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Journal of Applied Mathematics
Volume 2010, Article ID 851037, 10 pages
Research Article

Dynamical System and Nonlinear Regression for Estimate Host-Parasitoid Relationship

Grupo de Plagas Agrícolas, Dirección de Protección de Plantas, Centro Nacional de Sanidad Agropecuaria, Apartado 10 San José de las Lajas, 32700 La Habana, Cuba

Received 21 May 2010; Accepted 15 September 2010

Academic Editor: Nguyen Van Minh

Copyright © 2010 Ileana Miranda Cabrera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The complex relationships of a crop with the pest, its natural enemies, and the climate factors exist in all the ecosystems, but the mathematic models has studied only some components to know the relation cause-effect. The most studied system has been concerned with the relationship pest-natural enemies such as prey-predator or host-parasitoid. The present paper shows a dynamical system for studying the relationship host-parasitoid (Diaphorina citri, Tamarixia radiata) and shows that a nonlinear model permits the estimation of the parasite nymphs using nymphs healthy as the known variable. The model showed the functional answer of the parasitoid, in which a point arrives that its density is not augmented although the number host increases, and it becomes necessary to intervene in the ecosystem. A simple algorithm is used to estimate the parasitoids level using the priori relationship between the host and the climate factors and then the nonlinear model.