Application of pair approximation method to modeling and analysis of a marriage network

Numerous studies on marital issues have frequently resorted to statistical analysis or mathematical modeling on a well-mixed homogeneous population. However, such mathematical models have largely ignored the effects of heterogeneous contact pattern among individuals of the population. In this paper, we propose a pair model to describe the evolution of a marriage network, where an unmarried male and an unmarried female become friends with a certain probability through the introduction of their common friends. For convenience this probability is termed as the introduction probability. A threshold is obtained to determine whether there is a married couple or not. We verify the model by good agreement between the numerical solution of the model, computational simulations and the real marriage data in Beijing. The results show that the positive equilibrium of the model is steady and increases with the threshold. Moreover, the introduction probability contributes to increase both the threshold and the married population size. Furthermore, it is found that increasing the number of same sex friends, and balancing the sex ratio can also enlarge the married population size. All these results can provide some insights into the evolution and the structure of the marriage network.