Abstract：Biological invasion is now one of the six hot research topics in modern ecology. Modeling the invasion processes, the diffusions and the spreading mechanisms of invasive species including diseases is important not only for theoretical purposes, but also for practical purposes, such as in ecological risk assessments, and optimal control and management of those invasive species. In this paper, the widely adopted models of biological invasion are systematically reviewed such as diffusion-reaction equations, integral-difference models, space-discrete models, and stochastic models. The fundamental issues of modeling biological invasions are discussed, and the characteristics and analytic conditions of various models are analyzed with typical examples and recent research results. Various modeling techniques are compared, and some commonly used methods in solving biological invasion models are outlined, including numerical computing and simulating, exact solutions, methods for functional differential equation and qualitative analysis of differential equations. Some key and unsolved problems in building mathematical models of biological invasion, and future research directions are also discussed.
2011, Vol. 29 
