About: Stochastic Modeling of an Infectious Disease, Part I: Understand the Negative Binomial Distribution and Predict an Epidemic More Reliably

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About: Stochastic Modeling of an Infectious Disease, Part I: Understand the Negative Binomial Distribution and Predict an Epidemic More Reliably Goto Sponge NotDistinct Permalink

An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	Stochastic Modeling of an Infectious Disease, Part I: Understand the Negative Binomial Distribution and Predict an Epidemic More Reliably
Creator	Kobayashi, Hisashi
source	ArXiv
abstract	Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts often grossly wrong, concerning the numbers of people who get infected or die? The purpose of this study is to better understand the stochastic nature of an epidemic disease, and answer the above questions. Much of the work on infectious diseases has been based on%22SIR deterministic models,%22(Kermack and McKendrick:1927.) We will explore stochastic models that can capture the essence of the seemingly erratic behavior of an infectious disease. A stochastic model, in its formulation, takes into account the random nature of an infectious disease. The stochastic model we study here is based on the%22birth-and-death process with immigration%22(BDI for short), which was proposed in the study of population growth or extinction of some biological species. The BDI process model ,however, has not been investigated by the epidemiology community. The BDI process is one of a few birth-and-death processes, which we can solve analytically. Its time-dependent probability distribution function is a%22negative binomial distribution%22with its parameter $r$ less than $1$. The%22coefficient of variation%22of the process is larger than $/sqrt{1/r}>1$. Furthermore, it has a long tail like the zeta distribution. These properties explain why infection patterns exhibit enormously large variations. The number of infected predicted by a deterministic model is much greater than the median of the distribution. This explains why any forecast based on a deterministic model will fail more often than not.
has issue date	2020-06-02(xsd:dateTime)
has license	arxiv
sha1sum (hex)	69a5540f2081c512fee25d58a4993946ff3f9b0d
resource representing a document's title	Stochastic Modeling of an Infectious Disease, Part I: Understand the Negative Binomial Distribution and Predict an Epidemic More Reliably
resource representing a document's body	covid:69a5540f2081c512fee25d58a4993946ff3f9b0d#body_text
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