scholarly journals Near-exact explicit asymptotic solution of the SIR model well above the epidemic threshold

2021 ◽  
Author(s):  
Gregory Kozyreff
Keyword(s):  
Asymptotic Solution ◽  
Asymptotic Expansions ◽  
Qualitative Agreement ◽  
Sir Model ◽  
Inflexion Point ◽  
Good Qualitative Agreement ◽  
Epidemic Threshold ◽  
Analytical Estimate ◽  
Epidemic Curve ◽  
Reproduction Numbers

A simple and explicit expression of the solution of the SIR epidemiological model of Kermack and McKendrick is constructed in the asymptotic limit of large basic reproduction numbers $\ro$. The proposed formula yields good qualitative agreement already when $\ro\geq3$ and rapidly becomes quantitatively accurate as larger values of $\ro$ are assumed. The derivation is based on the method of matched asymptotic expansions, which exploits the fact that the exponential growing phase and the eventual recession of the outbreak occur on distinct time scales. From the newly derived solution, an analytical estimate of the time separating the first inflexion point of the epidemic curve from the peak of infections is given.

scholarly journals An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Said Gounane ◽  
Yassir Barkouch ◽  
Abdelghafour Atlas ◽  
Mostafa Bendahmane ◽  
Fahd Karami ◽  
...  
Keyword(s):  
Mathematical Theory ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Threshold ◽  
Social Distancing ◽  
Sir Epidemic ◽  
Proposed Model ◽  
Disease Spreading ◽  
The Government ◽  
The Impact

Abstract Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

scholarly journals The Deterministic Evolution Of Illicit Drug Consumption Within a Given Population

2018 ◽  
Vol 62 ◽  
pp. 139-157 ◽  
Author(s):  
Yusra Bibi Ruhomally ◽  
Nabeelah Banon Jahmeerbaccus ◽  
Muhammad Zaid Dauhoo
Keyword(s):  
Drug Users ◽  
Illicit Drug ◽  
Drug Consumption ◽  
Dynamic Evolution ◽  
Evidence Based ◽  
Relative Importance ◽  
Epidemic Threshold ◽  
Drug Usage ◽  
Policy Makers ◽  
Reproduction Numbers

We study the NERA model that describes the dynamic evolution of illicit drug usage in a population. The model consists of nonusers (N) and three categories of drug users: the experimental (E) category, the recreational (R) category and the addict (A) category. Two epidemic threshold term known as the reproduction numbers, R0 and μ are defined and derived. Sensitivity analysis of R0 on the parameters are performed in order to determine their relative importance to illicit drug prevalence. The local and global stability of the equilibrium states are also analysed. We also prove that a transcritical bifurcation occurs at R0 = 1. It is shown that an effective campaign of prevention can help to fight against the prevalence of illicit drug consumption. We demonstrate persistence when R0 > 1 and conditions for the extinction of drug consumption are also established. Numerical simulations are performed to verify our model. Our results show that the NERA model can assist policy makers in targeting prevention for maximum effectiveness and can be used to adopt evidence-based policies to better monitor and quantify drug use trends.

Stresses in an Infinite Strip Containing a Semi-Infinite Crack

1966 ◽  
Vol 33 (2) ◽  
pp. 356-362 ◽  
Author(s):  
W. G. Knauss
Keyword(s):  
Fracture Mechanics ◽  
Stress Field ◽  
Asymptotic Solution ◽  
Asymptotic Expansions ◽  
Region Of Interest ◽  
Graphical Form ◽  
Finite Width ◽  
Infinite Strip ◽  
Arbitrary Length ◽  
Laboratory Investigations

Stresses in an infinitely long strip of finite width containing a straight semi-infinite crack have been calculated for the case that the clamped boundaries are displaced normal to the crack. The solution is obtained by the Wiener-Hopf technique. The stresses are given in the form of asymptotic expansions in the immediate crack tip vicinity and for a larger region of interest in graphical form. The effect of prescribing displacements on the boundary close to a crack instead of stresses far away is discussed briefly. Together with an asymptotic solution for a small crack, the result is used to estimate the stress field around a crack of arbitrary length in an infinite strip. The usefulness of this crack geometry in laboratory investigations of fracture mechanics is pointed out.

scholarly journals Prediction of peak and termination of novel coronavirus COVID-19 epidemic in Iran

2020 ◽  
Vol 31 (11) ◽  
pp. 2050152
Author(s):  
Sepehr Rafieenasab ◽  
Amir-Pouyan Zahiri ◽  
Ehsan Roohi
Keyword(s):  
Statistical Data ◽  
Sir Model ◽  
Model Parameters ◽  
Peak Time ◽  
Infected People ◽  
Epidemic Curve ◽  
Immunization Rates ◽  
Long Time ◽  
Novel Coronavirus ◽  
Official Data

The growth and development of COVID-19 transmission have significantly attracted the attention of many societies, particularly Iran, that have been struggling with this contagious, infectious disease since late February 2020. In this study, the known “Susceptible-Infectious-Recovered (SIR)” and some other mathematical approaches were used to investigate the dynamics of the COVID-19 epidemic to provide a suitable assessment of the COVID-19 virus epidemic in Iran. The epidemic curve and SIR model parameters were obtained with the use of Iran’s official data. The recovered people were considered alongside the official number of confirmed victims as the reliable long-time statistical data. The results offer important predictions of the COVID-19 virus epidemic such as the realistic number of victims, infection rate, peak time and other characteristics. Besides, the effectiveness of infection and immunization rates to the number of infected people and epidemic end time are reported. Finally, different suggestions for decreasing victims are offered.

scholarly journals Modelling the Effectiveness of Epidemic Control Measures in Preventing the Transmission of COVID-19 in Malaysia

2020 ◽  
Vol 17 (15) ◽  
pp. 5509 ◽  
Author(s):  
Balvinder Singh Gill ◽  
Vivek Jason Jayaraj ◽  
Sarbhan Singh ◽  
Sumarni Mohd Ghazali ◽  
Yoon Ling Cheong ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Calibration ◽  
Reproduction Number ◽  
Close Contact ◽  
Movement Control ◽  
Control Measures ◽  
Seir Model ◽  
Epidemic Curve ◽  
Reproduction Numbers ◽  
Control Order

Malaysia is currently facing an outbreak of COVID-19. We aim to present the first study in Malaysia to report the reproduction numbers and develop a mathematical model forecasting COVID-19 transmission by including isolation, quarantine, and movement control measures. We utilized a susceptible, exposed, infectious, and recovered (SEIR) model by incorporating isolation, quarantine, and movement control order (MCO) taken in Malaysia. The simulations were fitted into the Malaysian COVID-19 active case numbers, allowing approximation of parameters consisting of probability of transmission per contact (β), average number of contacts per day per case (ζ), and proportion of close-contact traced per day (q). The effective reproduction number (Rt) was also determined through this model. Our model calibration estimated that (β), (ζ), and (q) were 0.052, 25 persons, and 0.23, respectively. The (Rt) was estimated to be 1.68. MCO measures reduce the peak number of active COVID-19 cases by 99.1% and reduce (ζ) from 25 (pre-MCO) to 7 (during MCO). The flattening of the epidemic curve was also observed with the implementation of these control measures. We conclude that isolation, quarantine, and MCO measures are essential to break the transmission of COVID-19 in Malaysia.

scholarly journals Highlights on Novel Technologies for the Detection of Antibodies to Ro60, Ro52, and SS-B

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. Infantino ◽  
C. Bentow ◽  
A. Seaman ◽  
M. Benucci ◽  
F. Atzeni ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Autoimmune Diseases ◽  
Qualitative Agreement ◽  
San Diego ◽  
Good Qualitative Agreement ◽  
Dot Blot ◽  
Systemic Autoimmune Diseases ◽  
Novel Technologies ◽  
Chemiluminescent Immunoassay ◽  
Inova Diagnostics

Objective. We aimed to compare a chemiluminescent immunoassay (CIA, QUANTA Flash) on BIO-FLASH with a multiplex flow immunoassay (MFI) on BioPlex 2200 for the detection of antibodies to Ro60, Ro52, and SS-B.Methods. The study included 241 samples, from patients suffering from systemic autoimmune diseases (n=108) as well as disease controls (n=133). All samples were tested for anti-Ro52, anti-Ro60, and anti-SS-B (La) antibodies on QUANTA Flash (INOVA Diagnostics, San Diego, USA) and BioPlex 2200 (Bio-Rad Laboratories Inc., Hercules, USA). Discrepant samples were tested by two independent methods: BlueDot/ANA and QUANTRIX Microarray (both D-tek, Belgium).Results. The overall qualitative agreements were 95.4% (95% confidence interval, CI 92.0–97.7%) for anti-Ro52, 98.8% (95% CI 96.4–99.7%) for anti-Ro60, and 91.7% (95% CI 87.5–94.9%) for anti-SS-B antibodies. There were 34 discrepant samples among all assays (20 anti-SS-B, 11 anti-Ro52, 3 anti-Ro60). 30/33 of retested samples (by D-tek dot blot) agreed with the QUANTA Flash results. Similar findings were obtained with QUANTRIX Microarray kit.Conclusion. QUANTA Flash and BioPlex 2200 show good qualitative agreement. The clinical performances were similar for anti-Ro52 and anti-Ro60 autoantibodies while differences were observed for anti-SS-B (La) antibodies.

Modeling of Martensite Accommodation Effect on Mechanical Behavior of Shape Memory Alloys

1999 ◽  
Vol 121 (1) ◽  
pp. 102-104 ◽  
Author(s):  
M. E. Evard ◽  
A. E. Volkov
Keyword(s):  
Experimental Data ◽  
Plastic Deformation ◽  
Shape Memory Alloys ◽  
Mechanical Behavior ◽  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
Qualitative Agreement ◽  
Strain Accumulation ◽  
Good Qualitative Agreement

An approach has been presented to account for micro-plastic deformation and stress produced by accommodation of martensite. This has made it possible to describe such phenomena as incomplete recovery of strain, strain accumulation at thermocycling, and repeated two-way shape memory effect. Results of modeling are in good qualitative agreement with experimental data.

Single Degree of Freedom Model for Thermoelastic Damping

2006 ◽  
Vol 74 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Jagannathan Rajagopalan ◽  
M. Taher A. Saif
Keyword(s):  
Heat Equation ◽  
Cantilever Beam ◽  
Qualitative Agreement ◽  
Degree Of Freedom ◽  
Arbitrary System ◽  
Thermoelastic Damping ◽  
Good Qualitative Agreement ◽  
Considerable Difficulty ◽  
Single Degree Of Freedom ◽  
Single Degree

Finding the thermoelastic damping in a vibrating body, for the most general case, involves the simultaneous solving of the three equations for displacements and one equation for temperature (called the heat equation). Since these are a set of coupled nonlinear partial differential equations there is considerable difficulty in solving them, especially for finite geometries. This paper presents a single degree of freedom (SDOF) model that explores the possibility of estimating thermoelastic damping in a body, vibrating in a particular mode, using only its geometry and material properties, without solving the heat equation. In doing so, the model incorporates the notion of “modal temperatures,” akin to modal displacements and modal frequencies. The procedure for deriving the equations that determine the thermoelastic damping for an arbitrary system, based on the model, is presented. The procedure is implemented for the specific case of a rectangular cantilever beam vibrating in its first mode and the resulting equations solved to obtain the damping behavior. The damping characteristics obtained for the rectangular cantilever beam, using the model, is compared with results previously published in the literature. The results show good qualitative agreement with Zener’s well known approximation. The good qualitative agreement between the predictions of the model and Zener’s approximation suggests that the model captures the essence of thermoelastic damping in vibrating bodies. The ability of this model to provide a good qualitative picture of thermoelastic damping suggests that other forms of dissipation might also be amenable for description using such simple models.

scholarly journals Measurement and prediction of binary mixture flash point

2013 ◽  
Vol 11 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Mariana Hristova
Keyword(s):  
Experimental Data ◽  
Binary Mixture ◽  
Binary Mixtures ◽  
Qualitative Agreement ◽  
Flash Point ◽  
Wilson Equation ◽  
Good Qualitative Agreement ◽  
Raoult’S Law ◽  
Raoult's Law

AbstractThe flash points of three binary mixtures, containing n-heptane, o-xylene, m-xylene and ethylbenzene, were measured by Pensky-Martens closed cup tester. The experimental data were compared with the calculated values using Liaw’s Model with the application of Raoult’s Law and Wilson equation. These equations were in good qualitative agreement.

Exploring Theories of Victimization Using a Mathematical Model of Burglary

2011 ◽  
Vol 48 (1) ◽  
pp. 83-109 ◽  
Author(s):  
Ashley B. Pitcher ◽  
Shane D. Johnson
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Qualitative Agreement ◽  
The Other ◽  
Residential Burglary ◽  
Foraging Activity ◽  
Good Qualitative Agreement ◽  
Agent Based ◽  
Stable Variation ◽  
Near Repeat

Research concerned with burglary indicates that it is clustered not only at places but also in time. Some homes are victimized repeatedly, and the risk to neighbors of victimized homes is temporarily elevated. The latter type of burglary is referred to as a near repeat. Two theories have been proposed to explain observed patterns. The boost hypothesis states that risk is elevated following an event reflecting offender foraging activity. The flag hypothesis, on the other hand, suggests that time-stable variation in risk provides an explanation where data for populations with different risks are analyzed in the aggregate. To examine this, the authors specify a series of discrete mathematical models of urban residential burglary and examine their outcomes using stochastic agent-based simulations. Results suggest that variation in risk alone cannot explain patterns of exact and near repeats, but that models which also include a boost component show good qualitative agreement with published findings.

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