This thesis presents mathematical models for three biological systems. The analysis of biological systems in population genetics, epidemiology and cellular dynamics has led us to the conclusion that they can be well described by ordinary differential equations. Population genetic model analysis showed that random pairing with other assumptions of the basic model of random mating leads to the preservation of genetic diversity within the population. When some of the assumptions of the model are not fulfilled, we consider the evolution of the genetic structure of the population. The aim of the second chapter is to give an elementary introduction to mathematical models that are used to explain epidemiologic phenomena and to assess vaccination strategies. Given the present trends in global warming, there is a need to predict the dynamics and transmission of mosquito-borne diseases with greater accuracy and over longer periods of time, both in constant and growing populations. In metabolic flux analysis an important issue concerns the number of distinct bioreactions that are generated when computing the EFMs. It may become very large because it combinatorially increases with the size of the underlying metabolic network. Therefore, there is clearly a need for reducing the model size as much as possible and trying to determine a minimal subset of bioreactions that are able to fully describe the available experimental data.