Mathematical Model for Two-Spotted Spider Mites System: Verification and Validation

This paper presents and compares four mathematical models with unique spatial effects for a prey-predator system, with Tetranychus urticae as prey and Phytoseiulus persimilis as predator. Tetranychus urticae, also known as two-spotted spider mite, is a harmful plant-feeding pest that causes damage to over 300 species of plants. Its predator, Phytoseiulus persimilis, a mite in the Family Phytoseiidae, effectively controls spider mite populations. In this study, we compared four mathematical models using a numerical simulation. These models include two known models: self-diffusion, and cross-diffusion, and two new models: chemotaxis effect model, and integro diffusion model, all with a Beddington-De Angelis functional response. The modeling results were validated by fitting experimental data. Results demonstrate that interaction scheme plays an important role in the prey-predator system and that the crossdiffusion model fits the real system best. The main contribution of this paper is in the two new models developed, as well as the validation of all the models using experimental data.