The development of a spatio-temporal model for water hyacinth biological control strategies

Abstract

A reaction-diffusion model for a temporally variable and spatially heterogeneous environment is developed to mathematically describe the spatial dynamics of water hyacinth and the interacting populations of the various life stages of the Neochetina eichhorniae weevil as a biological control agent on a bounded two-dimensional spatial domain. Difficulties encountered during the implementation of the model in MATLAB are discussed, including the implementation of time delays and spatial averaging. Conceptual validation tests indicate that the model may succeed in describing the spatio-temporal dynamics of the water hyacinth and weevil interaction. A modelling framework is thereby provided to evaluate the effectiveness of different biological control release strategies, providing guidance towards the optimal magnitude, timing, frequency and distribution of agent releases. Numerical results confirm the hypothesis that the seasonal timing of releases have a significant influence on the success of the control achieved. However, in order to ascertain the degree to which the model output realistically represent the real life water hyacinth and weevil interaction, predictive validation tests are proposed for further research.