Transient probabilities for a simple birth‐death‐immigration process under the influence of total catastrophes

Randall J Swift

doi:10.1155/s0161171201005762

Abstract

The transient probabilities for a simple birth‐death‐immigration process are considered. Catastrophes occur at a constant rate, and when they occur, reduce the population to size zero.

Highlights

A simple birth-death-immigration process is considered, which is influenced by total catastrophes which, when they occur, reduce the population size to zero
As in the simple birth-death process, births and deaths occur proportional to the population size with a birth rate λ > 0 and a death rate μ > 0
Immigration will occur independent of population size with rate α > 0

Summary

Introduction

A simple birth-death-immigration process is considered, which is influenced by total catastrophes which, when they occur, reduce the population size to zero. As in the simple birth-death process, births and deaths occur proportional to the population size with a birth rate λ > 0 and a death rate μ > 0. Immigration will occur independent of population size with rate α > 0. The occurrence of a catastrophe is independent of population size and will occur at a rate γ > 0.

Results

Conclusion