The COVID-19 pandemics challenges governments across the world.To develop adequate responses,they need accurate models for the spread of the disease.Using least squares,we fitted Bertalanffy-Pütter(BP)trend curve...The COVID-19 pandemics challenges governments across the world.To develop adequate responses,they need accurate models for the spread of the disease.Using least squares,we fitted Bertalanffy-Pütter(BP)trend curves to data about the first wave of the COVID-19 pandemic of 2020 from 49 countries and provinces where the peak of the first wave had been passed.BP-models achieved excellent fits(R-squared above 99%)to all data.Using them to smoothen the data,in the median one could forecast that the final count(asymptotic limit)of infections and fatalities would be 2.48 times(95%confidence limits 2.42-2.6)and 2.67 times(2.39-2.765)the total count at the respective peak(inflection point).By comparison,using logistic growth would evaluate this ratio as 2.00 for all data.The case fatality rate,defined as the quotient of the asymptotic limits of fatalities and confirmed infections,was in the median 4.85%(confidence limits 4.4%e6.5%).Our result supports the strategies of governments that kept the epidemic peak low,as then in the median fewer infections and fewer fatalities could be expected.展开更多
The Bertalanffy-Pütter (BP) five-parameter growth model provides a versatile framework for the modeling of growth. Using data from a growth experiment in literature about the average size-at-age of 24 species of ...The Bertalanffy-Pütter (BP) five-parameter growth model provides a versatile framework for the modeling of growth. Using data from a growth experiment in literature about the average size-at-age of 24 species of tropical trees over ten years in the same area, we identified their best-fit BP-model parameters. While different species had different best-fit exponent-pairs, there was a model with a good fit to 21 (87.5%) of the data </span><span style="font-family:Verdana;">(</span><span style="font-family:""><span style="font-family:Verdana;">“Good fit” means a </span><span style="font-family:Verdana;">normalized root-mean-squared-error <i></span><i><span style="font-family:Verdana;">NRMSE</span></i><span style="font-family:Verdana;"></i> below 2.5%. This threshold was the 95% quantile of the lognormal distribution that was fitted to the <i></span><i><span style="font-family:Verdana;">NRMSE</span></i><span style="font-family:Verdana;"></i> values for the best-fit models for the data)</span></span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;"> In view of the sigmoidal character of this model despite the early stand we discuss </span><span style="font-family:Verdana;">whether </span><span style="font-family:Verdana;">the setting of the growth experiment may have impeded growth.展开更多
The paper searched for raw data about wild-caught fish, where a sigmoidal growth function described the mass growth significantly better than non-sigmoidal functions. Specifically, von Bertalanffy’s sigmoidal growth ...The paper searched for raw data about wild-caught fish, where a sigmoidal growth function described the mass growth significantly better than non-sigmoidal functions. Specifically, von Bertalanffy’s sigmoidal growth function (metabolic exponent-pair a = 2/3, b = 1) was compared with unbounded linear growth and with bounded exponential growth using the Akaike information criterion. Thereby the maximum likelihood fits were compared, assuming a lognormal distribution of mass (i.e. a higher variance for heavier animals). Starting from 70+ size-at-age data, the paper focused on 15 data coming from large datasets. Of them, six data with 400 - 20,000 data-points were suitable for sigmoidal growth modeling. For these, a custom-made optimization tool identified the best fitting growth function from the general von Bertalanffy-Pütter class of models. This class generalizes the well-known models of Verhulst (logistic growth), Gompertz and von Bertalanffy. Whereas the best-fitting models varied widely, their exponent-pairs displayed a remarkable pattern, as their difference was close to 1/3 (example: von Bertalanffy exponent-pair). This defined a new class of models, for which the paper provided a biological motivation that relates growth to food consumption.展开更多
文摘The COVID-19 pandemics challenges governments across the world.To develop adequate responses,they need accurate models for the spread of the disease.Using least squares,we fitted Bertalanffy-Pütter(BP)trend curves to data about the first wave of the COVID-19 pandemic of 2020 from 49 countries and provinces where the peak of the first wave had been passed.BP-models achieved excellent fits(R-squared above 99%)to all data.Using them to smoothen the data,in the median one could forecast that the final count(asymptotic limit)of infections and fatalities would be 2.48 times(95%confidence limits 2.42-2.6)and 2.67 times(2.39-2.765)the total count at the respective peak(inflection point).By comparison,using logistic growth would evaluate this ratio as 2.00 for all data.The case fatality rate,defined as the quotient of the asymptotic limits of fatalities and confirmed infections,was in the median 4.85%(confidence limits 4.4%e6.5%).Our result supports the strategies of governments that kept the epidemic peak low,as then in the median fewer infections and fewer fatalities could be expected.
文摘The Bertalanffy-Pütter (BP) five-parameter growth model provides a versatile framework for the modeling of growth. Using data from a growth experiment in literature about the average size-at-age of 24 species of tropical trees over ten years in the same area, we identified their best-fit BP-model parameters. While different species had different best-fit exponent-pairs, there was a model with a good fit to 21 (87.5%) of the data </span><span style="font-family:Verdana;">(</span><span style="font-family:""><span style="font-family:Verdana;">“Good fit” means a </span><span style="font-family:Verdana;">normalized root-mean-squared-error <i></span><i><span style="font-family:Verdana;">NRMSE</span></i><span style="font-family:Verdana;"></i> below 2.5%. This threshold was the 95% quantile of the lognormal distribution that was fitted to the <i></span><i><span style="font-family:Verdana;">NRMSE</span></i><span style="font-family:Verdana;"></i> values for the best-fit models for the data)</span></span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;"> In view of the sigmoidal character of this model despite the early stand we discuss </span><span style="font-family:Verdana;">whether </span><span style="font-family:Verdana;">the setting of the growth experiment may have impeded growth.
文摘The paper searched for raw data about wild-caught fish, where a sigmoidal growth function described the mass growth significantly better than non-sigmoidal functions. Specifically, von Bertalanffy’s sigmoidal growth function (metabolic exponent-pair a = 2/3, b = 1) was compared with unbounded linear growth and with bounded exponential growth using the Akaike information criterion. Thereby the maximum likelihood fits were compared, assuming a lognormal distribution of mass (i.e. a higher variance for heavier animals). Starting from 70+ size-at-age data, the paper focused on 15 data coming from large datasets. Of them, six data with 400 - 20,000 data-points were suitable for sigmoidal growth modeling. For these, a custom-made optimization tool identified the best fitting growth function from the general von Bertalanffy-Pütter class of models. This class generalizes the well-known models of Verhulst (logistic growth), Gompertz and von Bertalanffy. Whereas the best-fitting models varied widely, their exponent-pairs displayed a remarkable pattern, as their difference was close to 1/3 (example: von Bertalanffy exponent-pair). This defined a new class of models, for which the paper provided a biological motivation that relates growth to food consumption.
