The role of fear in a time-variant prey–predator model with multiple delays and alternative food source to predator

We explore the dynamics of a time-variant prey–predator model of two species of fishes, namely Tenualosa ilisha (prey) and Macrognathus pancalus (predator). The prey exhibits anti-predatory behavior due to fear of predation. The prey equation is also equipped with age-based growth and harvestation terms to investigate the significance of maturity and harvest delay. The prey moves from saline water to freshwater for spawning, during which the predator feeds on an alternative food source. We explore the impact of this food source on the survival of prey. Starting with the sufficient conditions for positivity and boundedness of the solutions to the model, we find conditions for the existence of a stable global solution, periodic and almost periodic solutions. We find the range of existence for prey and predator populations and observe the interdependence between these values. According to our findings, just the fear of predation is enough to drive the prey population low. Even when the prey happens to be in an advantageous scenario, fear can still bring its population down, unless there are no or very few predators.