Mathematical Modeling of Occurrence and Population Density of Predatory Spider and Their Preys on Cotton Plants and Broad Bean in Two Governorates in Egypt

Abstract

The research presents a mathematical simulation of three kinds of pests and their predator for two plants: Cotton and broad bean. The study was applied in two regions in Egypt representing Upper Egypt and Delta. The study is based on similar field experimental results during the two successive years 2003-2004, 2004-2005 in Qaha station- Qalubia governorate and seds station–Beni sweif governorate. Four models are introduced according to the plant and the geographical regions. The data were fitted to continuous curves to enable the process of predicting the number of each kind of the involved species. Many functions are suggested to describe the effect of temperature and relative humidity on population. However, for particular plant in particular area, only narrow ranges occur for both temperature and humidity. A process of smoothing the data was necessary to avoid the very extreme points of sudden increase (due to migration or eggs hatching) which can not be taken into account in a mathematical model. After smoothing the data, a least square method was used to fit the points to continuous curves. Then an algorithm has been made aiming to predict the number of the preys and predator at any time by knowing the initial state of each of them. The modeling for anticipating the expected number of spiders and preys for the different months was achieved using a Microsoft Visual Studio program. Four models are constructed and they have been shown to be easy for users. A calibration for the model was examined using a comparison study between field and model results, and a reasonable matching was observed.