A mathematical model of algal blooms based on the characteristics of complex networks theory

To predict the outbreak time of algal blooms and its duration in an actual body of water, this paper developed a directed complex networks (CNs) model of algal blooms. This new model was based on the characteristics of CNs theory and the primary factors that influenced algal blooms. By calculating the shortest path and proposing a key degree node model, the role of each influencing factor during algal blooms was evaluated. Based on years of on-site monitoring data (collected from 1992 to 2000) concerning the Han River, a statistical characteristic function G that reflected the relationship between the statistical characteristics of dominant algae blooming and the degree of algal blooms pollution was proposed. The results indicate that the proposed function G is capable of effectively and semi-quantitatively characterizing the outbreak time and the duration of algal blooms. If the value of G in a body of water is less than 32.6, the body of water will outbreak an algal bloom. An increasingly smaller of G value indicates a greater degree of algal blooms pollution and longer bloom duration.

► We develop a directed complex networks (CNs) model of algal blooms.
► We use Floyd algorithm to find out the shortest path between each pair of nodes in the networks.
► We propose a statistical characteristics function G to predict algal blooms.
► The verifications indicate that G can effectively describe the state of algal blooms in a semi-quantitative way.