The convergence in distribution of some simple epidemics

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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, ∞).

Original languageEnglish
Pages (from-to)273-284
Number of pages12
JournalMathematical Biosciences
Issue number3-4
StatePublished - 1980
Externally publishedYes

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
  • Biochemistry, Genetics and Molecular Biology (all)
  • Immunology and Microbiology (all)
  • Agricultural and Biological Sciences (all)
  • Applied Mathematics


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