A quasistationary approach to the research of insect distribution in the forest system

A mathematical model of insect pest spreading in the forest system, representing the system of two differential equations in partial derivatives, has been developed. The influence of one population on another is considered in the model. In the equation of plant pest population evolution such parameters as transfer by wind in one direction and casual transversal displacement are considered. In the equation of evolution of population of trees it is taken into account that they are immobile and destroyed by plant pests. The corresponding schedules of insect distribution and lines of identical concentration are built. The initial distribution of trees was chosen in the form of four isolated groves. After clarification of distribution of insects on the forest area, the share of the trees destroyed after a meeting with plant pests was calculated. The corresponding three-dimensional schedules of populations of the trees which remained in each grove after interaction with insects were constructed. Numerical experiments for the purpose of clarification of percent of a loss in each of the groves at various instants are put and comparison of results to data of analytical researches is carried out. The examined model, reflecting some actual processes in forest system, may be used for calculation of influence of plant pests on trees for other configurations of forest systems. Bibliogr. 39. Il. 4. Tables 3.