Impact of stochastic perturbation on the persistence and extinction risk of a multi-delayed prey–predator system in non-autonomous environment

Dynamical characteristics of a stochastically perturbed system are drastically different from those of a deterministic system. This study deals with the dynamics of a stochastically perturbed time-variant prey–predator model of aquatic animals hilsa (prey) and eel (predator). It is a well-known fact that overfishing and indiscriminate fishing of juvenile hilsa have led to a drastic fall in its population. To save the hilsa population from becoming extinct, we equip our model with age-structured growth and harvest in hilsa and study the effect of environmental noise on both prey and predator populations. We formulate predator’s consumption using Beddington–DeAngelis functional response which also provides access to some alternative food source in the absence of prey. We obtain sufficient conditions for persistence in the mean, extinction, and global attractivity and prove stochastic ultimate boundedness and the existence of a unique positive periodic solution. We have included many numerical examples to validate the analytical results. Through global sensitivity analysis using the partial rank correlation coefficient technique, we observed the environmental noise to be of great influence on the prey–predator population.