Dynamics of Single-City Influenza with Seasonal Forcing: From Regularity to Chaos

Seasonal and epidemic influenza continue to cause concern, reinforced by connections between human and avian influenza, and H1N1 swine influenza. Models summarize ideas about disease mechanisms, help understand contributions of different processes, and explore interventions. A compartment model of single-city influenza is developed. It is mechanism-based on lower-level studies, rather than focussing on predictions. It is deterministic, without non-disease-status stratification. Categories represented are susceptible, infected, sick, hospitalized, asymptomatic, dead from flu, recovered, and one in which recovered individuals lose immunity. Most categories are represented with sequential pools with first-order kinetics, giving gamma-function progressions with realistic dynamics. A virus compartment allows representation of environmental effects on virus lifetime, thence affecting reproductive ratio. The model's behaviour is explored. It is validated without significant tuning against data on a school outbreak. Seasonal forcing causes a variety of regular and chaotic behaviours, some being typical of seasonal and epidemic flu. It is suggested that models use sequential stages for appropriate disease categories because this is biologically realistic, and authentic dynamics is required if predictions are to be credible. Seasonality is important indicating that control measures might usefully take account of expected weather.

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An epidemic model for non-first-order transmission kinetics

PLoS ONE ◽

10.1371/journal.pone.0247512 ◽

2021 ◽

Vol 16 (3) ◽

pp. e0247512

Author(s):

Eun-Young Mun ◽

Feng Geng

Keyword(s):

Epidemic Model ◽

Disease Transmission ◽

Transmission Rate ◽

Early Stage ◽

Compartmental Models ◽

Control Measures ◽

Chemical Reaction Kinetics ◽

Rate Law ◽

First Order ◽

First Order Kinetics

Compartmental models in epidemiology characterize the spread of an infectious disease by formulating ordinary differential equations to quantify the rate of disease progression through subpopulations defined by the Susceptible-Infectious-Removed (SIR) scheme. The classic rate law central to the SIR compartmental models assumes that the rate of transmission is first order regarding the infectious agent. The current study demonstrates that this assumption does not always hold and provides a theoretical rationale for a more general rate law, inspired by mixed-order chemical reaction kinetics, leading to a modified mathematical model for non-first-order kinetics. Using observed data from 127 countries during the initial phase of the COVID-19 pandemic, we demonstrated that the modified epidemic model is more realistic than the classic, first-order-kinetics based model. We discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n. While k finds utility in evaluating the effectiveness of control measures due to its responsiveness to external factors, n is more closely related to the intrinsic properties of the epidemic agent, including reproductive ability. The rate law for the modified compartmental SIR model is generally applicable to mixed-kinetics disease transmission with heterogeneous transmission mechanisms. By analyzing early-stage epidemic data, this modified epidemic model may be instrumental in providing timely insight into a new epidemic and developing control measures at the beginning of an outbreak.

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Photo-catalytic degradation of gaseous pollutants in paper mills of southern China

TAPPI Journal ◽

10.32964/tj17.03.167 ◽

2018 ◽

Vol 17 (03) ◽

pp. 167-178 ◽

Cited By ~ 2

Author(s):

Xin Tong ◽

Jiao Li ◽

Jun Ma ◽

Xiaoquan Chen ◽

Wenhao Shen

Keyword(s):

Degradation Rate ◽

Southern China ◽

Catalytic Degradation ◽

Pulp And Paper ◽

Gaseous Pollutants ◽

Pulp And Paper Mills ◽

Paper Mills ◽

Initial Concentration ◽

First Order ◽

First Order Kinetics

Studies were undertaken to evaluate gaseous pollutants in workplace air within pulp and paper mills and to consider the effectiveness of photo-catalytic treatment of this air. Ambient air at 30 sampling sites in five pulp and paper mills of southern China were sampled and analyzed. The results revealed that formaldehyde and various benzene-based molecules were the main gaseous pollutants at these five mills. A photo-catalytic reactor system with titanium dioxide (TiO2) was developed and evaluated for degradation of formaldehyde, benzene and their mixtures. The experimental results demonstrated that both formaldehyde and benzene in their pure forms could be completely photo-catalytic degraded, though the degradation of benzene was much more difficult than that for formaldehyde. Study of the photo-catalytic degradation kinetics revealed that the degradation rate of formaldehyde increased with initial concentration fitting a first-order kinetics reaction. In contrast, the degradation rate of benzene had no relationship with initial concentration and degradation did not conform to first-order kinetics. The photo-catalytic degradation of formaldehyde-benzene mixtures indicated that formaldehyde behaved differently than when treated in its pure form. The degradation time was two times longer and the kinetics did not reflect a first-order reaction. The degradation of benzene was similar in both pure form and when mixed with formaldehyde.

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Kinetic of oxidation of methyl orange by vanadium(V) under conditions VO2+ and decavanadates coexist: Catalysis by Triton X-100 micellar medium

10.31221/osf.io/m9g7p ◽

2019 ◽

Author(s):

Chem Int

Keyword(s):

Methyl Orange ◽

Solution Ph ◽

Vanadium Concentration ◽

Limiting Behavior ◽

First Order ◽

First Order Kinetics ◽

Ph Range ◽

Kinetic Pattern ◽

Triton X ◽

Kinetics Of

The kinetics of oxidation of methyl orange by vanadium(V) {V(V)} has been investigated in the pH range 2.3-3.79. In this pH range V(V) exists both in the form of decavanadates and VO2+. The kinetic results are distinctly different from the results obtained for the same reaction in highly acidic solution (pH < 1) where V(V) exists only in the form of VO2+. The reaction obeys first order kinetics with respect to methyl orange but the rate has very little dependence on total vanadium concentration. The reaction is accelerated by H+ ion but the dependence of rate on [H+] is less than that corresponding to first order dependence. The equilibrium between decavanadates and VO2+ explains the different kinetic pattern observed in this pH range. The reaction is markedly accelerated by Triton X-100 micelles. The rate-[surfactant] profile shows a limiting behavior indicative of a unimolecular pathway in the micellar pseudophase.

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Biodegradation rates of aromatic contaminants in biofilm reactors

Water Science & Technology ◽

10.2166/wst.1995.0027 ◽

1995 ◽

Vol 31 (1) ◽

pp. 117-128 ◽

Cited By ~ 8

Author(s):

Jean-Pierre Arcangeli ◽

Erik Arvin

Keyword(s):

Aromatic Hydrocarbons ◽

Competitive Inhibition ◽

Removal Rate ◽

First Order ◽

Biofilm Reactors ◽

First Order Kinetics ◽

Reducing Conditions ◽

Low Concentrations ◽

Degradation Rates ◽

Order Surface

This study has shown that microorganisms can adapt to degrade mixtures of aromatic pollutants at relatively high rates in the μg/l concentration range. The biodegradation rates of the following compounds were investigated in biofilm systems: aromatic hydrocarbons, phenol, methylphenols, chlorophenols, nitrophenol, chlorobenzenes and aromatic nitrogen-, sulphur- or oxygen-containing heterocyclic compounds (NSO-compounds). Furthermore, a comparison with degradation rates observed for easily degradable organics is also presented. At concentrations below 20-100 μg/l the degradation of the aromatic compounds was typically controlled by first order kinetics. The first-order surface removal rate constants were surprisingly similar, ranging from 2 to 4 m/d. It appears that NSO-compounds inhibit the degradation of aromatic hydrocarbons, even at very low concentrations of NSO-compounds. Under nitrate-reducing conditions, toluene was easily biodegraded. The xylenes and ethylbenzene were degraded cometabolically if toluene was used as a primary carbon source; their removal was influenced by competitive inhibition with toluene. These interaction phenomena are discussed in this paper and a kinetic model taking into account cometabolism and competitive inhibition is proposed.

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In-vitro Kinetic Hydrolysis Study of Metronidazole Derivatives with Carvacrol and Eugenol Using Validated RP-HPLC Method

Current Pharmaceutical Analysis ◽

10.2174/1573412916999200529123151 ◽

2020 ◽

Vol 16 ◽

Author(s):

M. Alarjah

Keyword(s):

Half Life ◽

Hplc Method ◽

Hydrolysis Rate ◽

First Order ◽

First Order Kinetics ◽

Rp Hplc ◽

Pharmacokinetic Properties ◽

Pseudo First Order ◽

Kinetic Hydrolysis

Background: Prodrugs principle is widely used to improve the pharmacological and pharmacokinetic properties of some active drugs. Much effort was made to develop metronidazole prodrugs to enhance antibacterial activity and or to improve pharmacokinetic properties of the molecule or to lower the adverse effects of metronidazole. Objective: In this work, the pharmacokinetic properties of some of monoterpenes and eugenol pro metronidazole molecules that were developed earlier were evaluated in-vitro. The kinetic hydrolysis rate constants and half-life time estimation of the new metronidazole derivatives were calculated using the validated RP-HPLC method. Method: Chromatographic analysis was done using Zorbbax Eclipse eXtra Dense Bonding (XDB)-C18 column of dimensions (250 mm, 4.6 mm, 5 μm), at ambient column temperature. The mobile phase was a mixture of sodium dihydrogen phosphate buffer of pH 4.5 and methanol in gradient elution, at 1ml/min flow rate. The method was fully validated according to the International Council for Harmonization (ICH) guidelines. The hydrolysis process carried out in an acidic buffer pH 1.2 and in an alkaline buffer pH 7.4 in a thermostatic bath at 37ºC. Results: The results followed pseudo-first-order kinetics. All metronidazole prodrugs were stable in the acidic pH, while they were hydrolysed in the alkaline buffer within a few hours (6-8 hr). The rate constant and half-life values were calculated, and their values were found to be 0.082- 0.117 hr-1 and 5.9- 8.5 hr., respectively. Conclusion: The developed method was accurate, sensitive, and selective for the prodrugs. For most of the prodrugs, the hydrolysis followed pseudo-first-order kinetics; the method might be utilised to conduct an in-vivo study for the metronidazole derivatives with monoterpenes and eugenol.

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Decomposition of 4,4'-(Diazoamino)-bis(5-methoxy-2-methylbenezenesulfonic Acid) in Solutions ofFD&C Red No. 40

Journal of AOAC INTERNATIONAL ◽

10.1093/jaoac/67.4.844 ◽

1984 ◽

Vol 67 (4) ◽

pp. 844-845

Author(s):

Naomi Richfield-Fratz

Keyword(s):

Liquid Chromatography ◽

Aqueous Solutions ◽

Borate Buffer ◽

Sodium Borate ◽

First Order ◽

First Order Kinetics ◽

Color Additive ◽

Sodium Borate Buffer

Abstract 4,4'-(Diazoamino)-bis(5-methoxy-2-methylbenzenesuIfonic acid), when present as a reaction by-product in FD&C Red No. 40, is shown to decompose rapidly in aqueous solutions of the color additive. The decomposition is halted by the addition of sodium borate buffer. Quantitationly liquid chromatography shows that decomposition is nonlinear with time and follows approximate first order kinetics.

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Comparative Study of Chemical Stability of Two H1Antihistaminic Drugs, Terfenadine and ItsIn VivoMetabolite Fexofenadine, Using LC-UV Methods

Journal of Analytical Methods in Chemistry ◽

10.1155/2019/5790404 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10

Author(s):

Anna Gumieniczek ◽

Anna Berecka-Rycerz ◽

Rafał Pietraś ◽

Izabela Kozak ◽

Karolina Lejwoda ◽

...

Keyword(s):

Comparative Study ◽

Chemical Stability ◽

First Order ◽

First Order Kinetics ◽

Kinetics Of Degradation ◽

Effects Of Temperature ◽

High Doses ◽

Antihistaminic Drugs ◽

Kinetics Of

A comparative study of chemical stability of terfenadine (TER) and itsin vivometabolite fexofenadine (FEX) was performed. Both TER and FEX were subjected to high temperature at different pH and UV/VIS light at different pH and then quantitatively analyzed using new validated LC-UV methods. These methods were used to monitor the degradation processes and to determine the kinetics of degradation for both the compounds. As far as the effects of temperature and pH were concerned, FEX occurred more sensitive to degradation than TER. As far as the effects of UV/VIS light and pH were concerned, the both drugs were similarly sensitive to high doses of light. Using all stress conditions, the processes of degradation of TER and FEX followed the first-order kinetics. The results obtained for these two antihistaminic drugs could be helpful in developing their new derivatives with higher activity and stability at the same time.

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The conversion of ethylene to ethylidyne on Pt(111): non-first order kinetics and ensemble effects

Surface Science ◽

10.1016/0039-6028(94)91298-x ◽

1994 ◽

Vol 301 (1-3) ◽

pp. 177-196 ◽

Cited By ~ 29

Author(s):

W. Erley ◽

Y. Li ◽

D.P. Land ◽

John C. Hemminger

Keyword(s):

First Order ◽

First Order Kinetics ◽

Ensemble Effects

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Bleaching of chlorophylls by UV irradiation in vitro: The effects on chlorophyll organization in acetone and n-hexane

Journal of the Serbian Chemical Society ◽

10.2298/jsc0803271z ◽

2008 ◽

Vol 73 (3) ◽

pp. 271-282 ◽

Cited By ~ 12

Author(s):

Jelena Zvezdanovic ◽

Dejan Markovic

Keyword(s):

Uv Irradiation ◽

Photosynthetic Pigments ◽

Energy Input ◽

First Order ◽

First Order Kinetics ◽

Uv Photons ◽

The Stability ◽

Major Factors

The stability of chlorophylls toward UV irradiation was studied by Vis spectrophotometry in extracts containing mixtures of photosynthetic pigments in acetone and n-hexane. The chlorophylls underwent destruction (bleaching) obeying first-order kinetics. The bleaching was governed by three major factors: the energy input of the UV photons, the concentration of the chlorophylls and the polarity of the solvent, implying different molecular organizations of the chlorophylls in the two solvents.

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