Mathematical Modeling of Population Growth for Single Species

Abstract

Mathematical models play an important role in studying the change of population qualitatively and quantitatively. It is based on the specific property of population growth. The research results are helpful to predict the developing tendency of role of change of population size. In this article we consider modeling of a single species in cases where spatial variation is not present or is not important. In such case we can simply examine the temporal evolution of the system. The model has been observed to give very well fits to population data in numerous, disparate, scenarios ranging from bacteria and yeast to rats and sheep. The increasing study of realistic and practically useful mathematical models in population biology, whether we are dealing with a human population with or without its age distribution, population of an endangered species, bacterial or viral growth and so on, is a reflection of their use in helping to understand the dynamic processes involved and in making practical predictions. Single species models are of relevance to laboratory studies in particular but in the real world can reflect a telescoping of effects which influence the population dynamic.We start with the simplest exponential model presented by Malthus in 1798 and then the improved model presented by Verhulst (1838, 1845). We also illustrate a particular model ''Insect outbreak model: spruce Budworm'', which exhibits two positive linearly stable steady state population that for the spruce budworm.