## Abstract

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 X_{n}(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 [α^{2}X_{n}(t){n −X_{n}(t) +X_{n}(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 X_{n}(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t∈(0, t_{0}), and t_{0} is evaluated.

Original language | English |
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Pages (from-to) | 263-271 |

Number of pages | 9 |

Journal | Mathematical Biosciences |

Volume | 50 |

Issue number | 3-4 |

DOIs | |

State | Published - 1980 |

Externally published | Yes |

## 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