scholarly journals Flatten the Curve!

REGION ◽  
2020 ◽  
Vol 7 (2) ◽  
pp. 43-83
Author(s):  
Thomas Wieland
Keyword(s):  
Growth Rates ◽  
Growth Models ◽  
Regional Growth ◽  
Logistic Growth ◽  
School Closures ◽  
Epidemic Curve ◽  
Child Day Care ◽  
Voluntary Behavior ◽  
Before School ◽  
Novel Coronavirus

Since the emerging of the "novel coronavirus" SARS-CoV-2 and the corresponding respiratory disease COVID-19, the virus has spread all over the world. Being one of the most affected countries in Europe, in March 2020, Germany established several nonpharmaceutical interventions to contain the virus spread, including the closure of schools and child day care facilities (March 16-18, 2020) as well as a full "lockdown" with forced social distancing and closures of "nonessential" services (March 23, 2020). The present study attempts to analyze whether these governmental interventions had an impact on the declared aim of "flattening the curve", referring to the epidemic curve of new infections. This analysis is conducted from a regional perspective. On the level of the 412 German counties, logistic growth models were estimated based on daily infections (estimated from reported cases), aiming at determining the regional growth rate of infections and the point of inflection where infection rates begin to decrease and the curve flattens. All German counties exceeded the peak of new infections between the beginning of March and the middle of April. In a large majority of German counties, the epidemic curve has flattened before the "lockdown" was established. In a minority of counties, the peak was already exceeded before school closures. The growth rates of infections vary spatially depending on the time the virus emerged. Counties belonging to states which established an additional curfew show no significant improvement with respect to growth rates and mortality. Furthermore, mortality varies strongly across German counties, which can be attributed to infections of people belonging to the "risk group", especially residents of retirement homes. The decline of infections in absence of the "lockdown" measures could be explained by 1) earlier governmental interventions (e.g., cancellation of mass events, domestic quarantine), 2) voluntary behavior changes (e.g., physical distancing and hygiene), 3) seasonality of the virus, and 4) a rising but undiscovered level of immunity within the population. The results raise the question whether formal contact bans and curfews really contribute to curve flattening within a pandemic.

scholarly journals Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level

2020 ◽  
Author(s):  
Thomas Wieland
Keyword(s):  
Growth Rates ◽  
Growth Models ◽  
Regional Growth ◽  
Logistic Growth ◽  
School Closures ◽  
Epidemic Curve ◽  
Child Day Care ◽  
Curve Modeling ◽  
Before School ◽  
Novel Coronavirus

AbstractSince the emerging of the “novel coronavirus” SARS-CoV-2 and the corresponding respiratory disease COVID-19, the virus has spread all over the world. Being one of the most affected countries in Europe, in March 2020, Germany established several nonpharmaceutical interventions to contain the virus spread, including the closure of schools and child day care facilities (March 16-18, 2020) as well as a full “lockdown” with forced social distancing and closures of “nonessential” services (March 23, 2020). The present study attempts to analyze whether these governmental interventions had an impact on the declared aim of “flattening the curve”, referring to the epidemic curve of new infections. This analysis is conducted from a regional perspective. On the level of the 412 German counties, logistic growth models were estimated based on daily infections (estimated from reported cases), aiming at determining the regional growth rate of infections and the point of inflection where infection rates begin to decrease and the curve flattens. All German counties exceeded the peak of new infections between the beginning of March and the middle of April. In a large majority of German counties, the epidemic curve has flattened before the “lockdown” was established. In a minority of counties, the peak was already exceeded before school closures. The growth rates of infections vary spatially depending on the time the virus emerged. Counties belonging to states which established an additional curfew show no significant improvement with respect to growth rates and mortality. Furthermore, mortality varies strongly across German counties, which can be attributed to infections of people belonging to the “risk group”, especially residents of retirement homes. The results raise the question whether social ban measures and curfews really contribute to curve flattening within a pandemic.

Excitable and Nonexcitable Population Dynamics

2011 ◽  
Author(s):  
Kevin S. McCann
Keyword(s):  
Population Dynamics ◽  
Growth Rates ◽  
Growth Models ◽  
Population Models ◽  
Logistic Growth ◽  
Population Growth Rates ◽  
Discrete Equations ◽  
Sustained Oscillations ◽  
Continuous Models ◽  
Per Capita

This chapter examines the dynamics of basic population models, with a particular focus on the general biological conditions under which population dynamics are stabilized, or destabilized, by increased population growth rates. Three classes of population models are discussed in relation to excitable and nonexcitable interactions: continuous logistic growth models, discrete equations, and continuous models with stage-structured lags. The chapter shows how increasing per capita growth rates tend to stabilize population models as a result of excitable interactions; that is, when dynamic trajectories monotonically approach an equilibrium after a localized perturbation. However, lags in population models tend to give rise to dynamics with oscillatory decays to equilibrium or sustained oscillations around the carrying capacity. Such oscillatory decays or sustained oscillations are only further destabilized by increased growth or production rates. The chapter concludes with a review of empirical evidence for excitable dynamics.

scholarly journals Density-independent processes decouple component and ensemble density feedbacks

2021 ◽  
Author(s):  
Corey J. A. Bradshaw ◽  
Salvador Herrando-Perez
Keyword(s):  
Population Growth ◽  
Growth Rates ◽  
Carrying Capacity ◽  
Census Data ◽  
Growth Models ◽  
Structured Populations ◽  
Logistic Growth ◽  
Feedback Signal ◽  
Vital Rates ◽  
Population Growth Rates

Analysis of long-term trends in abundance provide insights into population dynamics. Population growth rates are the emergent interplay of fertility, survival, and dispersal, but the density feedbacks on some vital rates (component) can be decoupled from density feedback on population growth rates (ensemble). However, the mechanisms responsible for this decoupling are poorly understood. We simulated component density feedbacks on survival in age-structured populations of long-living vertebrates and quantified how imposed nonstationarity (density-independent mortality and variation in carrying-capacity) modified the ensemble feedback signal estimated from logistic-growth models to the simulated abundance time series. The statistical detection of ensemble density feedback was largely unaffected by density-independent processes, but catastrophic and proportional mortality eroded the effect of density-dependent survival on ensemble-feedback strength more strongly than variation in carrying capacity. Thus, phenomenological models offer a robust approach to capture density feedbacks from nonstationary census data when density-independent mortality is low.

scholarly journals Forecasting of COVID-19 epidemic size in four high hitting nations (USA, Brazil, India and Russia) by Fb-Prophet machine learning model

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gopi Battineni ◽  
Nalini Chintalapudi ◽  
Francesco Amenta
Keyword(s):  
Machine Learning ◽  
Design Methodology ◽  
Logistic Growth ◽  
Content Type ◽  
Epidemic Curve ◽  
Epidemic Size ◽  
Machine Learning Model ◽  
The Usa ◽  
Logistic Growth Model ◽  
Novel Coronavirus

PurposeAs of July 30, 2020, more than 17 million novel coronavirus disease 2019 (COVID-19) cases were registered including 671,500 deaths. Yet, there is no immediate medicine or vaccination for control this dangerous pandemic and researchers are trying to implement mathematical or time series epidemic models to predict the disease severity with national wide data.Design/methodology/approachIn this study, the authors considered COVID-19 daily infection data four most COVID-19 affected nations (such as the USA, Brazil, India and Russia) to conduct 60-day forecasting of total infections. To do that, the authors adopted a machine learning (ML) model called Fb-Prophet and the results confirmed that the total number of confirmed cases in four countries till the end of July were collected and projections were made by employing Prophet logistic growth model.FindingsResults highlighted that by late September, the estimated outbreak can reach 7.56, 4.65, 3.01 and 1.22 million cases in the USA, Brazil, India and Russia, respectively. The authors found some underestimation and overestimation of daily cases, and the linear model of actual vs predicted cases found a p-value (<2.2e-16) lower than the R2 value of 0.995.Originality/valueIn this paper, the authors adopted the Fb-Prophet ML model because it can predict the epidemic trend and derive an epidemic curve.

Dynamic Predictive Model for Growth of Bacillus cereus from Spores in Cooked Beans

2017 ◽  
Vol 81 (2) ◽  
pp. 308-315 ◽  
Author(s):  
Vijay K. Juneja ◽  
Abhinav Mishra ◽  
Abani K. Pradhan
Keyword(s):  
Bacillus Cereus ◽  
Growth Rates ◽  
Linear Models ◽  
Growth Models ◽  
Maximum Growth ◽  
Effect Of Temperature ◽  
Coefficient Of Determination ◽  
Growth Data ◽  
Three Phase ◽  
Primary Model

ABSTRACT Kinetic growth data for Bacillus cereus grown from spores were collected in cooked beans under several isothermal conditions (10 to 49°C). Samples were inoculated with approximately 2 log CFU/g heat-shocked (80°C for 10 min) spores and stored at isothermal temperatures. B. cereus populations were determined at appropriate intervals by plating on mannitol–egg yolk–polymyxin agar and incubating at 30°C for 24 h. Data were fitted into Baranyi, Huang, modified Gompertz, and three-phase linear primary growth models. All four models were fitted to the experimental growth data collected at 13 to 46°C. Performances of these models were evaluated based on accuracy and bias factors, the coefficient of determination (R2), and the root mean square error. Based on these criteria, the Baranyi model best described the growth data, followed by the Huang, modified Gompertz, and three-phase linear models. The maximum growth rates of each primary model were fitted as a function of temperature using the modified Ratkowsky model. The high R2 values (0.95 to 0.98) indicate that the modified Ratkowsky model can be used to describe the effect of temperature on the growth rates for all four primary models. The acceptable prediction zone (APZ) approach also was used for validation of the model with observed data collected during single and two-step dynamic cooling temperature protocols. When the predictions using the Baranyi model were compared with the observed data using the APZ analysis, all 24 observations for the exponential single rate cooling were within the APZ, which was set between −0.5 and 1 log CFU/g; 26 of 28 predictions for the two-step cooling profiles also were within the APZ limits. The developed dynamic model can be used to predict potential B. cereus growth from spores in beans under various temperature conditions or during extended chilling of cooked beans.

scholarly journals Forecasting COVID-19 cases in Algeria using logistic growth and polynomial regression models

2021 ◽  
Author(s):  
Mohamed LOUNIS ◽  
Babu Malavika
Keyword(s):  
Regression Model ◽  
Logistic Model ◽  
Polynomial Regression ◽  
Logistic Growth ◽  
The Novel ◽  
Logistic Growth Model ◽  
Polynomial Regression Models ◽  
Using Data ◽  
Novel Coronavirus ◽  
Polynomial Regression Model

Abstract The novel Coronavirus respiratory disease 2019 (COVID-19) is still expanding through the world since it started in Wuhan (China) on December 2019 reporting a number of more than 84.4 millions cases and 1.8 millions deaths on January 3rd 2021.In this work and to forecast the COVID-19 cases in Algeria, we used two models: the logistic growth model and the polynomial regression model using data of COVID-19 cases reported by the Algerian ministry of health from February 25th to December 2nd, 2020. Results showed that the polynomial regression model fitted better the data of COVID-19 in Algeria the Logistic model. The first model estimated the number of cases on January, 19th 2021 at 387673 cases. This model could help the Algerian authorities in the fighting against this disease.

scholarly journals The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

2018 ◽  
Author(s):  
Emanuel A. Fronhofer ◽  
Lynn Govaert ◽  
Mary I. O’Connor ◽  
Sebastian J. Schreiber ◽  
Florian Altermatt
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Level ◽  
Logistic Growth ◽  
Population Densities ◽  
Density Regulation ◽  
Logistic Growth Model ◽  
Regulation Functions ◽  
Consumer Resource ◽  
Population Growth Models

AbstractThe logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

scholarly journals Building reaction kinetic models for amiloid fibril growth

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1607311 ◽  
Author(s):  
Svetoslav Marinov Markov
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Reaction Kinetic ◽  
Growth Models ◽  
Reaction Network ◽  
Network Models ◽  
Point Of View ◽  
Logistic Growth ◽  
Sigmoidal Functions ◽  
Methodological Aspects

In this work we  discuss some methodological aspects of the creation and formulation of mathematical  models describing the growth of species from the point of view of reaction kinetics. Our discussion is based on familiar examples of growth models such as logistic growth and enzyme kinetics. We   propose several reaction network  models  for  the amiloid fibrillation processes in the citoplasm. The solutions of the models are sigmoidal functions graphically visualized using  the computer algebra system   Mathematica.

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