Simulations and parameter estimation of a trap-insect model using a finite element approach. (English) Zbl 1519.92342
Summary: Estimating pest population size is of utmost importance in biological control. However field experiments can be difficult and expensive to conduct, with no guarantee that useable results will be produced. In this context, the development of mathematical models and numerical tools is crucial to improve the field experiments by suggesting relevant data which can be used to estimate parameters related to the pest’s biology and to the traps (e.g. duration of the experiments, distance of the releases, etc.). Here we develop a trap-insect model (TIM), based on coupled partial differential equations. The model is studied theoretically and a finite element algorithm is developed and implemented. A protocol for parameter estimation is also proposed and tested, with various data. Among other results, we show that entomological knowledge is absolutely necessary for efficient estimation of parameters, in particular population size.
MSC:
| 92D45 | Pest management |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35D30 | Weak solutions to PDEs |
Keywords:
partial differential equations; chemotaxis; finite element method; parameter estimation; insect trappingReferences:
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