Richards Model Research Articles

A linear Lagrangian model predictive controller of macro- and micro- variable speed limits to eliminate freeway jam waves

Variable speed limits (VSLs) are a common traffic control measure to resolve freeway jam waves. State-of-the-art model predictive control (MPC) approaches of VSLs are developed based on Eulerian Lighthill-Whitham and Richards (LWR) models, where the decision variables are flows between road segments. It is difficult to implement constraints on speeds that are necessary in typical real-world speed limit systems, because converting flow to speed results in nonlinear and non-convex optimization formulations. In this paper, we develop a new MPC of VSLs based on a discrete Lagrangian LWR model, in which the decision variables are average speeds of vehicle groups. This allows formulating speed constraints as control constraints rather than state constraints in the MPC problem. The optimization of vehicle groups speeds is formulated as a linear programming problem which can be solved efficiently. We further integrate the presented MPC to a hierarchical VSL control framework leveraging connected vehicles. The presented MPC decides the optimal target speed of each vehicle group led by a connected automated vehicle (CAV) at the upper macroscopic level with a prediction horizon of 20 min. At the lower microscopic level, CAVs randomly distributed in mixed traffic are regarded as actuators of the upper layer. Microscopic CAV accelerations are optimized in a short horizon of the order 5–10 s so that the human-driven vehicles following them reach the target speed from the upper layer in an efficient and smooth manner. The presented MPC and the hierarchical control approach are tested in microscopic simulation environments. Simulation results show that (i) the presented MPC resolves freeway jam waves efficiently with reasonable safety constraints implemented, and (ii) the presented hierarchical control approach can effectively resolve jam waves in a single-lane freeway, even though the penetration rate of CAVs is as low as 5%.

Alkaline pretreatment of tannery wastewater impact on biochemical methane potential tests: experimental study and kinetic modeling

Studies were carried out on anaerobic digestion of tannery wastewater obtained from leather processing. Degassed activated sludge biomass collected from a wastewater treatment plant was used as source of microorganisms. The study was carried out to examine the impact of alkaline pretreatment on a real tannery wastewater prior anaerobic digestion process. Bio-methane potential tests were conducted at 35±2°C on tannery wastewater pretreated by adding different volumes of 2N NaOH solution up to set pH values at 9, 10, 11, and 12, respectively. NaOH solution addition resulted in a partial removal of total Cr showing efficiency from 16.84 to 95.72% as well as in an increase of the soluble chemical oxygen demand concentration from 8.53 to 29.02%. The effects of this pretreatment affected significantly the results obtained with bio-methane potential tests that showed methane production from all the pretreated tannery wastewater samples much higher than from that unpretreated. Finally, the lag phase duration and the maximum specific methane production rate of the anaerobic digestion process were evaluated by fitting the experimental results from bio-methane potential tests with the following three models: (i) the modified Gompertz model, (ii) the Logistic function, and (iii) the Richards model. All the previous models showed a high level of accordance with the experimental data, even though Richards model resulted in being the most accurate.

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.

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.

Investigation of the settlement prediction in soft soil by Richards Model: based on a linear least squares-iteration method

Investigation of the settlement prediction in soft soil by Richards Model: based on a linear least squares-iteration method

The impact of crude glycerol from biodiesel production and its trace element content on biomethane production in a batch experiment: modelling as a step towards impartial routine comparison of results

In this study, crude glycerol from the biodiesel industry was tested as a co-substrate in biogas production. To investigate the influence of crude glycerol and the underlying trace element (TE) content on the efficiency of biomethane production, a batch experiment using Automatic Methane Potential Test System (AMPTS II) was carried out. The single addition of crude glycerol significantly contributed only to the total content of K (14.4%), Si (17.3%), and P (11.6%), whereas the contributions of other metals were within the range of other substrates. The addition of crude glycerol increased biomethane production, however, its utilization beyond 1% of total volume resulted in prolonged lag phase and final cessation of biomethane production. The negative effects of inorganic salts present in crude glycerol were reflected in progressively diminishing parts of glycerol and methanol being utilized in its anaerobic digestion, posing serious problems for daily routine use. A nonlinear least square regression analysis was performed to fit the Gompertz, Logistic, Transfer, and Richards models to biomethane production. The most suitable model was the Richards model, exhibiting the best fit to the experimental curves for complex substrates. Glycerol fractions remaining after biodiesel production have to be pre-tested for their negative effects on the content of TEs and inorganic salts, lag phase in biogas production, before they are used as co-substrates in biogas production phase.

Entropy solutions for a two-phase transition model for vehicular traffic with metastable phase and time depending point constraint on the density flow

We consider a macroscopic two-phase transition model for vehicular traffic flow subject to a point constraint on the density flux. The two phases correspond to light and heavy traffic and their dynamics are described respectively by the Lighthill–Whitham–Richards model and the Aw–Rascle–Zhang model. Their intersection, the so-called metastable phase, is assumed to be non empty. The discrete in time point constraint mechanism, inducing flux limitation at bottlenecks, is explored within this two-phase model. We introduce a new definition of admissible solutions for the Cauchy problem, for which we prove existence and we provide a characterization. In particular, these admissible solutions attain the maximal flux allowed by the constraint whenever it is enforced, which guarantees compatibility of the constructed solutions with the modeling assumption imposed at the level of the Riemann solver. These results rely on the wave-front tracking method and on adaptation of the specific entropies and renormalization properties introduced in Andreainov, Donadello, Rosini, M3AS (2016) while dealing with the Aw–Rascle–Zhang model with point constraint.

Modeling the Epidemic Growth of Preprints on COVID-19 and SARS-CoV-2

The response of the scientific community to the global health emergency caused by the COVID-19 pandemic has produced an unprecedented number of manuscripts in a short period of time, the vast majority of which have been shared in the form of preprints posted on online preprint repositories before peer review. This surge in preprint publications has in itself attracted considerable attention, although mostly in the bibliometrics literature. In the present study we apply a mathematical growth model, known as the generalized Richards model, to describe the time evolution of the cumulative number of COVID-19 related preprints. This mathematical approach allows us to infer several important aspects concerning the underlying growth dynamics, such as its current stage and its possible evolution in the near future. We also analyze the rank-frequency distribution of preprints servers, ordered by the number of COVID-19 preprints they host, and find that it follows a power law in the low rank (high frequency) region, with the high rank (low frequency) tail being better described by a q-exponential function. The Zipf-like law in the high frequency regime indicates the presence of a cumulative advantage effect, whereby servers that already have more preprints receive more submissions.

COMPARISON OF THREE NONLINEAR MODELS TO DESCRIBE THE GROWTH CURVE OF HOLSTEIN-FRIESIAN BULLS RAISED UNDER EGYPTIAN CONDITIONS

The current study aimed to estimate the growth curve parameters through three non-linear models (logistic, Gompertz and Richards) to determine which model best fits the data. A total number of 1566 monthly live weight records of 87 Holstein- Friesian bulls collected between 2017-2019 from a Holstein-Friesian herd cattle that belongs to the Association of Livestock Development (EL- Lahhamy farm), located thirty kilometers west of Fayoum governrate. In this work, the parameters of studied models, asymptotic weight (A), Constant of integration (b), and the maturation rate (K) ranged from 626.15 kg to 879.82 kg, 2.708 to 11.08, and 0.0035 to 0.008, respectively. According to the studied parameters of growth functions, Gompertz reached the highest numerical estimated value for (A) and the Logistic function had the lowest value. Parameter (K) estimate by the Gompertz model was similar to that obtained by the Richards model; both values were lower than those attained through the Logistic model (0.008). The inflection point traits, time at Point of inflection (IPT) and weight at Point of inflection (IPW) estimates ranged from 300.64 kg to 314.59 kg and 323.92 days to 336.14 days, respectively. The Richards model has the highest estimates of IPW and IPT compared to the other models, also it had the best adjustment according to model goodness of fit criteria, by having the lowest values for Akaike information criterion (AIC), Schwarz Bayesian information criterion( BIC), Mean square error (MSE) and highest : coefficient of determination (R 2 ) 82236.80, 83265.51, 317.37 and 0.9983.

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 (BWs), harvest length (HL), and growth parameters derived from the Richards model. For this purpose, individual BW of 1,088 mink measured seven times in 3-wk intervals (weeks 13 to 31 of life) were used for growth curve modeling using the Richards model. The BW traits included BW 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 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 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 with HL indicated that selection for higher α, AIP, and WIP values would increase HL. Parameters k and m had nonsignificant (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.

Ensemble bootstrap methodology for forecasting dynamic growth processes using differential equations: application to epidemic outbreaks

BackgroundEnsemble modeling aims to boost the forecasting performance by systematically integrating the predictive accuracy across individual models. Here we introduce a simple-yet-powerful ensemble methodology for forecasting the trajectory of dynamic growth processes that are defined by a system of non-linear differential equations with applications to infectious disease spread.MethodsWe propose and assess the performance of two ensemble modeling schemes with different parametric bootstrapping procedures for trajectory forecasting and uncertainty quantification. Specifically, we conduct sequential probabilistic forecasts to evaluate their forecasting performance using simple dynamical growth models with good track records including the Richards model, the generalized-logistic growth model, and the Gompertz model. We first test and verify the functionality of the method using simulated data from phenomenological models and a mechanistic transmission model. Next, the performance of the method is demonstrated using a diversity of epidemic datasets including scenario outbreak data of the Ebola Forecasting Challenge and real-world epidemic data outbreaks of including influenza, plague, Zika, and COVID-19.ResultsWe found that the ensemble method that randomly selects a model from the set of individual models for each time point of the trajectory of the epidemic frequently outcompeted the individual models as well as an alternative ensemble method based on the weighted combination of the individual models and yields broader and more realistic uncertainty bounds for the trajectory envelope, achieving not only better coverage rate of the 95% prediction interval but also improved mean interval scores across a diversity of epidemic datasets.ConclusionOur new methodology for ensemble forecasting outcompete component models and an alternative ensemble model that differ in how the variance is evaluated for the generation of the prediction intervals of the forecasts.

Comparison of nonlinear mathematical models for lamb growth analysis.

With the objective to determine the best mathematical model that could demonstrate the relationship between body weight and age in crossbred sheep, and to evaluate its applicability in different farms, 9985 live weight records of 837 crossbred lambs of Texel, Ile de France, Suffolk, and Hampshire Down breeds were used. Brody, von Bertalanffy, Richards, Logistic, and Gompertz models were fitted to the weight data, which were compared based on adjusted R2, Syx%, chi-square, and Kolmogorov-Smirnov tests, as well as residual analysis. After selecting the model, lambs whose weights at different ages fell within, below, or above ±20% of the values predicted by the model were classified as medium, low, or high performance, respectively. To validate the model, we used a validation dataset comprising 2898 weights of lambs from 6 different farms. Based on statistical analysis and biological characteristics (sigmoid trend of weight over time, weight at birth, and standard deviation), the model that best represented the growth of the lambs was the Richards model. The percentage of lambs classified as below, within, and above the predicted values based on the model was highly similar for the original and validation data, which indicates that this model could be used in different farms. It was concluded that the Richards model best described the live weight growth of crossbred lambs and aided in classifying the lambs as high, medium, or low performance, thereby providing a complementary tool in management decision-making.

Exactly solvable SIR models, their extensions and their application to sensitive pandemic forecasting.

The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection rates and solved explicitly when the control parameter depends on the accumulated infections at time t. Numerical results are presented by way of comparison. Autonomous and non-autonomous generalizations of SIR for interacting regions are also considered, including non-separability for two or more interacting regions. A reduction of simple SIR models to one variable leads us to a generalized logistic model, Richards model, which we use to fit Mexico’s COVID-19 data up to day number 134. Forecasting scenarios resulting from various fittings are discussed. A critique to the applicability of these models to current pandemic outbreaks in terms of robustness is provided. Finally, we obtain the bifurcation diagram for a discretized version of Richards model, displaying period doubling bifurcation to chaos.

Short-term real-time prediction of total number of reported COVID-19 cases and deaths in South Africa: a data driven approach

BackgroundThe rising burden of the ongoing COVID-19 epidemic in South Africa has motivated the application of modeling strategies to predict the COVID-19 cases and deaths. Reliable and accurate short and long-term forecasts of COVID-19 cases and deaths, both at the national and provincial level, are a key aspect of the strategy to handle the COVID-19 epidemic in the country.MethodsIn this paper we apply the previously validated approach of phenomenological models, fitting several non-linear growth curves (Richards, 3 and 4 parameter logistic, Weibull and Gompertz), to produce short term forecasts of COVID-19 cases and deaths at the national level as well as the provincial level. Using publicly available daily reported cumulative case and death data up until 22 June 2020, we report 5, 10, 15, 20, 25 and 30-day ahead forecasts of cumulative cases and deaths. All predictions are compared to the actual observed values in the forecasting period.ResultsWe observed that all models for cases provided accurate and similar short-term forecasts for a period of 5 days ahead at the national level, and that the three and four parameter logistic growth models provided more accurate forecasts than that obtained from the Richards model 10 days ahead. However, beyond 10 days all models underestimated the cumulative cases. Our forecasts across the models predict an additional 23,551–26,702 cases in 5 days and an additional 47,449–57,358 cases in 10 days. While the three parameter logistic growth model provided the most accurate forecasts of cumulative deaths within the 10 day period, the Gompertz model was able to better capture the changes in cumulative deaths beyond this period. Our forecasts across the models predict an additional 145–437 COVID-19 deaths in 5 days and an additional 243–947 deaths in 10 days.ConclusionsBy comparing both the predictions of deaths and cases to the observed data in the forecasting period, we found that this modeling approach provides reliable and accurate forecasts for a maximum period of 10 days ahead.

Modeling the Methane Production Kinetics of Anaerobic Co-Digestion of Agricultural Wastes Using Sigmoidal Functions

The modified sigmoidal bacteria growth functions (the modified Gompertz, logistic, and Richards) were used to evaluate the methane production process kinetics of agricultural wastes. The mesophilic anaerobic co-digestion experiments were conducted with various agricultural wastes as feedstocks, including cow manure, corn straw, grape leaves, vines, wine residue, strawberry leaves, and tomato leaves. The results showed that anaerobic co-digestion of cow manure and other agricultural wastes increased the methane yields while it prolonged the lag phase time. Compared with the modified Gompertz and logistic models, the modified Richards model obtained higher correlation coefficients and was able to fit experimental data better. The results of this study were expected to determine a suitable model to simulate and study the kinetic process of anaerobic co-digestion with mixed agricultural wastes as feedstocks.

Türkiye'de 17 Mart ile 12 Temmuz 2020 Arasında COVID-19 Vakaları Kullanılarak Büyüme Modellerinin Belirlenmesi Üzerine Bir Çalışma: Kesitsel Çalışma

Objective: We use the most frequently used growth functions in the literature for estimating Turkey's cumulative number of confirmed coronavirus disease-2019 (COVID-19) cases. We analyze Brody, Bertalanffy, Logistic, Generalized Logistic, Gompertz, Richards, Negative Exponential, Stevens, and Tanaka models for determining the appropriate model. Material and Methods: The number of cases of COVID-19 in Turkey between March 17, 2020 and July 12, 2020 were included in the study. The data used in the study were obtained from Johns Hopkins University. We used the most frequently used Non-linear growth models in the literature for estimating Turkey's cumulative number of confirmed COVID-19 cases. Matlab software was used to estimate the parameters in the models studied. non-linear least squares regression function is used in Matlab software. Results: According to the estimation results, the best fitting model is the Richards model in terms of both the mean squared error and R2 (coefficient of determination). Conclusion: We recommend to use the Richards model in modeling the cumulative COVID-19 cases. For estimating the future cases, it will be appropriate to use the Richards model. In addition, estimates of the number of daily cases obtained from the Richards model are not compatible with the actual number of daily cases. This may occur because estimations on these growth models can sometimes lead to erroneous results.

A Growth Performance and Nonlinear Growth Curve Functions of Large- and Normal-Sized Japanese Quail (Coturnix japonica).

This study aimed to evaluate the differences between the growth patterns of large- and normal-sized Japanese quail strains and their F1 progeny, by fitting their growth parameter values to five nonlinear regression growth models (Weibull, Logistic, Gompertz, Richards, and Brody). The Richards model presented the best fit for both sexes of the large-sized quail strain, whereas the Gompertz model presented the best fit for both sexes of the normal-sized quail strain, based on goodness-of-fit criteria (higher adjusted R2 and lower Akaike and Bayesian information criteria). Both sexes of F1 birds derived from the cross between normal-sized females and large-sized males were best fitted by the Richards model. In contrast, growth parameters of the F1 birds derived from the cross between large-sized females and normal-sized males were best fitted to the Gompertz model. The data could be fitted nearly as well to the Weibull and Logistic models as to the Richards and Gompertz models. The Brody model presented the poorest fit for the growth parameter values. The results indicated that the Richards and Gompertz models could best describe the growth characteristics of both large- and normal-sized quails. Moreover, the observed growth pattern of the F1 birds was likely inherited from the male parental strain. To the best of our knowledge, this is the first study comparing the growth curves of the reciprocal F1 generations with their parental strains in quails.

Comparison of non-linear models to describe the growth in the Andalusian turkey breed

Seven non-linear growth models were compared in the Andalusian turkey, an endangered native breed. To this aim, turkeys were weekly weighted until they reached 35 weeks. The goodness-of-fit and flexibility criteria of Brody, Von Bertalanffy, Verhulst, Logistic, Gompertz, Richards, and Sinusoidal growth models were evaluated to quantify their ability to describe the biological growth curve. Goodness-of-fit criteria were assessed comparing the mean squared error (MSE) and adjusted determination coefficient (Pseudo-R2), while the flexibility criteria of Akaike (AIC) and Bayesian information criteria (BIC) were evaluated to quantify the explanatory and predictive ability of the models tested. Afterward, all criteria were considered in a combined index to determine the most efficient model to describe and predict growth patterns. The best-fitting model for males growth was Logistic (MSE: 250,349.87; Pseudo-R2: 0.97) which also reported the best explanatory and predictive properties (AIC: 18,949.25; BIC: 18,963.24), while best goodness-of-fit criteria, explanatory and predictive capacity in females were reported for the Richards model (MSE: 144,432.45; Pseudo-R2: 0.95; AIC: 17,529.83; BIC: 17,549.02, respectively). Von Bertalanffy and Richards models underestimated the weight at early age stages, contrary to Logistic and Verhulst models. The asymptotic weight was higher in males than in females at all evaluated models, being 11,085.37 g for Logistic and 5,706.38 g for Richards, respectively. In conclusion, a marked sexual dimorphism is evident, with females reaching maturity earlier than males. The higher inflection point in males may enable their relatively easier commercial standardisation than in turkey hens. Highlights Logistic was the best fitting model for males' growth and Richards for females. Females reach maturity earlier than males with higher rates of maturity. Andalusian turkey breed shows an intense sexual dimorphism.

Choice of non-linear models to determine the growth curve of meat-type quail

ABSTRACT: The objective of this study was to compare non-linear models fitted to the growth curves of quail to determine which model best describes their growth and check the similarity between models by analyzing parameter estimates.Weight and age data of meat-type European quail (Coturnix coturnix coturnix) of three lines were used, from an experiment in a 2 × 4 factorial arrangement in a completely randomized design, consisting of two metabolizable energy levels, four crude protein levels and six replicates. The non-linear Brody, Von Bertalanffy, Richards, Logistic and Gompertz models were used. To choose the best model, the Adjusted Coefficient of Determination, Convergence Rate, Residual Mean Square, Durbin-Watson Test, Akaike Information Criterion and Bayesian Information Criterion were applied as goodness-of-fit indicators. Cluster analysis was performed to check the similarity between models based on the mean parameter estimates. Among the studied models, Richards’ was the most suitable to describe the growth curves. The Logistic and Richards models were considered similar in the analysis with no distinction of lines as well as in the analyses of Lines 1, 2 and 3.

Global Assessment of the Impact of Masking on COVID-19: A Country Level Comparative and Retrospective Analyses Using the Richards Model

Background: Within four months since the first reported case in Wuhan, China, corona virus disease 2019 (COVID-19) spread to more than 200 countries. Since the initially reported cases in each country until mid-August 2020, country-specific interventions on masking were decentralized. Many types of masks are effective under laboratory conditions. But people wear mask inconsistently and imperfectly in the real-world. The extent by which the effectiveness of masking when mandated at a country level for multiple countries/regions reduces severe acute respiratory syndrome 2 (SARS-CoV-2) transmission has not been analyzed. Additionally, the question exists if the type of mask worn, i.e., cloth mask, surgical mask, and bandana, were effective in halting the transmission of SARS-CoV-2. Therefore, using the Richards model, a phenomenological method, we investigated differences in the infection rate (r), turning point (ti), and curve steepness (α) of the COVID-19 outbreak among 177 countries to assess the impact of masking policy and the type of mask in containing the COVID-19.Methods: We used the daily cumulative infection cases from the first reported case until August 19, 2020 for 177 countries/region taken from www.ourworldindata.org , a publicly available COVID-19 data repository. Using data for each country, we derived the r, ti, and α of COVID-19 by fitting them to the Richards model. Data fitting was performed manually in IgorPro software. We evaluated goodness of fit by minimizing the χ2 .Findings: Our analysis revealed that global COVID-19 estimates of α = 0.009 – 4.3 (95% confidence interval (CI95%), 0.005 – 0.680), r = 0.008 – 0.50 (CI95%: 0.0001 – 0.0045), and ti = 0.58 – 315.92 (CI95%: 0.02 – 36.85). The estimated range was within the limit for both countries with and without mask mandates for single and multiple wave cases. Additionally, an early masking mandate did not correlate with a shorter ti. Interpretation: Based on the phenomenological Richards model, this retrospective study’s findings indicate no significant difference in r, ti, and α between countries with and without mask mandate. Therefore, many laboratory and modeling studies on masking did not translate to a measurable difference in the real world for many countries based on our fitting. Effectiveness of masking coupled with other non-pharmaceutical interventions depends on the measures carried out by a specific country/region. This result implies that mask enforcement policy and the type of mask use (e.g., surgical, cloth) could not have significantly reduced SARS-CoV-2 transmission. Therefore, more stringent protection such as N95 combined with other control measures such as enhanced indoor ventilation, a longer social distancing recommendation may be necessary to disrupt SARS-CoV-2 transmission effectively. Therefore, selecting the mask type is critical to effectively disrupt the transmission of SARS-COV-2, which is primarily transmitted via aerosols.Funding Information: None.Declaration of Interests: We have no competing interest to declare.