Today, the development of mathematical models for population growth is of great importance in many fields. The growth and decline of real populations can in many cases be well approximated by the solutions of differential equations. However, there are many situations in which the essentially random nature of population growth should be taken into account. This leads us to consider stochastic models. In this paper, we derive the population moments of a birth and death diffusion model with immigration and a general catastrophe process, under the assumption that the catastrophe rate is small.