The convergence in distribution of some simple epidemics

Naftali A. Langberg

doi:10.1016/0025-5564(80)90042-5

The convergence in distribution of some simple epidemics

Research output: Contribution to journal › Article › peer-review

Abstract

A group of n susceptible individuals exposed to a simple epidemic is modeled by a stochastic process X_n(t), t∈[0, ∞), representing the number of infective individuals at time t. In this paper our analysis is restricted to two classes of simple epidemic models. It is shown, for the first class of simple epidemics, that X_n(t) converges in distribution as n→∞ to a negative binomial random variable, and that EX_n(t), Var{X_n(t)} converge as n→∞ for all t∈(0, ∞). For the second class of simple epidemics it is shown that X_n(t), with suitable standardization, converges in distribution as n→∞ to a normal variable for all tϵ(0, ∞).

Original language	English
Pages (from-to)	273-284
Number of pages	12
Journal	Mathematical Biosciences
Volume	50
Issue number	3-4
DOIs	https://doi.org/10.1016/0025-5564(80)90042-5
State	Published - 1980
Externally published	Yes

Bibliographical note

Funding Information:
*Supported by Air Force Office of Scientific Research AFSC, USAF, AFOSR 76-3 109.

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/0025-5564(80)90042-5

Cite this

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title = "The convergence in distribution of some simple epidemics",

abstract = "A group of n susceptible individuals exposed to a simple epidemic is modeled by a stochastic process Xn(t), t∈[0, ∞), representing the number of infective individuals at time t. In this paper our analysis is restricted to two classes of simple epidemic models. It is shown, for the first class of simple epidemics, that Xn(t) converges in distribution as n→∞ to a negative binomial random variable, and that EXn(t), Var{Xn(t)} converge as n→∞ for all t∈(0, ∞). For the second class of simple epidemics it is shown that Xn(t), with suitable standardization, converges in distribution as n→∞ to a normal variable for all tϵ(0, ∞).",

author = "Langberg, {Naftali A.}",

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PY - 1980

Y1 - 1980

N2 - A group of n susceptible individuals exposed to a simple epidemic is modeled by a stochastic process Xn(t), t∈[0, ∞), representing the number of infective individuals at time t. In this paper our analysis is restricted to two classes of simple epidemic models. It is shown, for the first class of simple epidemics, that Xn(t) converges in distribution as n→∞ to a negative binomial random variable, and that EXn(t), Var{Xn(t)} converge as n→∞ for all t∈(0, ∞). For the second class of simple epidemics it is shown that Xn(t), with suitable standardization, converges in distribution as n→∞ to a normal variable for all tϵ(0, ∞).

AB - A group of n susceptible individuals exposed to a simple epidemic is modeled by a stochastic process Xn(t), t∈[0, ∞), representing the number of infective individuals at time t. In this paper our analysis is restricted to two classes of simple epidemic models. It is shown, for the first class of simple epidemics, that Xn(t) converges in distribution as n→∞ to a negative binomial random variable, and that EXn(t), Var{Xn(t)} converge as n→∞ for all t∈(0, ∞). For the second class of simple epidemics it is shown that Xn(t), with suitable standardization, converges in distribution as n→∞ to a normal variable for all tϵ(0, ∞).

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EP - 284

JO - Mathematical Biosciences

JF - Mathematical Biosciences

IS - 3-4

ER -

The convergence in distribution of some simple epidemics

Abstract

Bibliographical note

ASJC Scopus subject areas

UN SDGs

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