×

The survival analysis for a single-species population model in a polluted environment. (English) Zbl 1128.92046

Summary: This paper concentrates on studying the long-term behavior of a single-species population living in a polluted environment. A new mathematical model is derived assuming that a born organism takes with it a quantity of internal toxicant, and the amount of toxicant stored in each living organism which dies is drifted into the environment. Sufficient criteria for uniform persistence, weak persistence in the mean or extinction of the population are obtained. Also we find some sufficient conditions, depending on the parameters of the model and the clean up rate, under which the population will be persistent.

MSC:

92D40 Ecology
34D99 Stability theory for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Shukla, J. B.; Agrawal, A.; Dubey, B.; Sinha, P., Existence and survival of two competing species in a polluted environment: a mathematical model, J. Biol. Syst., 9, 89-103 (2001)
[2] Woodman, J. N.; Cowling, E. B., Airborne chemicals and forest health, Environ. Sci. Technol., 21, 120-126 (1987)
[3] Otto, K., Diseases of Marine Animals, vol. 1 (1980), Wiley: Wiley New York
[4] Fleming, R. N.; Pantell, R. H., The conflict between consumption and pollution, IEEE Trans. Syst. Man Cybernet. SMC-4, 2, 204-208 (1974) · Zbl 0297.90019
[5] Hallam, T. G.; Clark, C. E.; Lassider, R. R., Effects of toxicant on population: a qualitative approach I. Equilibriu environmental exposure, Ecol. Modell., 8, 291-304 (1983) · Zbl 0548.92018
[6] Hallam, T. G.; Clark, C. E.; Jordan, G. S., Effects of toxicant on population: a qualitative approach II. First order kinetics, J. Math. Biol., 18, 25-37 (1983) · Zbl 0548.92019
[7] Hallam, T. G.; Deluua, J. T., Effects of toxicant on population: a qualitative approach III. Environmental and food chain pathways, J. Theor. Biol., 109, 411-429 (1984)
[8] Huaping, L.; Zhien, Ma, The threshold of survival system of two species in polluted environment, J. Math. Biol., 30, 1, 49-62 (1991) · Zbl 0745.92028
[9] Zhien, Ma; Baojun, Song; Hallam, T. G., The threshold of survival for systems in a fluctuating environment, Bull. Math. Biol., 51, 3, 311-324 (1989) · Zbl 0676.92010
[10] Zhien, Ma; Guirong, Cui; Wendi, Wang, Persistence and extinction of a population in a polluted environment, Math. Biosci., 101, 75-97 (1990) · Zbl 0714.92027
[11] Srinivasu, P. D.N., Control of environmental pollution to conserve a population, Nonlinear Anal., 3, 397-411 (2002) · Zbl 0998.92042
[12] Thomas, D. M.; Snell, T. W.; Joffer, S. M., A control problem in a polluted environment, Math. Biosci., 133, 139-163 (1996) · Zbl 0844.92026
[13] Zerong, He; Zhien, Ma, On the effects of pollution and catch to a Logistic population, J. Biomath., 12, 3, 230-237 (1997) · Zbl 0888.92037
[14] Buonomo, B.; Di Liddo, A.; Sgura, I., A diffusive-convective model for the dynamics of population-toxicant intentions:some analytical and numerical results, Math. Bios., 157, 37-64 (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.