The asymptotic normality of a simple batch epidemic process

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A group of n susceptible individuals exposed to a contagious disease isconsidered. It is assumed that at each point in time one or more susceptible individuals can contract the disease. The progress of this simple batch epidemic is modeled by a stochastic process Xn(t), t∈[0, ∞), representing the number of infectiveindividuals at time t. In this paper our analysis is restricted to simple batch epidemics with transition rates given by [α2Xn(t){n −Xn(t) +Xn(0)}]1/2, t∈[0, ∞), α∈(0, ∞). This class of simple batch epidemics generalizes a model used and motivated by McNeil (1972) to describe simple epidemic situations. It is shown for this class of simple batch epidemics, that Xn(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t∈(0, t0), and t0 is evaluated.

Original languageEnglish
Pages (from-to)263-271
Number of pages9
JournalMathematical Biosciences
Issue number3-4
StatePublished - 1980
Externally publishedYes

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


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