The Population Mean and its Variance in the Presence of Genocide for a Simple Birth-Death-Immigration-Emigration using the Probability Generating Function

Abstract

This paper discusses on simple birth-death-immigration-emigration (BDIE) processes with genocide to stochastic differential equations (SDE) model. The general Solution for the distribution of the size of the population at any instant in time is obtained in the form of a probability generating function (PGF).The exact solution; mean and variance are derived for constant birth, death, immigration, emigration and catastrophe rates. Key words: Genocide, Catastrophe, BDIE, SDE, PGF