scholarly journals Kinetics methods for clinical epidemiology problems

2015 ◽  
Vol 112 (46) ◽  
pp. 14150-14155 ◽  
Author(s):  
Alexandru Dan Corlan ◽  
John Ross
Keyword(s):  
Clinical Epidemiology ◽  
Meta Analysis ◽  
Reaction Rates ◽  
Mass Action ◽  
Reaction Systems ◽  
Disease Epidemiology ◽  
Mass Action Law ◽  
The Individual ◽  
Kinetics Of ◽  
Stochastic Kinetics

Calculating the probability of each possible outcome for a patient at any time in the future is currently possible only in the simplest cases: short-term prediction in acute diseases of otherwise healthy persons. This problem is to some extent analogous to predicting the concentrations of species in a reactor when knowing initial concentrations and after examining reaction rates at the individual molecule level. The existing theoretical framework behind predicting contagion and the immediate outcome of acute diseases in previously healthy individuals is largely analogous to deterministic kinetics of chemical systems consisting of one or a few reactions. We show that current statistical models commonly used in chronic disease epidemiology correspond to simple stochastic treatment of single reaction systems. The general problem corresponds to stochastic kinetics of complex reaction systems. We attempt to formulate epidemiologic problems related to chronic diseases in chemical kinetics terms. We review methods that may be adapted for use in epidemiology. We show that some reactions cannot fit into the mass-action law paradigm and solutions to these systems would frequently exhibit an antiportfolio effect. We provide a complete example application of stochastic kinetics modeling for a deductive meta-analysis of two papers on atrial fibrillation incidence, prevalence, and mortality.

Kinetics of esterification of monoisopropylphenols with phosphoryl trichloride

1989 ◽  
Vol 54 (5) ◽  
pp. 1311-1317
Author(s):  
Miroslav Magura ◽  
Ján Vojtko ◽  
Ján Ilavský
Keyword(s):  
Liquid Phase ◽  
Rate Constants ◽  
Reaction Rates ◽  
Activation Energies ◽  
The Individual ◽  
Kinetics Of

The kinetics of liquid-phase isothermal esterification of POCl3 with 2-isopropylphenol and 4-isopropylphenol have been studied within the temperature intervals of 110 to 130 and 90 to 110 °C, respectively. The rate constants and activation energies of the individual steps of this three-step reaction have been calculated from the values measured. The reaction rates of the two isomers markedly differ: at 110 °C 4-isopropylphenol reacts faster by the factors of about 7 and 20 for k1 and k3, respectively. This finding can be utilized in preparation of mixed triaryl phosphates, since the alkylation mixture after reaction of phenol with propene contains an excess of 2-isopropylphenol over 4-isopropylphenol.

scholarly journals A Delay Differential Equation approach to model the COVID-19 pandemic

2021 ◽  
Author(s):  
Ilya Kiselev ◽  
I.R. Akberdin ◽  
F.A. Kolpakov
Keyword(s):  
Infectious Disease ◽  
Incubation Period ◽  
Population Group ◽  
Mass Action ◽  
Virus Spread ◽  
Disease Epidemiology ◽  
Epidemic Dynamics ◽  
Infectious Disease Epidemiology ◽  
Mass Action Law ◽  
Delay Differential

SEIR (Susceptible - Exposed - Infected - Recovered) approach is a classic modeling method that has frequently been applied to the study of infectious disease epidemiology. However, in the vast majority of SEIR models and models derived from them transitions from one population group to another are described using the mass-action law which assumes population homogeneity. That causes some methodological limitations or even drawbacks, particularly inability to reproduce observable dynamics of key characteristics of infection such as, for example, the incubation period and progression of the disease's symptoms which require considering different time scales as well as probabilities of different disease trajectories. In this paper, we propose an alternative approach to simulate the epidemic dynamics that is based on a system of differential equations with time delays to precisely reproduce a duration of infectious processes (e.g. incubation period of the virus) and competing processes like transition from infected state to the hospitalization or recovery. The suggested modeling approach is fundamental and can be applied to the study of many infectious disease epidemiology. However, due to the urgency of the COVID-19 pandemic we have developed and calibrated the delay-based model of the epidemic in Germany and France using the BioUML platform. Additionally, the stringency index was used as a generalized characteristic of the non-pharmaceutical government interventions implemented in corresponding countries to contain the virus spread. The numerical analysis of the calibrated model demonstrates that adequate simulation of each new wave of the SARS-CoV-2 virus spread requires dynamic changes in the parameter values during the epidemic like reduction of the population adherence to non-pharmaceutical interventions or enhancement of the infectivity parameter caused by an emergence of novel virus strains with higher contagiousness than original one. Both models may be accessed and simulated at https://gitlab.sirius-web.org/covid-19/dde-epidemiology-model utilizing visual representation as well as Jupyter Notebook.

scholarly journals Diagnostic value of the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration equations in diabetic patients: a systematic review and meta-analysis

2020 ◽  
Vol 48 (6) ◽  
pp. 030006052092595
Author(s):  
Xie Lingli ◽  
Zhang Qing ◽  
Xia Wenfang
Keyword(s):  
Chronic Kidney Disease ◽  
Kidney Disease ◽  
Renal Disease ◽  
Meta Analysis ◽  
Diagnostic Value ◽  
Cochrane Library ◽  
Diabetic Patients ◽  
Disease Epidemiology ◽  
Individual Level ◽  
The Individual

Background The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Modification of Diet in Renal Disease (MDRD) equations are common for calculating estimated glomerular filtration rate (eGFR). Unlike CKD, the key pathological change of diabetic kidney disease (DKD) is glomerulosclerosis. Methods To conduct a meta-analysis of the diagnostic performance of the CKD-EPI and MDRD equations in diabetic patients, we searched PubMed, Embase and the Cochrane Library for studies comparing standard GFR (sGFR) with eGFR using these two equations. Results Thirteen studies of 7192 diabetic patients reporting data on bias or accuracy were included. At the study level, both equations underestimated eGFR. CKD-EPI was more accurate in studies with mean GFR ≥60 mL/minute/1.73 m2. At the individual level, both equations overestimated GFR by 6.38 mL/minute/1.73 m2 (95% confidence interval [CI] 2.67–10.1) and 7.65 mL/minute/1.73 m2 (95% CI 2.78–12.52), respectively, for sGFR < 90 mL/minute/1.73 m2. The CKD-EPI equation was 7.61% (95% CI 4.66–10.56) more accurate in subjects with sGFR > 90 mL/minute/1.73 m2. The CKD-EPI equation performed poorly in diabetic patients. Conclusions The CKD-EPI equation can be used to estimate GFR in patients with incipient DKD, but has drawbacks. Improved eGFR equations suitable for diabetic populations are needed.

Kinetics of 1-butanol, di-(1-butyl) ether and 1-butene reactions on aluminas partially deactivated by sodium

1989 ◽  
Vol 54 (11) ◽  
pp. 2985-2997 ◽  
Author(s):  
František Krampera ◽  
Ludvík Beránek
Keyword(s):  
Vapour Phase ◽  
Reaction Rates ◽  
Product Formation ◽  
Sodium Content ◽  
Butyl Ether ◽  
Deactivation Kinetics ◽  
Two Factors ◽  
Best Fitting ◽  
The Individual ◽  
Kinetics Of

The initial rates of six reactions taking place in 1-butanol dehydration at 260 °C in vapour phase were measured on aluminia samples differing in sodium content. The reactants were 1-butanol, di-(1-butyl) ether and 1-butene, resp. The parameters of the best fitting rate equation for each reaction were evaluated. The reaction rates as well as the rate constants and adsorption coefficients of the individual reactions show different sensitivity to datalyst acidity. Therefore, the selectivity of product formation can be influenced by sodium content of the catalyst. The selectivities (with the exception of 1-butene izomerization) strongly depend also on the partial pressure of the starting reactants. Thus, these two factors can be used to control the selectivity for preparative purposes. The results of this paper clearly demonstrate the nonseparability of the deactivation kinetics in 1-butanol dehydration on sodium poisoned aluminas.

Kinetics of Triplet Sublevel Selective Photochemical Reactions in the Solid State

1981 ◽  
Vol 36 (7) ◽  
pp. 743-750
Author(s):  
Manfred Gehrtz ◽  
Christoph Bräuchle ◽  
Jürgen Voitländer
Keyword(s):  
Solid State ◽  
Reaction Rates ◽  
Photochemical Reactions ◽  
Solid State Reactions ◽  
Physical Activation ◽  
Zero Field ◽  
Excited Triplet ◽  
The Individual ◽  
Activation Rates ◽  
Kinetics Of

Abstract A detailed description of the overall kinetics of photochemical reactions has to deal with photo-physical activation and de-activation rates as well as with true photochemical rates. Based on the hypothesis that for photoreactions involving the lowest excited triplet state the chemical reaction rates of the individual triplet zero-field levels have different values, a method is presented for the evaluation of these rates from bulk measurements under steady state illumination conditions. The complications arising from the detection of solid state reactions are discussed, and a simple solution is given, illustrated by a numerical example.

scholarly journals Delving deeper: Relating the behaviour of a metabolic system to the properties of its components using symbolic metabolic control analysis

2018 ◽  
Author(s):  
Carl D. Christensen ◽  
Jan-Hendrik S. Hofmeyr ◽  
Johann M. Rohwer
Keyword(s):  
Reaction Rates ◽  
Mass Action ◽  
Control Analysis ◽  
Metabolic System ◽  
Flux Control ◽  
Symbolic Control ◽  
Mechanistic Understanding ◽  
The Individual ◽  
High Level ◽  
Molecular Components

AbstractHigh-level behaviour of metabolic systems results from the properties of, and interactions between, numerous molecular components. Reaching a complete understanding of metabolic behaviour based on the system’s components is therefore a difficult task. This problem can be tackled by constructing and subsequently analysing kinetic models of metabolic pathways since such models aim to capture all the relevant properties of the system components and their interactions.Symbolic control analysis is a framework for analysing pathway models in order to reach a mechanistic understanding of their behaviour. By providing algebraic expressions for the sensitivities of system properties, such as metabolic fluxor steady-state concentrations, in terms of the properties of individual reactions it allows one to trace the high level behaviour back to these low level components. Here we apply this method to a model of pyruvate branch metabolism inLactococcus lactisin order to explain a previously observed negative flux response towards an increase in substrate concentration. With this method we are able to show, first, that the sensitivity of flux towards changes in reaction rates (represented by flux control coefficients) is determined by the individual metabolic branches of the pathway, and second, how the sensitivities of individual reaction rates towards their substrates (represented by elasticity coefficients) contribute to this flux control. We also quantify the contributions of enzyme binding and mass-action to enzyme elasticity separately, which allows for an even finer-grained understanding of flux control.These analytical tools allow us to analyse the control properties of a metabolic model and to arrive at a mechanistic understanding of the quantitative contributions of each of the enzymes to this control. Our analysis provides an example of the descriptive power of the general principles of symbolic control analysis.Author summaryMetabolic networks are complex systems consisting of numerous individual molecular components. The properties of these components, together with their non-linear interactions, give rise to high-level observed behaviour of the system in which they reside. Therefore, in order to fully understand the behaviour of a metabolic system, one has to consider the properties of all of its components. The analysis of computer models that capture and represent these systems and their components simplifies this task by allowing for an easy way to isolate the effects of each individual component. In this paper we use the framework of symbolic control analysis to investigate the sensitivity of the rate of flow of matter through one of the branches in a particular metabolic pathway towards changes in the rates of individual reactions. Here we are able to quantify how certain chains of reactions, individual reactions, and even thermodynamic and kinetic aspects of individual reactions contribute to the overall sensitivity of the rate of matter-flow. Thus, we are able to trace the behaviour of the system as a whole in a mechanistic way to the properties of the individual molecular components.

scholarly journals Development of a Simple Kinetic Mathematical Model of Aggregation of Particles or Clustering of Receptors

Life ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 97
Author(s):  
Andrei K. Garzon Dasgupta ◽  
Alexey A. Martyanov ◽  
Aleksandra A. Filkova ◽  
Mikhail A. Panteleev ◽  
Anastasia N. Sveshnikova
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Cluster Formation ◽  
Quantitative Description ◽  
Membrane Receptors ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Clustering Model ◽  
Mass Action Law ◽  
Kinetics Of

The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D.

scholarly journals A model of carbon dioxide dissolution and mineral carbonation kinetics

2009 ◽  
Vol 466 (2117) ◽  
pp. 1265-1290 ◽  
Author(s):  
Mark J. Mitchell ◽  
Oliver E. Jensen ◽  
K. Andrew Cliffe ◽  
M. Mercedes Maroto-Valer
Keyword(s):  
Carbon Dioxide ◽  
Mass Action ◽  
Mineral Carbonation ◽  
Leading Order ◽  
Full System ◽  
Mass Action Law ◽  
Gaseous Carbon Dioxide ◽  
Equilibrium Concentrations ◽  
Kinetics Of ◽  
Independent Parameters

The kinetics of the dissolution of carbon dioxide in water and subsequent chemical reactions through to the formation of calcium carbonate, a system of reactions integral to carbon sequestration and anthropogenic ocean acidification, is mathematically modelled using the mass action law. This group of reactions is expressed as a system of five coupled nonlinear ordinary differential equations, with 14 independent parameters. The evolution of this system to equilibrium at 25 ° C and 1 atm, following an instantaneous injection of gaseous carbon dioxide, is simulated. An asymptotic analysis captures the leading-order behaviour of the system over six disparate time scales, yielding expressions for all species in each time scale. These approximations show excellent agreement with simulations of the full system, and give remarkably simple formulae for the equilibrium concentrations.

scholarly journals Stochastic simulation platform for visualization and estimation of transcriptional kinetics

2019 ◽  
Author(s):  
Gennady Gorin ◽  
Mengyu Wang ◽  
Ido Golding ◽  
Heng Xu
Keyword(s):  
Rna Synthesis ◽  
Reaction Rates ◽  
Gillespie Algorithm ◽  
Simulation Framework ◽  
Dimensional Parameter ◽  
Turn On ◽  
Optimization Heuristics ◽  
Simulated Gene Expression ◽  
Kinetics Of ◽  
Stochastic Kinetics

AbstractWe present an implementation of the Gillespie algorithm that simulates the stochastic kinetics of nascent and mature RNA. Our model includes two-state gene regulation, RNA synthesis initiation and stepwise elongation, release to the cytoplasm, and stepwise degradation, a granular description currently tractable only by simulation. To facilitate comparison with experimental data, the algorithm predicts fluorescent probe signals measurable by single-cell RNA imaging. We approach the inverse problem of estimating underlying parameters in a five-dimensional parameter space and suggest optimization heuristics that successfully recover known reaction rates from simulated gene expression turn-on data. The simulation framework includes a graphical user interface, available as a MATLAB app at https://data.caltech.edu/records/1287.

Kinetics of hydrogenation of alkynes and dienes on palladium catalyst

1987 ◽  
Vol 52 (12) ◽  
pp. 2909-2917 ◽  
Author(s):  
Libor Červený ◽  
Šárka Řehůřková
Keyword(s):  
Activated Carbon ◽  
Palladium Catalyst ◽  
Atmospheric Pressure ◽  
Reaction Rates ◽  
Initial Reaction ◽  
Hydrogenation Rate ◽  
Substrate Structure ◽  
The Individual ◽  
Kinetics Of ◽  
Relative Adsorption

Alkynic and dienic substrates (C6-C10) in hexane and methanol were hydrogenated over a catalyst of 3% Pd on activated carbon at 20 °C and atmospheric pressure. The initial reaction rates were measured for the individual substrates; the hydrogenation rates of the olefinic substances formed were also determined if the hydrogenation was selective. The selectivities in competitive hydrogenations of substrate pairs were established and the relative adsorption coefficients of the substrates were calculated from them. The effect of the substrate structure and the solvent effect on the hydrogenation rate and relative adsorptivity are discussed for the alkynic and dienic substances studied.

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