### Abstract

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.

Original language | English |
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Pages (from-to) | 14-38 |

Number of pages | 25 |

Journal | Mathematical Biosciences |

Volume | 196 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2005 |

### Keywords

- Birth and death process
- Environmental variability
- Logistic equation
- Markov chain
- Mathematical model
- Persistence time
- Stochastic differential equation