scholarly journals Anticipating trajectories of exponential growth

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Florian Hutzler ◽  
Fabio Richlan ◽  
Michael Christian Leitner ◽  
Sarah Schuster ◽  
Mario Braun ◽  
...  
Keyword(s):  
Growth Rates ◽  
Exponential Growth ◽  
Early Phase ◽  
Growth Curves ◽  
Epidemiological Data ◽  
Logarithmic Scaling

Humans grossly underestimate exponential growth, but are at the same time overconfident in their (poor) judgement. The so-called ‘exponential growth bias' is of new relevance in the context of COVID-19, because it explains why humans have fundamental difficulties to grasp the magnitude of a spreading epidemic. Here, we addressed the question, whether logarithmic scaling and contextual framing of epidemiological data affect the anticipation of exponential growth. Our findings show that underestimations were most pronounced when growth curves were linearly scaledandframed in the context of a more advanced epidemic progression. For logarithmic scaling, estimates were much more accurate, on target for growth rates around 31%, and not affected by contextual framing. We conclude that the logarithmic depiction is conducive for detecting exponential growth during an early phase as well as resurgences of exponential growth.

scholarly journals sparse-growth-curve: a Computational Pipeline for Parsing Cellular Growth Curves with Low Temporal Resolution

2021 ◽  
Vol 10 (19) ◽  
Author(s):  
Chuankai Cheng ◽  
J. Cameron Thrash
Keyword(s):  
Temporal Resolution ◽  
Growth Curve ◽  
Growth Rates ◽  
Exponential Growth ◽  
Software Package ◽  
Growth Curves ◽  
Cellular Growth ◽  
Computational Pipeline ◽  
Growth Phases ◽  
Time Data

ABSTRACT Here, we introduce a Python-based repository, sparse-growth-curve, a software package designed for parsing cellular growth curves with low temporal resolution. The repository uses cell density and time data as the input, automatically separates different growth phases, calculates the exponential growth rates, and produces multiple graphs to aid in interpretation.

scholarly journals A Hybrid Modeling Technique of Epidemic Outbreaks with Application to COVID-19 Dynamics in West Africa

Biology ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 365
Author(s):  
Chénangnon Frédéric Tovissodé ◽  
Jonas Têlé Doumatè ◽  
Romain Glèlè Kakaï
Keyword(s):  
West Africa ◽  
Growth Curve ◽  
Exponential Growth ◽  
Latency Period ◽  
Growth Curves ◽  
Exponential Growth Phase ◽  
Model Framework ◽  
Logistic Regression Models ◽  
Containment Measures ◽  
Reporting Data

The widely used logistic model for epidemic case reporting data may be either restrictive or unrealistic in presence of containment measures when implemented after an epidemic outbreak. For flexibility in epidemic case reporting data modeling, we combined an exponential growth curve for the early epidemic phase with a flexible growth curve to account for the potential change in growth pattern after implementation of containment measures. We also fitted logistic regression models to recoveries and deaths from the confirmed positive cases. In addition, the growth curves were integrated into a SIQR (Susceptible, Infective, Quarantined, Recovered) model framework to provide an overview on the modeled epidemic wave. We focused on the estimation of: (1) the delay between the appearance of the first infectious case in the population and the outbreak (“epidemic latency period”); (2) the duration of the exponential growth phase; (3) the basic and the time-varying reproduction numbers; and (4) the peaks (time and size) in confirmed positive cases, active cases and new infections. The application of this approach to COVID-19 data from West Africa allowed discussion on the effectiveness of some containment measures implemented across the region.

Effect of Sodium Nitrite on Growth of Shigella flexneri

1991 ◽  
Vol 54 (6) ◽  
pp. 424-428 ◽  
Author(s):  
LAURA L. ZAIKA ◽  
ANNA H. KIM ◽  
LOUISE FORD
Keyword(s):  
Exponential Growth ◽  
Shigella Flexneri ◽  
Salt Content ◽  
Brain Heart Infusion ◽  
Growth Curves ◽  
Inhibitory Effect ◽  
Plate Count ◽  
Generation Times ◽  
High Salt Content ◽  
Lag Times

A partial factorial design study of the effect of NaNO2 (0, 100, 200, 1000 ppm) in combination with NaCl (0.5, 2.5, 4.0%), pH (7.5, 6.5, 5.5), and temperature (37, 28, 19°C) on growth of Shigella flexneri is reported. Experiments were done aerobically in brain-heart infusion medium, using an inoculum of 1 × 103 CFU/ml. Growth curves were fitted from plate count data by the Gompertz equation; exponential growth rates, lag times, generation times, and maximum populations were derived for all variable combinations. In the absence of nitrite, the organism grew well under all test conditions at 37 and 28°C but did not grow at 19°C at pH 5.5 nor at pH 7.5 with 4% NaCl. Nitrite did not affect growth in media of pH 7.5 at 37 and 28°C. At pH 6.5 growth was inhibited by 1000 ppm NaNO2. The organism failed to grow at 19°C at all nitrite levels in the presence of 2.5 or 4.0% NaCl. The inhibitory effect of nitrite was much greater in media of pH 5.5 and increased with increasing salt levels. More inhibition was apparent at 28 than at 37°C. While lack of growth was used as a paradigm of the effect of nitrite on S. flexneri, nitrite also increased the lag and generation times and decreased the exponential growth rate. Results indicated that NaNO2 in combinations with low temperature, low pH, and high salt content can effectively inhibit the growth of S. flexneri.

A STUDY OF RATES OF GROWTH OF YORKSHIRE, LACOMBE, LANDRACE, AND CROSSBRED PIGS FROM BIRTH TO 200 LB

1964 ◽  
Vol 44 (3) ◽  
pp. 315-319
Author(s):  
J. M. Bell
Keyword(s):  
Growth Rates ◽  
Early Life ◽  
Growth Curves ◽  
Rates Of Growth ◽  
Similar Growth ◽  
Crossbred Pigs

Growth records were obtained from 12 research establishments across Canada for pigs fed according to current (1960–63) recommendations of nutrition and management. Growth curves showing age in days and weight in pounds are presented for the various breeds and crossbreds, for between-station comparisons, for comparison of upper and lower quartiles in purebred pigs, and for comparison of growth rates of purebreds with that of Yorkshires of 20 to 25 years ago.Age at 200 lb averaged from 152 to 187 days, among 10 stations for the Yorkshire breed. Pigs of each of the pure breeds reached 200 lb about 3 weeks earlier than that indicated in previous studies. Crossbred pigs of each of four different crosses grew more rapidly than average Yorkshires, some reaching 200 lb in 140 days and having gains in excess of 2.3 lb/day during the finishing period. Yorkshire, Lacombe, and Landrace pigs had similar growth curves. The upper quartile averaged 1.8 and the lower 1.4 lb/day gain between 100 and 200 lb weights. Slow-maturing pigs tended to be below average throughout life but differences in maturity between stations seemed to reflect differing rates of gain in early life, since finishing period gains were similar in 8 of 10 stations.

A multitype decomposable age-dependent branching process and its applications

1995 ◽  
Vol 32 (3) ◽  
pp. 591-608 ◽  
Author(s):  
Chinsan Lee ◽  
Grace L. Yang
Keyword(s):  
Tumor Growth ◽  
Life Span ◽  
Growth Rates ◽  
Exponential Growth ◽  
Branching Process ◽  
Asymptotic Formulas ◽  
Stage Model ◽  
Two Stage ◽  
Markov Branching Process ◽  
Age Dependent

Asymptotic formulas for means and variances of a multitype decomposable age-dependent supercritical branching process are derived. This process is a generalization of the Kendall–Neyman–Scott two-stage model for tumor growth. Both means and variances have exponential growth rates as in the case of the Markov branching process. But unlike Markov branching, these asymptotic moments depend on the age of the original individual at the start of the process and the life span distribution of the progenies.

Development of a Model To Predict Growth of Clostridium perfringens in Cooked Beef during Cooling

2005 ◽  
Vol 68 (2) ◽  
pp. 336-341 ◽  
Author(s):  
SARAH SMITH-SIMPSON ◽  
DONALD W. SCHAFFNER
Keyword(s):  
Food Safety ◽  
Clostridium Perfringens ◽  
Exponential Growth ◽  
Growth Curves ◽  
Policy Implications ◽  
Individual Growth ◽  
Performance Standard ◽  
Square Root ◽  
Time Model ◽  
New Model

The objective of this work was to develop a new model to predict the growth of Clostridium perfringens in cooked meat during cooling. All data were collected under changing temperature conditions. Individual growth curves were fit using DMFit. Germination outgrowth and lag (GOL) time was modeled versus temperature at the end of GOL using conservative assumptions. Each growth curve was used to estimate a series of exponential growth rates at a series of temperatures. The square-root model was used to describe the relationship between the square root of the average exponential growth rate and effective temperature. Predictions from the new model were in close agreement with the data used to create the model. When predictions from the model were compared with new observations, fail-dangerous predictions were made a majority of the time. When GOL time was predicted exactly, many fail-dangerous predictions shifted toward the fail-safe direction. Two important facts regarding C. perfringens should impact future modeling research with this organism and may have broader food safety policy implications: (i) the normal variability in the response of the organism from replicate to replicate may be quite large (1 log CFU) and may exceed the current U.S. Food Safety Inspection Service performance standard, and (ii) the accuracy of the GOL time model has a profound influence upon the overall prediction, with small differences in GOL time prediction (~1 h) having a very large effect on the predicted final concentration of C. perfringens.

Effect of altering the protein intake of spring-born calves on calf performance

2005 ◽  
Vol 2005 ◽  
pp. 192-192
Author(s):  
H. C. F. Wicks ◽  
R. J. Fallon ◽  
J. Twigge ◽  
L. E. R. Dawson
Keyword(s):  
Protein Content ◽  
Growth Rates ◽  
Early Phase ◽  
Protein Intake ◽  
Crude Protein ◽  
Milk Replacer ◽  
Crude Protein Content ◽  
Holstein Friesian ◽  
Calf Performance

Results of a recent study (Wicks et al. 2005) indicate that increasing the protein content of the milk replacer fed to autumn-born Holstein-Friesian calves reduced growth rates in the first 8 weeks of life. Van Amburgh et al., (2001) previously suggested that increasing both milk replacer intake and protein content maximised the growth of calves during this early phase of life. An experiment was undertaken to investigate the influence of level of milk replacer and crude protein content on calf performance during the first 8 weeks of life of spring-born calves.

Age, growth and sex determination in a population of smooth snakes, Coronella austriaca in southern England

2004 ◽  
Vol 25 (2) ◽  
pp. 137-150 ◽  
Author(s):  
Keyword(s):  
Sex Determination ◽  
Age Structure ◽  
Growth Rates ◽  
Growth Curves ◽  
Tail Length ◽  
Daily Growth ◽  
Southern England ◽  
The Difference ◽  
The Relationship ◽  
Coronella Austriaca

AbstractBetween 1992-2001 a study of individually marked smooth snakes Coronella austriaca was done in Wareham Forest, southern England. The sex of individual snakes was determined using the relationship between tail length and snout-vent length, and the presence/absence of a hemi-penes swelling at the base of the tail. Males had longer tails than females at all ages/sizes and the difference between the sexes increased with increasing snout-vent length. Using multiple captures of known individuals over many years, size related daily growth rates were determined for each sex that enabled growth curves to be produced. The age structure of the population was determined for each complete year of the study. Very few young small snakes were captured each year. Of all the females who were potentially able to breed, only the oldest, and therefore largest, did so.

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