Abstract:
We present a mathematical model for the dynamics of a population whose members are affected by ingested pollutants. We assume that a pollutant decomposition product is harmful for the individua and raises the incidence of their death. We describe the equations of the model and study the properties of their solutions, including the existence and stability of equilibrium states. We obtain conditions for the degeneration of the population and conditions guaranteeing its sustainment at nonzero stationary levels. We include the results of a numerical simulation.
Keywords:
population dynamics, nonstationary medium, mathematical model, influence of pollutants.
Citation:
N. V. Pertsev, G. E. Tsaregorodtseva, “A mathematical model for the dynamics of a population affected by pollutants”, Sib. Zh. Ind. Mat., 13:1 (2010), 109–120; J. Appl. Industr. Math., 5:1 (2011), 94–103
\Bibitem{PerTsa10}
\by N.~V.~Pertsev, G.~E.~Tsaregorodtseva
\paper A mathematical model for the dynamics of a~population affected by pollutants
\jour Sib. Zh. Ind. Mat.
\yr 2010
\vol 13
\issue 1
\pages 109--120
\mathnet{http://mi.mathnet.ru/sjim600}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2839589}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 1
\pages 94--103
\crossref{https://doi.org/10.1134/S199047891101011X}
Linking options:
https://www.mathnet.ru/eng/sjim600
https://www.mathnet.ru/eng/sjim/v13/i1/p109
This publication is cited in the following 5 articles:
Tandon A., Jyotsna K., “Modeling the Effects of Environmental Pollution Intensified By Urbanization on Human Population”, Int. J. Model. Simul. Sci. Comput., 7:3 (2016), UNSP 1650013
N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Statisticheskoe modelirovanie dinamiki populyatsii, razvivayuschikhsya v usloviyakh vozdeistviya toksichnykh veschestv”, Sib. zhurn. industr. matem., 14:2 (2011), 84–94
N. V. Pertsev, K. K. Loginov, “Stokhasticheskaya model dinamiki biologicheskogo soobschestva v usloviyakh potrebleniya osobyami vrednykh pischevykh resursov”, Matem. biologiya i bioinform., 6:1 (2011), 1–13
N.V. Pertsev, N.V. Pertsev, “Stochastic model of dynamics of biological community in conditions of consumption by individuals of harmful food resources”, Math.Biol.Bioinf., 6:1 (2011), 1
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