Abstract
The widespread problem of water pollution due to enhanced concentration of anthropogenic effluents is becoming a global issue. Public environmental awareness may be a plausible factor for the control of toxicants in the aquatic medium. The present paper is devoted to study the impact of awareness among human on reduction of environmental toxins affecting planktonic system. The provision of awareness among people helps to maintain the ecological balance of the system by reducing the input rate of toxicants through anthropogenic sources. The conditions for existence and local asymptotic stability of all feasible steady states of the system are derived. Our study reveals that the system is stable for low or high input rate of toxicants, but for intermediate ranges, the system produces oscillations by destroying the stable dynamics. Moreover, for very large level of pollutants, zooplankton disappears from the system. Importantly, the limited supply of additional food to zooplankton prevents the crash of aquatic food web system. Sensitivity results evoke that environmental toxins can be reduced to a low level by imparting awareness among human, thereby maintaining the rhythm of the planktonic ecosystem.
Similar content being viewed by others
References
Antweiler, R.C., Patton, C.J., Taylor, H.E.: Nutrients, in chemical data for water samples collected during four upriver cruises on the Mississippi river between New Orleans, Louisiana, and Minneapolis, Minnesota. May 1990–April 1992, J.A. Moody, ed., U.S. Geological Survey Open-File Report, 94–523, 89–125 (1995)
Bester, K., Huhnerfuss, H., Brockmann, U., Rick, H.J.: Biological effects of triazine herbicide contamination on marine phytoplankton. Arch. Environ. Contam. Toxicol. 29, 277–283 (1995)
Biswas, S., Tiwari, P.K., Kang, Y., Pal, S.: Effects of zooplankton selectivity on phytoplankton in an ecosystem affected by free-viruses and environmental toxins. Math. Biosci. Eng. 17(2), 1272–1317 (2020)
Bortz, D.M., Nelson, P.W.: Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics. Bull. Math. Biol. 66, 1009–1026 (2004)
Chakraborty, S., Chattopadhyay, J.: Nutrient-phytoplankton-zooplankton dynamics in the presence of additional food source - A mathematical study. J. Biol. Syst. 16(04), 547–564 (2008)
Chattopadhyay, J.: Effect of toxic substances on a two-species competitive system. Ecol. Model. 84, 287–289 (1996)
Hallam, T., Deluna, J.: Effects of toxicants on populations: a qualitative approaches III. environmental and food chain pathways. J. Theor. Biol. 109, 411–429 (1984)
Huang, Y.J., Jiang, Z.B., Zeng, J.N., et al.: The chronic effects of oil pollution on marine phytoplankton in a subtropical bay. Chin. Environ. Monit. Assess. 176(1), 517–530 (2011)
Kumar, A., Srivastava, P.K., Takeuchi, Y.: Modeling the role of information and limited optimal treatment on disease prevalence. J. Theor. Biol. 414, 103–119 (2017)
Liu, Y., Cui, J.: The impact of media convergence on the dynamics of infectious diseases. Int. J. Biomath. 1, 65–74 (2008)
Lopes, C., Péry, A.R.R., Chaumot, A., Charles, S.: Ecotoxicology and population dynamics: using DEBtox models in a leslie modeling approach. Ecol. Model. 188(1), 30–40 (2005)
Mandal, A., Tiwari, P.K., Samanta, S., Venturino, E., Pal, S.: A nonautonomous model for the effect of environmental toxins on plankton dynamics. Nonlinear Dyn. 99, 3373–3405 (2020)
Miao, A.J., Schwehr, K.A., Xu, C., et al.: The algal toxicity of silver engineered nanoparticles and detoxification by exopolymeric substances. Environ. Pollut. 157, 3034–3041 (2009)
Miller, R.J., Bennett, S., Keller, A.A., Pease, S., Lenihan, H.S.: \(\text{ TiO}_2\) nanoparticles are phototoxic to marine phytoplankton. PLoS ONE 7(1), e30321 (2012)
Misra, A.K., Sharma, A., Li, J.: A mathematical model for control of vector borne diseases through media campaigns. Discrete Contin. Dyn. Syst. Ser. B 18(7), 1909–1927 (2013)
Misra, A.K., Sharma, A., Shukla, J.B.: Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases. Math. Comput. Model. 53, 1221–1228 (2011)
Misra, A.K., Singh, R.K., Tiwari, P.K., Khajanchi, S., Kang, Y.: Dynamics of algae blooming: effects of budget allocation and time delay. Nonlinear Dyn. 100, 1779–1807 (2020)
Misra, A.K., Tiwari, P.K., Chandra, P.: Modeling the control of algal bloom in a lake by applying some external efforts with time delay. Differ. Equ. Dyn. Syst. (2017). https://doi.org/10.1007/s12591-017-0383-5
Misra, A.K., Tiwari, P.K., Venturino, E.: Modeling the impact of awareness on the mitigation of algal bloom in a lake. J. Biol. Phys. 42, 147–165 (2016)
Misra, A.K., Verma, M.: Impact of environmental education on mitigation of carbon dioxide emissions: a modelling study. Int. J. Glob. Warm. 7(4), 466–486 (2015)
Moraïtou-Apostolopoulou, M., Ignatiades, L.: Pollution effects on the phytoplankton-zooplankton relationships in an inshore environment. Hydrobiologia 75(2), 259–266 (1980)
Mukherjee, D.: Persistence and global stability of a population in a polluted environment with delay. J. Biol. Syst. 10(3), 225–232 (2002)
Navarro, E., Piccapietra, F., Wagner, B., et al.: Toxicity of silver nanoparticles to Chlamydomonas reinhardtii. Environ. Sci. Technol. 42(23), 8959–8964 (2008)
Panja, P., Mondal, S.K., Jana, D.K.: Effects of toxicants on phytoplankton-zooplankton-fish dynamics and harvesting. Chaos Solitons Fract. 104, 389–399 (2017)
Preston, B.L., Snell, T.W.: Direct and indirect effects of sublethal toxicant exposure on population dynamics of freshwater rotifers: a modeling approach. Aquat. Toxicol. 52(2), 87–99 (2001)
Rana, S., Samanta, S., Bhattacharya, S., et al.: The effect of nanoparticles on plankton dynamics: a mathematical model. BioSystems 127, 28–41 (2015)
Saha, T., Bandyopadhyay, M.: Dynamical analysis of toxin producing phytoplankton-zooplankton interactions. Nonlinear Anal. RWA 10, 314–332 (2009)
Shukla, J.B., Lata, K., Misra, A.K.: Modeling the depletion of a renewable resource by population and industrialization: effect of technology on its conservation. Nat. Resour. Model. 24(2), 242–267 (2011)
Shukla, J.B., Sharma, S., Dubey, B., Sinha, P.: Modeling the survival of a resource-dependent population: effects of toxicants (pollutants) emitted from external sources as well as formed by its precursors. Nonlinear Anal. RWA 10(1), 54–70 (2009)
Smith, H.L.: The Rosenzweig–Macarthur Predator–Prey Model. School of Mathematical and Statistical Sciences, Arizona State University, Phoenix (2008)
Tchounwou, P.B., Yedjou, C.G., Patlolla, A.K., Sutton, D.J.: Heavy metals toxicity and the environment. Mol. Clin. Environ. Toxicol. 101, 133–164 (2012)
U.S. Environmental Protection Agency Great Lakes National Program Office Significant Activities Report. http://www.epa.gov/glnpo/aoc/waukegan.html. Accessed 5 July 2020
Yu, X., Yuan, S., Zhang, T.: Survival and ergodicity of a stochastic phytoplankton-zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment. Appl. Math. Comput. 347, 249–264 (2019)
Acknowledgements
Authors thank the anonymous reviewers for valuable comments, which contributed to the improvement in the presentation of the paper. The research work of Arindam Mandal is supported by University Grants Commision, Government of India, New Delhi in the form of Senior Research Fellowship (Ref.No:19/06/2016(i)EU-V). Pankaj Kumar Tiwari is thankful to University Grants Commissions, New Delhi, India for providing financial support in form of D. S. Kothari post-doctoral fellowship (No.F.4-2/2006 (BSR)/MA/17-18/0021). The research of Samares Pal is partially supported by Science and Engineering Research Board, Government of India (Grant No. CRG/2019/003248).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix A
with
Appendix B
with
Rights and permissions
About this article
Cite this article
Mandal, A., Tiwari, P.K. & Pal, S. Impact of awareness on environmental toxins affecting plankton dynamics: a mathematical implication. J. Appl. Math. Comput. 66, 369–395 (2021). https://doi.org/10.1007/s12190-020-01441-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-020-01441-5