Statistical modeling of the dynamics of populations affected by toxic pollutants

N. V. Pertsev ; B. Yu. Pichugin ; K. K. Loginov

Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 84-94

Résumé

We present a stochastic model describing the dynamics of competing populations whose individua are affected by toxic pollutants. In order to construct the model, we use a probabilistic analog of the Lotka–Volterra model as a multidimensional inhomogeneous nonlinear birth and death process. We complement the postulates of the birth and death process with a description of the mechanism how? the toxic substance affects the death rate. We construct recurrences describing the dynamics of the population and the quantity of the toxic substance in the environment. We develop an algorithm for modeling the dynamics of populations and the quantity of the toxic substance basing on the Monte-Carlo method. We present the results of simulations studying degeneration conditions for one of the two competing populations, as well as conditions which guarantee that their numbers are maintained at nonzero stationary levels. In order to study analytically the behavior of the expected values of the populations we construct an auxiliary model as a system of nonlinear differential equations.