Additional Information about Infectious Diseases
Lyle D. Broemeling in Bayesian Analysis of Infectious Diseases, 2021
“Where are the masks going?” he asked. “Are they going out the back door?” He later added “We do have a problem of hoarding. We have some health care workers, some hospital frankly – individual hospitals and hospital chains – we have then hoarding equipment, including ventilators.” The President’s dismissal of the magnitude of these numbers may indicate a lack of understanding or disregard of exponential growth that plagues a large portion of the population. Even many who are well educated do not understand the concept and often use the term “exponential growth” or “exponentially” as hyperbole instead of a description of a trend in growth or acceleration. Why should we care about this apparently arcane mathematical principle? Because, under our current circumstances, misunderstanding or disregard of exponential growth and the decisions made based on the misunderstanding or disregard might have extremely grave consequences.
Exponential Functions
Kate McCombe, Lara Wijayasiri, Paul Hatton, David Bogod in The Primary FRCA Structured Oral Examination Study Guide 2, 2017
Give some examples of exponential processes. Exponential decay curves: Nitrogen washout during pre-oxygenationLung volumes during passive expirationDrug wash-out curvesRadionuclide materials undergoing radioactive decay.Exponential growth curves: Bacterial growthDrug wash-in curvesLung volumes during positive pressure ventilation (with pressurecontrolled ventilation).
Prelude: Preliminary Tools and Foundations
Albert Vexler, Alan D. Hutson in Statistics in the Health Sciences, 2018
Note that oftentimes measurements related to biological processes follow a log-normal distribution (Koch, 1966). For example, exponential growth is combined with further symmetrical variation: with a mean concentration of, say, 106 bacteria, one cell division more or less will result in or cells. Therefore, the range will be multiplied or divided by 2 around the mean, that is, the density is asymmetrical. Such skewed distributions of these types of biological processes have long been known to fit the log-normal distribution function (Powers, 1936; Sinnott, 1937). Skewed distributions that often closely fit the log-normal distribution are particularly common when mean values are low, variances are large, and values of random variables cannot be negative, as is the case, for instance, with species abundance and lengths of latent periods of infectious diseases (Lee and Wang, 2013; Balakrishnan et al., 1994). Limpert et al. (2001) discussed various applications of log-normal distributions in different fields of science, including geology, human medicine, environment, atmospheric sciences, microbiology, plant physiology and the social sciences.
Transmissibility and mortality trends of COVID-19 epidemic in Egypt
Published in Alexandria Journal of Medicine, 2020
Mohamed Masoud, Gihan Gewaifel, Nahla Gamaleldin
The first part of data (from day 1 to day 35) was examined to identify the subset that represents the best fit for the exponential growth. Values of R2, adjusted R2 and residual sum of squares (RSS) have been estimated using (IBM SPSS statistics for windows version 22, 2013, Armonk, NY, USA. IBM Corp.) to evaluate the model fit for each subset. Three data subsets were examined; data subset of day 1–35, day 22–35, and day 25–35. Figure (2a, b, and c, respectively). The cumulative number of the data subset of day 25–35 (from 9/3/2020 to 19/3/2020) was the closest to the exponential growth as it had the highest values of R2 and adjusted R2, and had the lowest RSS value, Figure 2(c). So, it was used for estimation of the growth rate, and subsequently the doubling time and R0.
Mathematical models of tumor cell proliferation: A review of the literature
Published in Expert Review of Anticancer Therapy, 2018
Angela M. Jarrett, Ernesto A.B.F. Lima, David A. Hormuth, Matthew T. McKenna, Xinzeng Feng, David A. Ekrut, Anna Claudia M. Resende, Amy Brock, Thomas E. Yankeelov
where t, and g is the growth rate of the tumor cells, which can be a function. Equation (1) is an example of an ODE because there is only one independent variable; in this case, t is such a variable representing time. For the simplest (and most common) version of Equation (1), g is simply a constant value, r. In this case, Equation (1) literally means that the change in population per time is equal to the constant rate r times the current population size. In particular, if r > 0, Equation (1) predicts an ever-increasing population size. When this ODE is solved (where g is a constant r), the result is the equation for exponential growth: N0 is the initial population size. Alternatively, the population can be represented using logistic growth, limiting population growth based on the ratio between population density and the carrying capacity,
Developmental exposure to the A6-pesticide causes changes in tyrosine hydroxylase gene expression, neurochemistry, and locomotors behavior in larval zebrafish
Published in Toxicology Mechanisms and Methods, 2022
Ahmed Nasri, Pierre-André Lafon, Amine Mezni, Philippe Clair, Nicolas Cubedo, Ezzeddine Mahmoudi, Hamouda Beyrem, Mireille Rossel, Véronique Perrier
The exponential growth of the world’s population has necessitated the use of intensive production systems in agriculture globally (Köhler and Triebskorn 2013). The over-the-top use of synthetic pesticides and improve crop yields places great strain on natural resources (Liu et al. 2015). The use of chemical pesticides has led to the appearance of several impacts in the environment, including toxic effects on the non-target organism (Hannachi et al. 2022). The arrival of new technologies such as high throughput screening and mass spectrometry in the 1990s boosted “green” chemistry, i.e. the identification of new molecules extracted from plants, and the production of derived molecules with improved properties (Benelli et al. 2016). This “green” chemistry aims to design industrial processes that are more respectful of the environment and to generate products that are more harmless to non-target organisms . These pesticides of plant origin or biopesticides are currently being explored as promising alternatives to synthetic pesticides (Benelli et al. 2016) because they are considered less harmful to non-target organisms since they are of natural origin (Shao and Zhang 2017). A6 is a biopesticide derived from the molecule α-terthienyl which was originally isolated from plants such as Asteraceae (Nivsarkar et al. 2001) for its blue fluorescent properties (Zechmeister and Sease 1947), as well as being described to have herbicidal activity (Friedman and Friedman 1995).
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