investigating the impact of driver heterogeneity on macroscopic relations of traffic flow, both through simulations and analytically. The results show that both static and dynamic macroscopic characteristics of the model, such as average speed, capacity drop and flow rate evolution at a bottleneck, are consistent with the deterministic version with an equivalent jam density, which is the harmonic mean of the distribution. Establishing the theoretical way to average the parameters will allow us to develop some control strategies for connected AV in a mixed environment to control the platoon behavior and drive traffic flow to the desired state. In this line, this paper discusses the relation between the desired AV characteristics and the market penetration rate to maximize the flow rate at bottlenecks by reducing the capacity drop effects. This further motivates future research on the technology development for AVs.

Generalized Richards model for predicting COVID-19 dynamics in Saudi Arabia based on particle swarm optimization Algorithm.

COVID-19 pandemic is spreading around the world becoming thus a serious concern for health, economic and social systems worldwide. In such situation, predicting as accurately as possible the future dynamics of the virus is a challenging problem for scientists and decision-makers. In this paper, four phenomenological epidemic models as well as Suspected-Infected-Recovered (SIR) model are investigated for predicting the cumulative number of infected cases in Saudi Arabia in addition to the probable end-date of the outbreak. The prediction problem is formulated as an optimization framework and solved using a Particle Swarm Optimization (PSO) algorithm. The Generalized Richards Model (GRM) has been found to be the best one in achieving two objectives: first, fitting the collected data (covering 223 days between March 2nd and October 10, 2020) with the lowest mean absolute percentage error (MAPE = 3.2889%), the highest coefficient of determination (R2 = 0.9953) and the lowest root mean squared error (RMSE = 8827); and second, predicting a probable end date found to be around the end of December 2020 with a projected number of 378,299 at the end of the outbreak. The obtained results may help the decision-makers to take suitable decisions related to the pandemic mitigation and containment and provide clear understanding of the virus dynamics in Saudi Arabia.

Prediction of Microbial Population in Sorghum Fermentation through Mathematical Models

The mathematical models can be used as a tool in predicting microbial population in sorghum fermentation, either spontaneous fermentation or fermentation with the addition of lactic acid bacteria (LAB) inoculum. Gompertz model modified by Gibson, Gompertz model modified by Zwietering, Baranyi-Robert model, Fujikawa model, Richards model, Schnute model were used in predicting the growth of lactic acid bacteria (LAB) and coliform bacteria during spontaneous fermentation, and also the growth of LAB during fermentation with the addition of inoculum. Meanwhile, there was death (inactivation) of coliform bacteria during sorghum fermentation with the addition of LAB inoculum. The Geeraerd model and the Gompertz model modified by Gil et al. were used to predict the inactivation. The accuracy and precision of models were evaluated based on the Root Mean of Sum Square Error (RMSE), coefficient of determination (R2), and curve fitting. Gompertz model modified by Gibson had the highest accuracy and precision, which was followed by the accuracy of the Fujikawa model and Baranyi-Robert model in predicting the growth of LAB and the growth of coliform bacteria during spontaneous fermentation. Meanwhile, in predicting LAB growth during fermentation with the addition of inoculum, high accuracy and precision was obtained from Richards and Schnute models. In predicting the inactivation of coliform bacteria, Geeraerd model provided higher accuracy and precision compared to Gompertz model modified by Gil et al. Keywords: fermentation; inoculum; mathematical; model; sorghum; spontaneous

Lake recovery from eutrophication: Quantitative response of trophic states to anthropogenic influences

Lake eutrophication is a serious environmental problem worldwide, caused by both natural processes and anthropogenic influences. For effective lake eutrophication management, a variety of models have been designed to investigate the complex interrelationship between physical, chemical and biological factors and processes in lakes. However, these models are inconvenient for predictions of lake eutrophication in practical application. To date, very few studies have focused on lake eutrophication in terms of anthropogenic influences (such as sewage emissions and agricultural practices), which are more readily regulated than natural processes. Effective lake eutrophication prediction models should base primarily on facile controlled or predictable indicators. Therefore, to meet this requirement, we designed simple predictive models to determine the interrelationship between the trophic states of lakes and nutrient inputs, which is a direct measurement to characterize anthropogenic influences. Lake Taihu (China) was used as a representative eutrophic water body to assess the accuracy of the proposed predictive models. Firstly, to comprehensively understand the role of nutrient input indicators (NIIs) during eutrophication, Pearson correlation coefficient analysis was conducted on 7 NIIs and 38 types of algae. Secondly, based on the NIIs identified with high correlation coefficients, we modified three commonly used growth models (Gompertz, logistic and Richards) to describe the lake's trophic state. A particle swarm optimization algorithm (PSOA) was used to optimize model variables. Results showed that the mean absolute percentage errors of the optimized Gompertz, logistic and the Richards models were 2.95%, 2.88% and 2.17%, respectively. Finally, these optimized models were used to predict lake eutrophication under several different nutrient input scenarios. Two adjustment scenarios revealed remarkably satisfied trophic states (including roughly oligotrophic and even ultra-oligotrophic) by the 2030s. Our results show that these established models are a simple way to support lake restoration projects by setting realistic and effective targets.

Hysteresis and stop-and-go waves in traffic flows

Stop-and-go waves, also called phantom jams, are often observed in real traffic flows but can be produced neither by the classical Lighthill–Whitham–Richards (LWR) model nor by its known variants. To capture stop-and-go waves, we add hysteresis to the LWR model. For the model we propose, all possible viscous waves are found, and necessary and sufficient conditions for their existence are provided. In particular, deceleration and acceleration shocks appear; the latter were never rigorously defined before, in spite of the fact that they were observed in real traffic flows. Stop-and-go waves can be constructed by a pair of deceleration and acceleration shocks that completes a hysteresis cycle, illustrating how hysteresis loops lead to stop-and-go waves. In contrast, in the phase region where anticipation (i.e. negative hysteresis) loops exist, stop-and-go waves are not present, and speed variations decay. Riemann solutions are then found for all possible Riemann data. We explicitly show that, in the phase region where hysteresis loops exist, a sufficient deviation in speed of a few vehicles in an otherwise uniform car platoon can generate stop-and-go waves, confirming observations of real traffic experiments.

Modeling the Growth of Black Soldier Fly Hermetia illucens (Diptera: Stratiomyidae): An Approach to Evaluate Diet Quality.

The black soldier fly (BSF, Hermetia illucens (Linnaeus), Diptera: Stratiomyidae) is an edible insect widely reared by using various types of organic wastes as its diet. Developing tools to evaluate the growth performance of BSF is crucial for improving its production. In this study, we monitored the daily growth of BSF larvae reared with 10 diets with diverse nutritional quality and compared 7 growth models for quantifying growth performance. We found that BSF generally exhibited an S-shaped growth curve and that the Richards model was the best-fitting growth model. We estimated asymptotic growth limit (W∞) and constructed a time-series curve of absolute growth rate (AGR) by using the Richards model. We used Gaussian functions to estimate AGR parameters (maximum AGR, m; timing of maximum AGR, T; the deviation of AGR, d) to evaluate whether these parameters adequately quantify the growth performance of BSF. Correlation analysis showed that the AGR parameters were mostly independent of W∞ but were correlated with the duration of the larval stage, indicating that W∞ and the AGR parameters respond to different dietary factors. The results of pairwise comparisons showed that the diets rich in carbohydrates and protein had high W∞, m, and d, and early T. The diets with low levels of carbohydrates had low W∞, and the diets with low levels of protein had low m and d and delayed T. We conclude that the parameters estimated by the Richards model could be effective indices for evaluating the growth performance of BSF and their diet quality.