scholarly journals SIR model with general distribution function in the infectious period

2009 ◽  
Vol 388 (15-16) ◽  
pp. 3133-3142 ◽  
Author(s):  
Marcelo F.C. Gomes ◽  
Sebastián Gonçalves
Keyword(s):  
Distribution Function ◽  
Sir Model ◽  
General Distribution ◽  
Infectious Period

scholarly journals Epidemic Models with Random Infectious Period

2020 ◽  
Author(s):  
Germán Riaño
Keyword(s):  
Public Policy ◽  
Exponential Distribution ◽  
Numerical Experiments ◽  
Sir Model ◽  
Transmission Model ◽  
General Distribution ◽  
Infectious Period ◽  
Basic Model ◽  
Sir Epidemic ◽  
Lower Variability

In this paper, we present an extension to the classical SIR epidemic transmission model that uses any general probability distribution for the length of the infectious period. The classical SIR model implicitly requires an exponential distribution for the length of this period of time. We will show how a general distribution can be easily taken into account using the Transient Little Law and present numerical methods to solve the model in an efficient way. Our numerical experiments show that in the presence of a more realistic distribution, with lower variability than the exponential distribution, the size of peak of infected individuals on the graph will be higher and occur earlier. Conversely, a higher-variability distribution will lead to a lower peak that takes longer to dissipate. We also discuss some extensions to the basic model, to include variants like SEIRD and SIS. These findings should have profound and important consequences in the design of public policy.

scholarly journals Spillovers and R&D Incentive under Incomplete Information

2018 ◽  
Vol 6 (1-2) ◽  
pp. 50-65 ◽  
Author(s):  
Rittwik Chatterjee ◽  
Srobonti Chattopadhyay ◽  
Tarun Kabiraj
Keyword(s):  
Distribution Function ◽  
Incomplete Information ◽  
Private Information ◽  
Complete Information ◽  
Jel Classification ◽  
General Distribution ◽  
Two Stage ◽  
Stage Game ◽  
Alternative Scenarios

Spillovers of R&D outcome affect the R&D decision of a firm. The present paper discusses the R&D incentives of a firm when the extent of R&D spillover is private information to each firm. We construct a two-stage game involving two firms when the firms first decide simultaneously whether to invest in R&D or not, then they compete in quantity. Assuming general distribution function of firm types we compare R&D incentives of firms under alternative scenarios based on different informational structures. The paper shows that while R&D spillovers reduce R&D incentives under complete information unambiguously, however, it can be larger under incomplete information. JEL Classification: D43, D82, L13, O31

Asymptotic behavior of Hill's estimate and applications

1986 ◽  
Vol 23 (04) ◽  
pp. 922-936
Author(s):  
Gane Samb Lo
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Finite Number ◽  
Domain Of Attraction ◽  
Distribution Functions ◽  
Complete Theory ◽  
General Distribution ◽  
Stable Law ◽  
Biological Phenomena ◽  
Pareto’S Law

The problem of estimating the exponent of a stable law is receiving an increasing amount of attention because Pareto's law (or Zipf's law) describes many biological phenomena very well (see e.g. Hill (1974)). This problem was first solved by Hill (1975), who proposed an estimate, and the convergence of that estimate to some positive and finite number was shown to be a characteristic of distribution functions belonging to the Fréchet domain of attraction (Mason (1982)). As a contribution to a complete theory of inference for the upper tail of a general distribution function, we give the asymptotic behavior (weak and strong) of Hill's estimate when the associated distribution function belongs to the Gumbel domain of attraction. Examples, applications and simulations are given.

General distribution function for the superstatistics and new superstatistics with non-vanishing rth moments for even r

2018 ◽  
Vol 15 (07) ◽  
pp. 1850123 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Distribution Function ◽  
General Procedure ◽  
General Distribution ◽  
Boltzmann Factor ◽  
New Type

In this paper, the general procedure for obtaining the distribution for the superstatistics is presented. Besides, the new type of effective Boltzmann factor with non-vanishing [Formula: see text]th moments for even [Formula: see text] is presented and some examples are discussed.

Asymptotic behavior of Hill's estimate and applications

1986 ◽  
Vol 23 (4) ◽  
pp. 922-936 ◽  
Author(s):  
Gane Samb Lo
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Finite Number ◽  
Domain Of Attraction ◽  
Distribution Functions ◽  
Complete Theory ◽  
General Distribution ◽  
Stable Law ◽  
Biological Phenomena ◽  
Pareto’S Law

The problem of estimating the exponent of a stable law is receiving an increasing amount of attention because Pareto's law (or Zipf's law) describes many biological phenomena very well (see e.g. Hill (1974)). This problem was first solved by Hill (1975), who proposed an estimate, and the convergence of that estimate to some positive and finite number was shown to be a characteristic of distribution functions belonging to the Fréchet domain of attraction (Mason (1982)). As a contribution to a complete theory of inference for the upper tail of a general distribution function, we give the asymptotic behavior (weak and strong) of Hill's estimate when the associated distribution function belongs to the Gumbel domain of attraction. Examples, applications and simulations are given.

ARE THE STANDARDS IN PHYSIOLOGY AND MEDICINE?

2020 ◽  
Vol 6 (1) ◽  
pp. 27-31
Author(s):  
Valeriy Es'kov ◽  
P. Pyatin ◽  
L. Shakirova ◽  
A. Chertischev
Keyword(s):  
Distribution Function ◽  
Chaotic Behavior ◽  
General Distribution ◽  
Standard State ◽  
Standard Definition ◽  
New Science ◽  
New Methods ◽  
Series Of Experiments ◽  
Special Matrix ◽  
Cardio Vascular

Some scientists present the problem of physiology and medicine which are connected with new understanding of standard definition. The main goal of the article is connected with proving of standard absent in medicine according to stochastic and deterministic definition. Object and methods. One group of young woman was researching by cardio-vascular systems parameter (cardiointervals). It was registrated 15-th series of experiments any every series consists 15 number of cardiointervals samples (every sample consists 300 cardiointervals). So we calculate the special matrix for every series for it we calculate the number k of pair which has common general distribution. Results. All 225 such matrix present the number of such k (k≤20% for every matrix) it means that all samples are unique. Conclusion. It every sample is unique we cannot present the standard state of the cardio-respiratory system of the man. We have chaotic number of samples with unique it distribution function. The chaotic behavior we have for spectral density of it signals and for autocorrelation. So we need new methods for functional systems investigation which are not based on deterministic or stochastic sciences. We need new understanding of standard based on new science.

scholarly journals Observing the epidemiological SIR model on COVID-19 pandemic data

2021 ◽  
Vol 18 (1) ◽  
pp. 35
Author(s):  
Sergio Rojas
Keyword(s):  
Numerical Solutions ◽  
Disease Model ◽  
Vertical Motion ◽  
Undergraduate Curriculum ◽  
Sir Model ◽  
Infectious Period ◽  
Data Set ◽  
Physics Courses ◽  
Type Differential Equation ◽  
Introductory Physics Courses

This article shows that in the period January 22-June 04, 2020, the combined  data set of cumulative  recoveries and deaths from the current coronavirus COVID-19 pandemic falls on the Kermack and McKendrick approximated solution of the epidemiological {\sir} contagious disease model. Then, as an original contribution of this work, based on the knowledge of the infectious period of any epidemic, a methodology is presented that helps to find numerical solutions of the full {\sir} model that falls on the observed data of the epidemic in case it could be described by the {\sir} model. The methodology is first illustrated by finding a solution of the {\sir} model that falls on the epidemic data of the Bombay plague of 1905-06 analyzed by Kermack and McKendrick. After that, the methodology is applied on analyzing the previously considered coronavirus COVID-19 pandemic data set. Moreover,  since the Kermack and McKendrick approximated solution of the {\sir} model comes from solving a Riccati type differential equation, commonly found when studying (in introductory physics courses) the vertical motion of objects on a resistive medium, enough details are given in the article so the epidemiological {\sir} model can be used as an additional example for enhancing and enriching the undergraduate curriculum Physics courses for Biology, Life Sciences, Medicine and/or Computational Modeling.

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