Abstract
Effect of anti-predator defense due to fear of predator felt by prey and effect of toxic substance released by external sources on prey–predator system is a serious mater of concern in mathematical biology. In the proposed model we have discussed a prey–predator system in which both the species are infected by environmental toxicant. In our consideration prey species is directly infected by environmental toxicant and predator gets infected by consuming infected prey. Prey’s growth rate is assumed to be affected by fear of predator. In this work the proposed predator–prey model is analyzed in presence of environmental fluctuation, i.e., stochastic analysis of this model is discussed. Using Itô formula: positivity, boundedness, uniform continuity criterion and global attractivity of solutions of this system have been established. Conditions for which the prey as well as the predator goes extinct have been derived. Conditions for persistence of the system have also been discussed. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different levels of toxicant and different levels of fear have been demonstrated by depicting figures in numerical simulation using MATLAB.
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The authors are grateful to the anonymous referees, Dr. Pasquale Vetro, Editor-in-Chief, for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly.
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Das, A., Samanta, G.P. Modelling the fear effect in a two-species predator–prey system under the influence of toxic substances. Rend. Circ. Mat. Palermo, II. Ser 70, 1501–1526 (2021). https://doi.org/10.1007/s12215-020-00570-x
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DOI: https://doi.org/10.1007/s12215-020-00570-x