THE MODEL OF ONE-TYPE POPULATION DYNAMICS IN SPACE AND TIME

Abstract

The paper considers the mathematical model of one-type population growth, evolving in time and twodimensional space, e. g. a population of agamogenetic bacterias on a plane. The area where bacterias grow is a rectangle, which is further divided into several identical rectangles. For each rectangular area the precise value of bacterias number is known. Time in this model is continuous. The model includes birth and moving between adjacent areas. The intensities of the movements are called random environment. In general, the random environment is assumed as inhomogeneous: the intensity of the bacterias’ movements depends on the current position and the chosen direction. Based on this model the authors formulated and solved the problem of predicting the growth of bacterias in time and estimating the number of bacterias in unobserved areas based on the known values in several observed areas in the moment of observation. To solve this problem the analytic form of the conditional mathematical expectation of the number of bacterias in each area was found. The paper is concluded with the results of a computer program solving these problems.

Keywords

• random walk, birth and death processes, semimartingale